******************************************************************************* ******************************************************************************* ********** *********** ********** "Establishment of *********** ********** the Direct Numerical Simulation Data Bases of *********** ********** Turbulent Transport Phenomena" *********** ********** *********** ********** Co-operative Research *********** ********** No. 02302043 *********** ********** *********** ********** Supported by the Ministry of Education, *********** ********** Science and Culture *********** ********** *********** ********** 1990 - 1992 *********** ********** *********** ********** *********** ********** *********** ********** *********** ********** N. Kasagi (Organizer) *********** ********** K. Horiuti, Y. Miyake, T. Miyauchi, Y. Nagano *********** ********** *********** ******************************************************************************* ******************************************************************************* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++ << CAUTION >> +++++++++++ ++++++++++ +++++++++++ ++++++++++ All rights are reserved by the computors of each data +++++++++++ ++++++++++ base. No part of the data described herein may be +++++++++++ ++++++++++ represented or otherwise used in any form without fully +++++++++++ ++++++++++ referring to this data base and the literature cited at +++++++++++ ++++++++++ the end of the data base. The original data base will +++++++++++ ++++++++++ be revised without notice, whenever necessary. Future +++++++++++ ++++++++++ revisions will be notified to those who register by +++++++++++ ++++++++++ writing to Research Organizer: +++++++++++ ++++++++++ +++++++++++ ++++++++++ N. Kasagi +++++++++++ ++++++++++ Department of Mechanical Engineering +++++++++++ ++++++++++ The University of Tokyo +++++++++++ ++++++++++ Bunkyo-ku, Tokyo 113 +++++++++++ ++++++++++ Japan. +++++++++++ ++++++++++ +++++++++++ ++++++++++ December 1990 +++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ =================== this data base begins from this line ====================== Test Case: Fully Developed Thermal Field in a 2-D Turbulent Channel Flow Code Number: CH122_PG.WL1 Date of Release: April 16, 1991 Date of Revision: March 1, 1992, May 1, 1993 Computors: Y. Tomita, N. Kasagi and A. Kuroda Department of Mechanical Engineering The University of Tokyo Bunkyo-ku, Tokyo 113 Nomenclature alfa = thermal diffusivity alfa_t = eddy diffusivity for heat delta = channel half width k_x, k_z = streamwise and spanwise wave numbers nu = kinematic viscocity nu_t = eddy diffusivity for momentum omega_y = vorticity component in the y-direction Pr = Prandtl number Pr_t = turbulent Prandtl number R(ab) = correlation coefficient between a and b Re_tau = Reynolds number based on u_tau, delta and nu Uc = channel center mean velocity u, v, w = streamwise, wall-normal and spanwise velocity fluctuations u_mean = mean temperature u_tau = friction velocity u_i = i-th component of velocity fluctuation u+, v+, w+ = u/u_tau, v/u_tau, w/u_tau t = temperature fluctuation t_mean = mean temperature t_tau = friction temperature t+ = t/t_tau x,y,z =streamwise, wall-normal, spanwise directions y+ = y*u_tau/nu 1. Description of Flow Field The flow field simulated is a fully developed two-dimensional turbulent flow between two parallel walls. The iso-flux condition is imposed on the walls so that the local mean temperature linearly increases in the streamwise direction. Hence, temperature is re-defined as the difference from the wall temperature, and both flow and thermal fields are homogeneous in the streamwise and spanwise directions; the turbulence statistics are dependent only upon the distance from the wall. The data presented here are non- dimensionalized by the wall variables, i.e., u_tau, nu and t_tau. The flow condition is specified by the mean pressure gradient imposed (or the friction velocity) and the distance between the walls (channel height). 2. Numerical Method Governing equations: a forth-order equation for v, second-order equation for omega_y, the continuity equation for flow field and the energy equation for thermal field. Discretization method: spectral method = 128 x 128 Fourier series in the x- and z-directions, and Chebyshev polynomials up to the order 97 in the y- direction (Chebyshev-tau method). Aliasing treatment: nonlinear terms computed with collocation grids 1.5 times finer in each direction. Grid spacing: 18.4 and 7.36 viscous units in the x- and z-directions and 0.08 to 4.9 viscous units in the y-direction. Time integration: second order Adams-Bashforth for the nonlinear terms and Crank-Nicolson for the diffusion terms. Size of computational box: 5*pai*delta x 2*delta x 2*pi*delta. Initial conditions: u', v' and u_mean given by the previous numerical results (see, Flow Case CH12__PG.WL1) and t' given as a product of u' and molecualr Prandtl number. Criterion for stationary state: identified by balance of the mean energy equation and also by stationary behavior of second, third and forth moments of temperature fluctuations. Error in continuity equation: not applicable Length of time integration for ensemble averaging: about 14.0*delta/u_tau (2100 nu/u_tau**2) after the fully developed state is reached. Computer: HITAC-S820/80 at the Computer Center of the University of Tokyo. Computation time: 5.3 sec CPU time per one time step. 3. Flow Conditions Re_tau = delta*u_tau/nu = 150 Re_bulk = 2*delta*Um/nu = 4560 Pr = 0.71 4. Numerical Data 4.1 Turbulence statistics j y+ t_mean/t_tau 1 0.000000E+00 -0.233019E-13 2 0.356959E-01 0.248786E-01 3 0.142767E+00 0.995030E-01 4 0.321162E+00 0.223834E+00 5 0.570795E+00 0.397803E+00 6 0.891549E+00 0.621284E+00 7 0.128327E+01 0.894045E+00 8 0.174577E+01 0.121564E+01 9 0.227884E+01 0.158526E+01 10 0.288221E+01 0.200140E+01 11 0.355560E+01 0.246159E+01 12 0.429869E+01 0.296199E+01 13 0.511113E+01 0.349714E+01 14 0.599252E+01 0.405986E+01 15 0.694246E+01 0.464149E+01 16 0.796048E+01 0.523239E+01 17 0.904611E+01 0.582264E+01 18 0.101988E+02 0.640289E+01 19 0.114181E+02 0.696493E+01 20 0.127033E+02 0.750224E+01 21 0.140538E+02 0.801017E+01 22 0.154691E+02 0.848588E+01 23 0.169484E+02 0.892819E+01 24 0.184910E+02 0.933724E+01 25 0.200962E+02 0.971423E+01 26 0.217632E+02 0.100610E+02 27 0.234913E+02 0.103801E+02 28 0.252796E+02 0.106739E+02 29 0.271272E+02 0.109451E+02 30 0.290333E+02 0.111962E+02 31 0.309970E+02 0.114296E+02 32 0.330173E+02 0.116473E+02 33 0.350933E+02 0.118514E+02 34 0.372240E+02 0.120435E+02 35 0.394084E+02 0.122251E+02 36 0.416454E+02 0.123975E+02 37 0.439340E+02 0.125619E+02 38 0.462730E+02 0.127193E+02 39 0.486615E+02 0.128702E+02 40 0.510981E+02 0.130153E+02 41 0.535819E+02 0.131550E+02 42 0.561115E+02 0.132898E+02 43 0.586858E+02 0.134197E+02 44 0.613036E+02 0.135449E+02 45 0.639635E+02 0.136656E+02 46 0.666645E+02 0.137821E+02 47 0.694051E+02 0.138945E+02 48 0.721840E+02 0.140030E+02 49 0.750000E+02 0.141077E+02 50 0.778517E+02 0.142089E+02 51 0.807377E+02 0.143064E+02 52 0.836567E+02 0.144003E+02 53 0.866073E+02 0.144906E+02 54 0.895880E+02 0.145770E+02 55 0.925975E+02 0.146599E+02 56 0.956343E+02 0.147389E+02 57 0.986970E+02 0.148143E+02 58 0.101784E+03 0.148857E+02 59 0.104894E+03 0.149532E+02 60 0.108026E+03 0.150166E+02 61 0.111177E+03 0.150757E+02 62 0.114347E+03 0.151304E+02 63 0.117534E+03 0.151807E+02 64 0.120736E+03 0.152265E+02 65 0.123953E+03 0.152677E+02 66 0.127181E+03 0.153042E+02 67 0.130421E+03 0.153360E+02 68 0.133670E+03 0.153629E+02 69 0.136927E+03 0.153849E+02 70 0.140190E+03 0.154021E+02 71 0.143457E+03 0.154144E+02 72 0.146728E+03 0.154218E+02 73 0.150000E+03 0.154244E+02 j y+ t_rms/t_tau 1 0.000000E+00 0.275251E-13 2 0.356959E-01 0.943025E-02 3 0.142767E+00 0.377169E-01 4 0.321162E+00 0.848494E-01 5 0.570795E+00 0.150809E+00 6 0.891549E+00 0.235546E+00 7 0.128327E+01 0.338909E+00 8 0.174577E+01 0.460511E+00 9 0.227884E+01 0.599490E+00 10 0.288221E+01 0.754223E+00 11 0.355560E+01 0.922042E+00 12 0.429869E+01 0.109909E+01 13 0.511113E+01 0.128038E+01 14 0.599252E+01 0.146026E+01 15 0.694246E+01 0.163286E+01 16 0.796048E+01 0.179286E+01 17 0.904611E+01 0.193602E+01 18 0.101988E+02 0.205945E+01 19 0.114181E+02 0.216174E+01 20 0.127033E+02 0.224277E+01 21 0.140538E+02 0.230345E+01 22 0.154691E+02 0.234545E+01 23 0.169484E+02 0.237080E+01 24 0.184910E+02 0.238178E+01 25 0.200962E+02 0.238061E+01 26 0.217632E+02 0.236937E+01 27 0.234913E+02 0.234994E+01 28 0.252796E+02 0.232395E+01 29 0.271272E+02 0.229282E+01 30 0.290333E+02 0.225778E+01 31 0.309970E+02 0.221984E+01 32 0.330173E+02 0.217983E+01 33 0.350933E+02 0.213845E+01 34 0.372240E+02 0.209630E+01 35 0.394084E+02 0.205380E+01 36 0.416454E+02 0.201130E+01 37 0.439340E+02 0.196900E+01 38 0.462730E+02 0.192701E+01 39 0.486615E+02 0.188549E+01 40 0.510981E+02 0.184457E+01 41 0.535819E+02 0.180431E+01 42 0.561115E+02 0.176472E+01 43 0.586858E+02 0.172581E+01 44 0.613036E+02 0.168758E+01 45 0.639635E+02 0.165001E+01 46 0.666645E+02 0.161301E+01 47 0.694051E+02 0.157659E+01 48 0.721840E+02 0.154072E+01 49 0.750000E+02 0.150532E+01 50 0.778517E+02 0.147023E+01 51 0.807377E+02 0.143543E+01 52 0.836567E+02 0.140099E+01 53 0.866073E+02 0.136694E+01 54 0.895880E+02 0.133330E+01 55 0.925975E+02 0.130005E+01 56 0.956343E+02 0.126720E+01 57 0.986970E+02 0.123476E+01 58 0.101784E+03 0.120286E+01 59 0.104894E+03 0.117158E+01 60 0.108026E+03 0.114099E+01 61 0.111177E+03 0.111132E+01 62 0.114347E+03 0.108285E+01 63 0.117534E+03 0.105574E+01 64 0.120736E+03 0.103018E+01 65 0.123953E+03 0.100641E+01 66 0.127181E+03 0.984631E+00 67 0.130421E+03 0.965075E+00 68 0.133670E+03 0.948018E+00 69 0.136927E+03 0.933714E+00 70 0.140190E+03 0.922312E+00 71 0.143457E+03 0.913934E+00 72 0.146728E+03 0.908763E+00 73 0.150000E+03 0.907009E+00 j y+ S(t) 1 0.000000E+00 -0.412173E-42 2 0.356959E-01 0.963253E+00 3 0.142767E+00 0.963248E+00 4 0.321162E+00 0.963172E+00 5 0.570795E+00 0.962699E+00 6 0.891549E+00 0.961040E+00 7 0.128327E+01 0.956657E+00 8 0.174577E+01 0.947164E+00 9 0.227884E+01 0.929512E+00 10 0.288221E+01 0.900667E+00 11 0.355560E+01 0.858566E+00 12 0.429869E+01 0.802833E+00 13 0.511113E+01 0.734861E+00 14 0.599252E+01 0.657358E+00 15 0.694246E+01 0.573663E+00 16 0.796048E+01 0.487129E+00 17 0.904611E+01 0.400701E+00 18 0.101988E+02 0.316715E+00 19 0.114181E+02 0.236843E+00 20 0.127033E+02 0.162156E+00 21 0.140538E+02 0.932101E-01 22 0.154691E+02 0.301768E-01 23 0.169484E+02 -0.270454E-01 24 0.184910E+02 -0.787389E-01 25 0.200962E+02 -0.125302E+00 26 0.217632E+02 -0.167204E+00 27 0.234913E+02 -0.204951E+00 28 0.252796E+02 -0.239042E+00 29 0.271272E+02 -0.269918E+00 30 0.290333E+02 -0.297916E+00 31 0.309970E+02 -0.323335E+00 32 0.330173E+02 -0.346597E+00 33 0.350933E+02 -0.368287E+00 34 0.372240E+02 -0.388952E+00 35 0.394084E+02 -0.408996E+00 36 0.416454E+02 -0.428705E+00 37 0.439340E+02 -0.448292E+00 38 0.462730E+02 -0.467898E+00 39 0.486615E+02 -0.487633E+00 40 0.510981E+02 -0.507588E+00 41 0.535819E+02 -0.527735E+00 42 0.561115E+02 -0.547845E+00 43 0.586858E+02 -0.567757E+00 44 0.613036E+02 -0.587448E+00 45 0.639635E+02 -0.607020E+00 46 0.666645E+02 -0.626545E+00 47 0.694051E+02 -0.646059E+00 48 0.721840E+02 -0.665468E+00 49 0.750000E+02 -0.684483E+00 50 0.778517E+02 -0.703020E+00 51 0.807377E+02 -0.721080E+00 52 0.836567E+02 -0.738384E+00 53 0.866073E+02 -0.754525E+00 54 0.895880E+02 -0.769362E+00 55 0.925975E+02 -0.782740E+00 56 0.956343E+02 -0.794374E+00 57 0.986970E+02 -0.804032E+00 58 0.101784E+03 -0.811260E+00 59 0.104894E+03 -0.815231E+00 60 0.108026E+03 -0.815483E+00 61 0.111177E+03 -0.812158E+00 62 0.114347E+03 -0.805352E+00 63 0.117534E+03 -0.794772E+00 64 0.120736E+03 -0.780685E+00 65 0.123953E+03 -0.763468E+00 66 0.127181E+03 -0.743362E+00 67 0.130421E+03 -0.721330E+00 68 0.133670E+03 -0.698900E+00 69 0.136927E+03 -0.677366E+00 70 0.140190E+03 -0.658112E+00 71 0.143457E+03 -0.642715E+00 72 0.146728E+03 -0.632625E+00 73 0.150000E+03 -0.629095E+00 j y+ F(t) 1 0.000000E+00 0.153638E-53 2 0.356959E-01 0.433679E+01 3 0.142767E+00 0.433678E+01 4 0.321162E+00 0.433639E+01 5 0.570795E+00 0.433369E+01 6 0.891549E+00 0.432383E+01 7 0.128327E+01 0.429772E+01 8 0.174577E+01 0.424230E+01 9 0.227884E+01 0.414393E+01 10 0.288221E+01 0.399496E+01 11 0.355560E+01 0.379895E+01 12 0.429869E+01 0.357023E+01 13 0.511113E+01 0.332849E+01 14 0.599252E+01 0.309277E+01 15 0.694246E+01 0.287774E+01 16 0.796048E+01 0.269252E+01 17 0.904611E+01 0.254110E+01 18 0.101988E+02 0.242352E+01 19 0.114181E+02 0.233720E+01 20 0.127033E+02 0.227823E+01 21 0.140538E+02 0.224220E+01 22 0.154691E+02 0.222478E+01 23 0.169484E+02 0.222209E+01 24 0.184910E+02 0.223073E+01 25 0.200962E+02 0.224791E+01 26 0.217632E+02 0.227142E+01 27 0.234913E+02 0.229961E+01 28 0.252796E+02 0.233115E+01 29 0.271272E+02 0.236498E+01 30 0.290333E+02 0.240036E+01 31 0.309970E+02 0.243686E+01 32 0.330173E+02 0.247429E+01 33 0.350933E+02 0.251251E+01 34 0.372240E+02 0.255110E+01 35 0.394084E+02 0.258975E+01 36 0.416454E+02 0.262869E+01 37 0.439340E+02 0.266829E+01 38 0.462730E+02 0.270884E+01 39 0.486615E+02 0.275061E+01 40 0.510981E+02 0.279380E+01 41 0.535819E+02 0.283823E+01 42 0.561115E+02 0.288343E+01 43 0.586858E+02 0.292936E+01 44 0.613036E+02 0.297640E+01 45 0.639635E+02 0.302497E+01 46 0.666645E+02 0.307524E+01 47 0.694051E+02 0.312744E+01 48 0.721840E+02 0.318128E+01 49 0.750000E+02 0.323653E+01 50 0.778517E+02 0.329405E+01 51 0.807377E+02 0.335435E+01 52 0.836567E+02 0.341699E+01 53 0.866073E+02 0.348106E+01 54 0.895880E+02 0.354601E+01 55 0.925975E+02 0.361153E+01 56 0.956343E+02 0.367708E+01 57 0.986970E+02 0.374160E+01 58 0.101784E+03 0.380309E+01 59 0.104894E+03 0.385844E+01 60 0.108026E+03 0.390604E+01 61 0.111177E+03 0.394593E+01 62 0.114347E+03 0.397714E+01 63 0.117534E+03 0.399757E+01 64 0.120736E+03 0.400732E+01 65 0.123953E+03 0.400570E+01 66 0.127181E+03 0.399164E+01 67 0.130421E+03 0.396656E+01 68 0.133670E+03 0.393383E+01 69 0.136927E+03 0.389616E+01 70 0.140190E+03 0.385797E+01 71 0.143457E+03 0.382513E+01 72 0.146728E+03 0.380279E+01 73 0.150000E+03 0.379480E+01 j y+ /(u_rms*t_rms) 1 0.000000E+00 0.155443E-29 0.139032E-02 2 0.356959E-01 0.111440E-03 0.928692E+00 3 0.142767E+00 0.178357E-02 0.929774E+00 4 0.321162E+00 0.903473E-02 0.931531E+00 5 0.570795E+00 0.285805E-01 0.933896E+00 6 0.891549E+00 0.698518E-01 0.936793E+00 7 0.128327E+01 0.144943E+00 0.940124E+00 8 0.174577E+01 0.268289E+00 0.943776E+00 9 0.227884E+01 0.455698E+00 0.947596E+00 10 0.288221E+01 0.722294E+00 0.951404E+00 11 0.355560E+01 0.107913E+01 0.954994E+00 12 0.429869E+01 0.152902E+01 0.958163E+00 13 0.511113E+01 0.206285E+01 0.960727E+00 14 0.599252E+01 0.265827E+01 0.962552E+00 15 0.694246E+01 0.328198E+01 0.963553E+00 16 0.796048E+01 0.389501E+01 0.963696E+00 17 0.904611E+01 0.445959E+01 0.962991E+00 18 0.101988E+02 0.494513E+01 0.961477E+00 19 0.114181E+02 0.533172E+01 0.959210E+00 20 0.127033E+02 0.561081E+01 0.956256E+00 21 0.140538E+02 0.578369E+01 0.952684E+00 22 0.154691E+02 0.585886E+01 0.948559E+00 23 0.169484E+02 0.584917E+01 0.943948E+00 24 0.184910E+02 0.576944E+01 0.938908E+00 25 0.200962E+02 0.563460E+01 0.933498E+00 26 0.217632E+02 0.545842E+01 0.927771E+00 27 0.234913E+02 0.525301E+01 0.921767E+00 28 0.252796E+02 0.502858E+01 0.915511E+00 29 0.271272E+02 0.479336E+01 0.909017E+00 30 0.290333E+02 0.455376E+01 0.902298E+00 31 0.309970E+02 0.431456E+01 0.895367E+00 32 0.330173E+02 0.407929E+01 0.888231E+00 33 0.350933E+02 0.385078E+01 0.880897E+00 34 0.372240E+02 0.363136E+01 0.873386E+00 35 0.394084E+02 0.342257E+01 0.865713E+00 36 0.416454E+02 0.322511E+01 0.857892E+00 37 0.439340E+02 0.303896E+01 0.849931E+00 38 0.462730E+02 0.286379E+01 0.841842E+00 39 0.486615E+02 0.269933E+01 0.833652E+00 40 0.510981E+02 0.254527E+01 0.825389E+00 41 0.535819E+02 0.240112E+01 0.817052E+00 42 0.561115E+02 0.226633E+01 0.808656E+00 43 0.586858E+02 0.214034E+01 0.800247E+00 44 0.613036E+02 0.202243E+01 0.791872E+00 45 0.639635E+02 0.191175E+01 0.783537E+00 46 0.666645E+02 0.180751E+01 0.775219E+00 47 0.694051E+02 0.170907E+01 0.766913E+00 48 0.721840E+02 0.161600E+01 0.758632E+00 49 0.750000E+02 0.152780E+01 0.750390E+00 50 0.778517E+02 0.144395E+01 0.742190E+00 51 0.807377E+02 0.136410E+01 0.734004E+00 52 0.836567E+02 0.128795E+01 0.725797E+00 53 0.866073E+02 0.121520E+01 0.717557E+00 54 0.895880E+02 0.114563E+01 0.709270E+00 55 0.925975E+02 0.107908E+01 0.700908E+00 56 0.956343E+02 0.101538E+01 0.692446E+00 57 0.986970E+02 0.954463E+00 0.683881E+00 58 0.101784E+03 0.896269E+00 0.675200E+00 59 0.104894E+03 0.840643E+00 0.666351E+00 60 0.108026E+03 0.787459E+00 0.657253E+00 61 0.111177E+03 0.736835E+00 0.647855E+00 62 0.114347E+03 0.689044E+00 0.638149E+00 63 0.117534E+03 0.644337E+00 0.628184E+00 64 0.120736E+03 0.602958E+00 0.618086E+00 65 0.123953E+03 0.565146E+00 0.608030E+00 66 0.127181E+03 0.531124E+00 0.598234E+00 67 0.130421E+03 0.501120E+00 0.588939E+00 68 0.133670E+03 0.475337E+00 0.580398E+00 69 0.136927E+03 0.453943E+00 0.572845E+00 70 0.140190E+03 0.437068E+00 0.566549E+00 71 0.143457E+03 0.424851E+00 0.561803E+00 72 0.146728E+03 0.417433E+00 0.558849E+00 73 0.150000E+03 0.414941E+00 0.557841E+00 j y+ - -/(v_rms*t_rms) (vt)_rms S(vt) F(vt) 1 0.000000E+00 0.144527E-31 0.310532E-02 0.464927E-29 0.000000E+00 0.000000E+00 2 0.356959E-01 0.211434E-07 0.212552E+00 0.193918E-06 -0.253670E+02 0.297610E+04 3 0.142767E+00 0.135925E-05 0.216806E+00 0.122172E-04 -0.253915E+02 0.295165E+04 4 0.321162E+00 0.156038E-04 0.224123E+00 0.135594E-03 -0.254166E+02 0.290629E+04 5 0.570795E+00 0.886559E-04 0.234768E+00 0.734789E-03 -0.253794E+02 0.282741E+04 6 0.891549E+00 0.342905E-03 0.248954E+00 0.267454E-02 -0.251264E+02 0.268604E+04 7 0.128327E+01 0.103910E-02 0.266730E+00 0.752797E-02 -0.244143E+02 0.244235E+04 8 0.174577E+01 0.265380E-02 0.287872E+00 0.176344E-01 -0.229909E+02 0.207265E+04 9 0.227884E+01 0.595443E-02 0.311804E+00 0.358674E-01 -0.207583E+02 0.160686E+04 10 0.288221E+01 0.120354E-01 0.337608E+00 0.650623E-01 -0.179133E+02 0.113270E+04 11 0.355560E+01 0.222685E-01 0.364112E+00 0.107288E+00 -0.148787E+02 0.737291E+03 12 0.429869E+01 0.381335E-01 0.390038E+00 0.163303E+00 -0.120680E+02 0.454967E+03 13 0.511113E+01 0.609404E-01 0.414166E+00 0.232422E+00 -0.971966E+01 0.274933E+03 14 0.599252E+01 0.915109E-01 0.435476E+00 0.312778E+00 -0.787725E+01 0.168060E+03 15 0.694246E+01 0.129918E+00 0.453234E+00 0.401824E+00 -0.647023E+01 0.105938E+03 16 0.796048E+01 0.175387E+00 0.467039E+00 0.496937E+00 -0.540349E+01 0.692468E+02 17 0.904611E+01 0.226369E+00 0.476815E+00 0.595884E+00 -0.459591E+01 0.469813E+02 18 0.101988E+02 0.280803E+00 0.482780E+00 0.697010E+00 -0.398514E+01 0.331165E+02 19 0.114181E+02 0.336422E+00 0.485376E+00 0.799173E+00 -0.352513E+01 0.243008E+02 20 0.127033E+02 0.391077E+00 0.485194E+00 0.901512E+00 -0.318195E+01 0.186498E+02 21 0.140538E+02 0.442959E+00 0.482888E+00 0.100317E+01 -0.292912E+01 0.150480E+02 22 0.154691E+02 0.490712E+00 0.479094E+00 0.110315E+01 -0.274514E+01 0.127903E+02 23 0.169484E+02 0.533456E+00 0.474377E+00 0.120020E+01 -0.261300E+01 0.114176E+02 24 0.184910E+02 0.570727E+00 0.469195E+00 0.129298E+01 -0.251943E+01 0.106209E+02 25 0.200962E+02 0.602399E+00 0.463896E+00 0.138010E+01 -0.245437E+01 0.101889E+02 26 0.217632E+02 0.628591E+00 0.458732E+00 0.146027E+01 -0.241083E+01 0.998830E+01 27 0.234913E+02 0.649602E+00 0.453877E+00 0.153243E+01 -0.238433E+01 0.993864E+01 28 0.252796E+02 0.665845E+00 0.449458E+00 0.159588E+01 -0.237167E+01 0.999161E+01 29 0.271272E+02 0.677807E+00 0.445571E+00 0.165025E+01 -0.237047E+01 0.101189E+02 30 0.290333E+02 0.685992E+00 0.442284E+00 0.169547E+01 -0.237899E+01 0.103041E+02 31 0.309970E+02 0.690855E+00 0.439624E+00 0.173164E+01 -0.239597E+01 0.105385E+02 32 0.330173E+02 0.692788E+00 0.437577E+00 0.175908E+01 -0.242041E+01 0.108161E+02 33 0.350933E+02 0.692156E+00 0.436121E+00 0.177824E+01 -0.245141E+01 0.111317E+02 34 0.372240E+02 0.689286E+00 0.435221E+00 0.178973E+01 -0.248807E+01 0.114822E+02 35 0.394084E+02 0.684464E+00 0.434817E+00 0.179417E+01 -0.252982E+01 0.118698E+02 36 0.416454E+02 0.677937E+00 0.434841E+00 0.179227E+01 -0.257613E+01 0.122952E+02 37 0.439340E+02 0.669932E+00 0.435233E+00 0.178470E+01 -0.262633E+01 0.127538E+02 38 0.462730E+02 0.660655E+00 0.435939E+00 0.177215E+01 -0.268004E+01 0.132440E+02 39 0.486615E+02 0.650293E+00 0.436906E+00 0.175516E+01 -0.273712E+01 0.137682E+02 40 0.510981E+02 0.638965E+00 0.438055E+00 0.173422E+01 -0.279753E+01 0.143298E+02 41 0.535819E+02 0.626758E+00 0.439308E+00 0.170976E+01 -0.286106E+01 0.149261E+02 42 0.561115E+02 0.613776E+00 0.440620E+00 0.168225E+01 -0.292715E+01 0.155520E+02 43 0.586858E+02 0.600105E+00 0.441936E+00 0.165208E+01 -0.299533E+01 0.162070E+02 44 0.613036E+02 0.585776E+00 0.443172E+00 0.161963E+01 -0.306546E+01 0.168971E+02 45 0.639635E+02 0.570787E+00 0.444229E+00 0.158522E+01 -0.313733E+01 0.176270E+02 46 0.666645E+02 0.555140E+00 0.445024E+00 0.154923E+01 -0.321089E+01 0.184020E+02 47 0.694051E+02 0.538882E+00 0.445488E+00 0.151199E+01 -0.328621E+01 0.192236E+02 48 0.721840E+02 0.522058E+00 0.445543E+00 0.147378E+01 -0.336315E+01 0.200896E+02 49 0.750000E+02 0.504690E+00 0.445122E+00 0.143493E+01 -0.344205E+01 0.210103E+02 50 0.778517E+02 0.486820E+00 0.444183E+00 0.139577E+01 -0.352281E+01 0.219898E+02 51 0.807377E+02 0.468523E+00 0.442678E+00 0.135657E+01 -0.360453E+01 0.230161E+02 52 0.836567E+02 0.449846E+00 0.440500E+00 0.131734E+01 -0.368641E+01 0.240782E+02 53 0.866073E+02 0.430800E+00 0.437519E+00 0.127813E+01 -0.376791E+01 0.251720E+02 54 0.895880E+02 0.411381E+00 0.433581E+00 0.123899E+01 -0.384800E+01 0.262966E+02 55 0.925975E+02 0.391600E+00 0.428538E+00 0.120003E+01 -0.392551E+01 0.274533E+02 56 0.956343E+02 0.371489E+00 0.422268E+00 0.116143E+01 -0.399847E+01 0.286243E+02 57 0.986970E+02 0.351090E+00 0.414635E+00 0.112339E+01 -0.406411E+01 0.297910E+02 58 0.101784E+03 0.330446E+00 0.405471E+00 0.108609E+01 -0.411986E+01 0.309527E+02 59 0.104894E+03 0.309570E+00 0.394601E+00 0.104972E+01 -0.416278E+01 0.320986E+02 60 0.108026E+03 0.288466E+00 0.381845E+00 0.101449E+01 -0.418826E+01 0.331891E+02 61 0.111177E+03 0.267151E+00 0.367009E+00 0.980592E+00 -0.419139E+01 0.342184E+02 62 0.114347E+03 0.245630E+00 0.349870E+00 0.948171E+00 -0.416685E+01 0.352005E+02 63 0.117534E+03 0.223899E+00 0.330259E+00 0.917403E+00 -0.410723E+01 0.361107E+02 64 0.120736E+03 0.201999E+00 0.308083E+00 0.888522E+00 -0.400343E+01 0.369137E+02 65 0.123953E+03 0.179963E+00 0.283262E+00 0.861684E+00 -0.384527E+01 0.375609E+02 66 0.127181E+03 0.157787E+00 0.255724E+00 0.837032E+00 -0.362355E+01 0.380358E+02 67 0.130421E+03 0.135479E+00 0.225475E+00 0.814819E+00 -0.332951E+01 0.383268E+02 68 0.133670E+03 0.113066E+00 0.192625E+00 0.795358E+00 -0.295585E+01 0.384395E+02 69 0.136927E+03 0.905612E-01 0.157369E+00 0.778938E+00 -0.249939E+01 0.384051E+02 70 0.140190E+03 0.679716E-01 0.120011E+00 0.765836E+00 -0.196241E+01 0.382721E+02 71 0.143457E+03 0.453243E-01 0.809730E-01 0.756306E+00 -0.135415E+01 0.380966E+02 72 0.146728E+03 0.226590E-01 0.407772E-01 0.750534E+00 -0.691790E+00 0.379260E+02 73 0.150000E+03 0.000000E+00 0.000000E+00 0.748605E+00 0.000000E+00 0.378465E+02 j y+ nu_t alfa_t Pr_t 1 0.000000E+00 0.165719E-31 0.195249E-31 0.920566E+00 2 0.356959E-01 0.298824E-07 0.294909E-07 0.101351E+01 3 0.142767E+00 0.192522E-05 0.189575E-05 0.101578E+01 4 0.321162E+00 0.221675E-04 0.217606E-04 0.101892E+01 5 0.570795E+00 0.126339E-03 0.123631E-03 0.102212E+01 6 0.891549E+00 0.489902E-03 0.478242E-03 0.102460E+01 7 0.128327E+01 0.148709E-02 0.145007E-02 0.102575E+01 8 0.174577E+01 0.380208E-02 0.370926E-02 0.102525E+01 9 0.227884E+01 0.854162E-02 0.835125E-02 0.102303E+01 10 0.288221E+01 0.173145E-01 0.169908E-01 0.101930E+01 11 0.355560E+01 0.322440E-01 0.317926E-01 0.101444E+01 12 0.429869E+01 0.559078E-01 0.554223E-01 0.100900E+01 13 0.511113E+01 0.912304E-01 0.909303E-01 0.100353E+01 14 0.599252E+01 0.141377E+00 0.141615E+00 0.998557E+00 15 0.694246E+01 0.209682E+00 0.210907E+00 0.994428E+00 16 0.796048E+01 0.299611E+00 0.302304E+00 0.991333E+00 17 0.904611E+01 0.414764E+00 0.419352E+00 0.989304E+00 18 0.101988E+02 0.558852E+00 0.565646E+00 0.988239E+00 19 0.114181E+02 0.735672E+00 0.744817E+00 0.987972E+00 20 0.127033E+02 0.949029E+00 0.960494E+00 0.988317E+00 21 0.140538E+02 0.120262E+01 0.121616E+01 0.989120E+00 22 0.154691E+02 0.149994E+01 0.151497E+01 0.990312E+00 23 0.169484E+02 0.184408E+01 0.185946E+01 0.991957E+00 24 0.184910E+02 0.223764E+01 0.225109E+01 0.994212E+00 25 0.200962E+02 0.268203E+01 0.268977E+01 0.997281E+00 26 0.217632E+02 0.317718E+01 0.317326E+01 0.100134E+01 27 0.234913E+02 0.372106E+01 0.369743E+01 0.100644E+01 28 0.252796E+02 0.430954E+01 0.425654E+01 0.101244E+01 29 0.271272E+02 0.493684E+01 0.484392E+01 0.101911E+01 30 0.290333E+02 0.559551E+01 0.545237E+01 0.102612E+01 31 0.309970E+02 0.627474E+01 0.607342E+01 0.103295E+01 32 0.330173E+02 0.696029E+01 0.669611E+01 0.103918E+01 33 0.350933E+02 0.763824E+01 0.730835E+01 0.104480E+01 34 0.372240E+02 0.829874E+01 0.790050E+01 0.104999E+01 35 0.394084E+02 0.893389E+01 0.846543E+01 0.105486E+01 36 0.416454E+02 0.953382E+01 0.899756E+01 0.105910E+01 37 0.439340E+02 0.100878E+02 0.949449E+01 0.106200E+01 38 0.462730E+02 0.105898E+02 0.995833E+01 0.106298E+01 39 0.486615E+02 0.110367E+02 0.103920E+02 0.106170E+01 40 0.510981E+02 0.114235E+02 0.107970E+02 0.105781E+01 41 0.535819E+02 0.117517E+02 0.111783E+02 0.105118E+01 42 0.561115E+02 0.120361E+02 0.115477E+02 0.104228E+01 43 0.586858E+02 0.122929E+02 0.119150E+02 0.103175E+01 44 0.613036E+02 0.125253E+02 0.122774E+02 0.102023E+01 45 0.639635E+02 0.127284E+02 0.126206E+02 0.100854E+01 46 0.666645E+02 0.128975E+02 0.129330E+02 0.997237E+00 47 0.694051E+02 0.130344E+02 0.132174E+02 0.986099E+00 48 0.721840E+02 0.131472E+02 0.134857E+02 0.974836E+00 49 0.750000E+02 0.132429E+02 0.137417E+02 0.963622E+00 50 0.778517E+02 0.133167E+02 0.139820E+02 0.952325E+00 51 0.807377E+02 0.133574E+02 0.142095E+02 0.939922E+00 52 0.836567E+02 0.133546E+02 0.144291E+02 0.925404E+00 53 0.866073E+02 0.132999E+02 0.146297E+02 0.908975E+00 54 0.895880E+02 0.131941E+02 0.147889E+02 0.892023E+00 55 0.925975E+02 0.130504E+02 0.148898E+02 0.876290E+00 56 0.956343E+02 0.128804E+02 0.149253E+02 0.862704E+00 57 0.986970E+02 0.126849E+02 0.149130E+02 0.850176E+00 58 0.101784E+03 0.124630E+02 0.148978E+02 0.836094E+00 59 0.104894E+03 0.122187E+02 0.149180E+02 0.818611E+00 60 0.108026E+03 0.119597E+02 0.149776E+02 0.798136E+00 61 0.111177E+03 0.117024E+02 0.150572E+02 0.776935E+00 62 0.114347E+03 0.114698E+02 0.151336E+02 0.757775E+00 63 0.117534E+03 0.112812E+02 0.152013E+02 0.742179E+00 64 0.120736E+03 0.111488E+02 0.152881E+02 0.729512E+00 65 0.123953E+03 0.110812E+02 0.154275E+02 0.718694E+00 66 0.127181E+03 0.110815E+02 0.155993E+02 0.710705E+00 67 0.130421E+03 0.111389E+02 0.157318E+02 0.707848E+00 68 0.133670E+03 0.112359E+02 0.157647E+02 0.711349E+00 69 0.136927E+03 0.113770E+02 0.156885E+02 0.721496E+00 70 0.140190E+03 0.116294E+02 0.155432E+02 0.739367E+00 71 0.143457E+03 0.122979E+02 0.154809E+02 0.770151E+00 72 0.146728E+03 0.167433E+02 0.165414E+02 0.889337E+00 73 0.150000E+03 -0.580318E+01 0.167898E+00 -0.345638E+02 4.2 Budgets of temperature variance, its dissipation rates and turbulent heat fluxes 4.2.1 Budget for temperature variance t+**2/2 j y+ Prod. Diss. Turb.Diff. Mole.Diff. 1 0.000000E+00 0.107490E-31 -0.983359E-01 0.881896E-07 0.983380E-01 2 0.356959E-01 0.635618E-07 -0.983364E-01 -0.163996E-07 0.983368E-01 3 0.142767E+00 0.172931E-05 -0.983519E-01 0.180951E-05 0.983480E-01 4 0.321162E+00 0.148404E-04 -0.984106E-01 0.198874E-04 0.983755E-01 5 0.570795E+00 0.743447E-04 -0.985312E-01 0.110623E-03 0.983454E-01 6 0.891549E+00 0.269640E-03 -0.987044E-01 0.413692E-03 0.980201E-01 7 0.128327E+01 0.787202E-03 -0.988623E-01 0.119673E-02 0.968756E-01 8 0.174577E+01 0.196219E-02 -0.988646E-01 0.286087E-02 0.940360E-01 9 0.227884E+01 0.432256E-02 -0.985202E-01 0.584952E-02 0.883402E-01 10 0.288221E+01 0.859196E-02 -0.976333E-01 0.104088E-01 0.786178E-01 11 0.355560E+01 0.156072E-01 -0.961046E-01 0.162665E-01 0.642066E-01 12 0.429869E+01 0.261216E-01 -0.940421E-01 0.224190E-01 0.454676E-01 13 0.511113E+01 0.405173E-01 -0.917861E-01 0.272452E-01 0.239758E-01 14 0.599252E+01 0.585246E-01 -0.898321E-01 0.289954E-01 0.224779E-02 15 0.694246E+01 0.790874E-01 -0.886564E-01 0.264713E-01 -0.169785E-01 16 0.796048E+01 0.100477E+00 -0.885184E-01 0.195365E-01 -0.315858E-01 17 0.904611E+01 0.120645E+00 -0.893704E-01 0.919480E-02 -0.405769E-01 18 0.101988E+02 0.137692E+00 -0.908977E-01 -0.278534E-02 -0.441285E-01 19 0.114181E+02 0.150254E+00 -0.926445E-01 -0.144675E-01 -0.432803E-01 20 0.127033E+02 0.157706E+00 -0.941681E-01 -0.242755E-01 -0.394256E-01 21 0.140538E+02 0.160139E+00 -0.951393E-01 -0.312760E-01 -0.339128E-01 22 0.154691E+02 0.158183E+00 -0.953722E-01 -0.352033E-01 -0.278304E-01 23 0.169484E+02 0.152763E+00 -0.948099E-01 -0.362926E-01 -0.219251E-01 24 0.184910E+02 0.144898E+00 -0.934801E-01 -0.350702E-01 -0.166555E-01 25 0.200962E+02 0.135534E+00 -0.914667E-01 -0.321801E-01 -0.122468E-01 26 0.217632E+02 0.125467E+00 -0.889005E-01 -0.282813E-01 -0.870115E-02 27 0.234913E+02 0.115309E+00 -0.859214E-01 -0.239477E-01 -0.591321E-02 28 0.252796E+02 0.105480E+00 -0.826402E-01 -0.196020E-01 -0.377263E-02 29 0.271272E+02 0.962395E-01 -0.791381E-01 -0.155221E-01 -0.217757E-02 30 0.290333E+02 0.877175E-01 -0.754912E-01 -0.118686E-01 -0.102361E-02 31 0.309970E+02 0.799662E-01 -0.717777E-01 -0.871661E-02 -0.202078E-03 32 0.330173E+02 0.729885E-01 -0.680621E-01 -0.609631E-02 0.379190E-03 33 0.350933E+02 0.667481E-01 -0.643886E-01 -0.397472E-02 0.768865E-03 34 0.372240E+02 0.611835E-01 -0.608005E-01 -0.228268E-02 0.100808E-02 35 0.394084E+02 0.562259E-01 -0.573280E-01 -0.959461E-03 0.112272E-02 36 0.416454E+02 0.518063E-01 -0.539837E-01 0.527505E-04 0.113673E-02 37 0.439340E+02 0.478521E-01 -0.507836E-01 0.790249E-03 0.111367E-02 38 0.462730E+02 0.442874E-01 -0.477352E-01 0.128781E-02 0.109220E-02 39 0.486615E+02 0.410445E-01 -0.448376E-01 0.163174E-02 0.106275E-02 40 0.510981E+02 0.380739E-01 -0.420856E-01 0.188846E-02 0.100403E-02 41 0.535819E+02 0.353373E-01 -0.394726E-01 0.207329E-02 0.923411E-03 42 0.561115E+02 0.327930E-01 -0.369966E-01 0.219643E-02 0.853608E-03 43 0.586858E+02 0.304060E-01 -0.346525E-01 0.228816E-02 0.790121E-03 44 0.613036E+02 0.281648E-01 -0.324488E-01 0.238410E-02 0.722478E-03 45 0.639635E+02 0.260719E-01 -0.303863E-01 0.249102E-02 0.646360E-03 46 0.666645E+02 0.241231E-01 -0.284614E-01 0.258245E-02 0.588958E-03 47 0.694051E+02 0.223021E-01 -0.266658E-01 0.265435E-02 0.556710E-03 48 0.721840E+02 0.205938E-01 -0.249723E-01 0.275562E-02 0.489867E-03 49 0.750000E+02 0.189912E-01 -0.233821E-01 0.286612E-02 0.412298E-03 50 0.778517E+02 0.174832E-01 -0.219020E-01 0.294117E-02 0.386244E-03 51 0.807377E+02 0.160489E-01 -0.205074E-01 0.300907E-02 0.383634E-03 52 0.836567E+02 0.146754E-01 -0.191828E-01 0.310116E-02 0.363625E-03 53 0.866073E+02 0.133659E-01 -0.179381E-01 0.320855E-02 0.346209E-03 54 0.895880E+02 0.121258E-01 -0.167681E-01 0.331942E-02 0.331027E-03 55 0.925975E+02 0.109555E-01 -0.156662E-01 0.343991E-02 0.303292E-03 56 0.956343E+02 0.985184E-02 -0.146384E-01 0.356002E-02 0.290198E-03 57 0.986970E+02 0.880585E-02 -0.136821E-01 0.367417E-02 0.302043E-03 58 0.101784E+03 0.781063E-02 -0.127819E-01 0.381074E-02 0.297265E-03 59 0.104894E+03 0.686732E-02 -0.119406E-01 0.396269E-02 0.287923E-03 60 0.108026E+03 0.597833E-02 -0.111653E-01 0.409881E-02 0.308446E-03 61 0.111177E+03 0.514524E-02 -0.104516E-01 0.422420E-02 0.336788E-03 62 0.114347E+03 0.437286E-02 -0.979072E-02 0.437115E-02 0.335025E-03 63 0.117534E+03 0.366420E-02 -0.919278E-02 0.451073E-02 0.336793E-03 64 0.120736E+03 0.301723E-02 -0.865848E-02 0.463230E-02 0.351883E-03 65 0.123953E+03 0.243195E-02 -0.817890E-02 0.475759E-02 0.354064E-03 66 0.127181E+03 0.191238E-02 -0.776246E-02 0.487683E-02 0.360416E-03 67 0.130421E+03 0.146081E-02 -0.740662E-02 0.497913E-02 0.375100E-03 68 0.133670E+03 0.107746E-02 -0.710357E-02 0.506766E-02 0.385771E-03 69 0.136927E+03 0.763542E-03 -0.685389E-02 0.514649E-02 0.384542E-03 70 0.140190E+03 0.519957E-03 -0.666294E-02 0.520998E-02 0.382686E-03 71 0.143457E+03 0.345813E-03 -0.653088E-02 0.524878E-02 0.393901E-03 72 0.146728E+03 0.240510E-03 -0.645482E-02 0.526245E-02 0.413613E-03 73 0.150000E+03 0.205118E-03 -0.642967E-02 0.526453E-02 0.422015E-03 4.2.2 Budget for dissipation rate of temparature variance e_t j y+ M.G.Prod. Turb.Prod. Dissipation Turb.Trans. Grad.Prod. Mole.Diff. 1 0.000000E+00 0.107897E-03 -0.401888E-18 -0.105910E-01 -0.790429E-07 -0.113794E-22 0.369889E-02 2 0.356959E-01 0.173197E-03 0.918715E-04 -0.413153E-02 0.306880E-04 -0.207577E-10 0.307084E-02 3 0.142767E+00 0.371408E-03 0.364556E-03 -0.304448E-02 0.121957E-03 -0.175531E-08 0.190176E-02 4 0.321162E+00 0.712037E-03 0.810412E-03 -0.294015E-02 0.272942E-03 -0.282073E-07 0.105784E-02 5 0.570795E+00 0.121692E-02 0.141723E-02 -0.353388E-02 0.480506E-03 -0.227950E-06 0.348318E-03 6 0.891549E+00 0.192165E-02 0.216093E-02 -0.434354E-02 0.731257E-03 -0.123711E-05 -0.511575E-03 7 0.128327E+01 0.286707E-02 0.298938E-02 -0.556067E-02 0.981694E-03 -0.512993E-05 -0.130100E-02 8 0.174577E+01 0.407874E-02 0.380834E-02 -0.719613E-02 0.114579E-02 -0.173253E-04 -0.185125E-02 9 0.227884E+01 0.553967E-02 0.449178E-02 -0.903557E-02 0.111674E-02 -0.491684E-04 -0.208679E-02 10 0.288221E+01 0.716930E-02 0.492859E-02 -0.110199E-01 0.839516E-03 -0.119063E-03 -0.182374E-02 11 0.355560E+01 0.882391E-02 0.508033E-02 -0.130112E-01 0.374243E-03 -0.247880E-03 -0.104954E-02 12 0.429869E+01 0.103246E-01 0.500687E-02 -0.147820E-01 -0.112502E-03 -0.445603E-03 -0.197738E-04 13 0.511113E+01 0.115034E-01 0.484191E-02 -0.161984E-01 -0.434390E-03 -0.693912E-03 0.945884E-03 14 0.599252E+01 0.122484E-01 0.473486E-02 -0.171427E-01 -0.489220E-03 -0.938463E-03 0.154505E-02 15 0.694246E+01 0.125252E-01 0.478979E-02 -0.175593E-01 -0.314515E-03 -0.110319E-02 0.161674E-02 16 0.796048E+01 0.123703E-01 0.503369E-02 -0.175434E-01 -0.489556E-04 -0.112367E-02 0.125777E-02 17 0.904611E+01 0.118659E-01 0.542663E-02 -0.172223E-01 0.156543E-03 -0.979008E-03 0.688088E-03 18 0.101988E+02 0.111110E-01 0.589734E-02 -0.167165E-01 0.216916E-03 -0.701080E-03 0.121311E-03 19 0.114181E+02 0.102009E-01 0.637780E-02 -0.161441E-01 0.133226E-03 -0.357618E-03 -0.290027E-03 20 0.127033E+02 0.921617E-02 0.682049E-02 -0.155565E-01 -0.382720E-04 -0.223895E-04 -0.509832E-03 21 0.140538E+02 0.821936E-02 0.720030E-02 -0.149668E-01 -0.228570E-03 0.249847E-03 -0.573254E-03 22 0.154691E+02 0.725490E-02 0.750896E-02 -0.143872E-01 -0.384091E-03 0.433717E-03 -0.534401E-03 23 0.169484E+02 0.635245E-02 0.774582E-02 -0.138107E-01 -0.485008E-03 0.529674E-03 -0.451218E-03 24 0.184910E+02 0.552951E-02 0.790880E-02 -0.132353E-01 -0.531680E-03 0.553901E-03 -0.353152E-03 25 0.200962E+02 0.479453E-02 0.799371E-02 -0.126733E-01 -0.536229E-03 0.528411E-03 -0.245003E-03 26 0.217632E+02 0.414942E-02 0.800300E-02 -0.121172E-01 -0.506518E-03 0.473974E-03 -0.151410E-03 27 0.234913E+02 0.359084E-02 0.794172E-02 -0.115599E-01 -0.449924E-03 0.406875E-03 -0.871735E-04 28 0.252796E+02 0.311203E-02 0.781536E-02 -0.110043E-01 -0.381653E-03 0.338424E-03 -0.467152E-04 29 0.271272E+02 0.270423E-02 0.763042E-02 -0.104539E-01 -0.318535E-03 0.275324E-03 -0.134537E-04 30 0.290333E+02 0.235812E-02 0.739400E-02 -0.990942E-02 -0.262578E-03 0.220648E-03 0.167842E-04 31 0.309970E+02 0.206573E-02 0.711515E-02 -0.937220E-02 -0.210724E-03 0.175073E-03 0.375879E-04 32 0.330173E+02 0.181958E-02 0.680380E-02 -0.884277E-02 -0.162539E-03 0.138061E-03 0.477448E-04 33 0.350933E+02 0.161167E-02 0.646672E-02 -0.832528E-02 -0.119775E-03 0.108633E-03 0.576930E-04 34 0.372240E+02 0.143495E-02 0.611457E-02 -0.782084E-02 -0.811036E-04 0.856023E-04 0.621532E-04 35 0.394084E+02 0.128409E-02 0.575783E-02 -0.733053E-02 -0.473993E-04 0.677212E-04 0.600478E-04 36 0.416454E+02 0.115499E-02 0.540247E-02 -0.686077E-02 -0.205718E-04 0.539560E-04 0.604727E-04 37 0.439340E+02 0.104442E-02 0.505713E-02 -0.641194E-02 -0.122725E-05 0.435318E-04 0.579888E-04 38 0.462730E+02 0.949071E-03 0.472140E-02 -0.598205E-02 0.132868E-04 0.357438E-04 0.537813E-04 39 0.486615E+02 0.865649E-03 0.439180E-02 -0.557088E-02 0.259872E-04 0.298630E-04 0.489304E-04 40 0.510981E+02 0.791901E-03 0.407614E-02 -0.518051E-02 0.358455E-04 0.253058E-04 0.440808E-04 41 0.535819E+02 0.725912E-03 0.377558E-02 -0.480902E-02 0.409326E-04 0.217935E-04 0.413997E-04 42 0.561115E+02 0.665723E-03 0.348779E-02 -0.445482E-02 0.451158E-04 0.191688E-04 0.371157E-04 43 0.586858E+02 0.610291E-03 0.321510E-02 -0.412424E-02 0.490180E-04 0.171136E-04 0.376438E-04 44 0.613036E+02 0.559569E-03 0.296204E-02 -0.381353E-02 0.497253E-04 0.152878E-04 0.355109E-04 45 0.639635E+02 0.513652E-03 0.273043E-02 -0.352549E-02 0.493578E-04 0.136294E-04 0.328148E-04 46 0.666645E+02 0.472050E-03 0.251905E-02 -0.326129E-02 0.484113E-04 0.122574E-04 0.304327E-04 47 0.694051E+02 0.433716E-03 0.232348E-02 -0.301411E-02 0.500532E-04 0.111962E-04 0.225824E-04 48 0.721840E+02 0.398004E-03 0.213873E-02 -0.278739E-02 0.507964E-04 0.103116E-04 0.224057E-04 49 0.750000E+02 0.364733E-03 0.196671E-02 -0.257724E-02 0.521768E-04 0.952061E-05 0.234255E-04 50 0.778517E+02 0.333640E-03 0.180992E-02 -0.237770E-02 0.539596E-04 0.893626E-05 0.173001E-04 51 0.807377E+02 0.304290E-03 0.166278E-02 -0.219237E-02 0.554067E-04 0.861462E-05 0.137794E-04 52 0.836567E+02 0.276467E-03 0.152505E-02 -0.202152E-02 0.552451E-04 0.837823E-05 0.157302E-04 53 0.866073E+02 0.250206E-03 0.139828E-02 -0.186020E-02 0.556446E-04 0.808795E-05 0.139176E-04 54 0.895880E+02 0.225666E-03 0.128027E-02 -0.171116E-02 0.584542E-04 0.777281E-05 0.121249E-04 55 0.925975E+02 0.202819E-03 0.117054E-02 -0.157373E-02 0.595977E-04 0.747696E-05 0.130504E-04 56 0.956343E+02 0.181465E-03 0.107068E-02 -0.144532E-02 0.596393E-04 0.727544E-05 0.123932E-04 57 0.986970E+02 0.161376E-03 0.980549E-03 -0.132644E-02 0.605155E-04 0.724703E-05 0.904559E-05 58 0.101784E+03 0.142412E-03 0.897058E-03 -0.121825E-02 0.597428E-04 0.731361E-05 0.962332E-05 59 0.104894E+03 0.124618E-03 0.820276E-03 -0.111836E-02 0.597226E-04 0.737404E-05 0.104454E-04 60 0.108026E+03 0.108044E-03 0.750571E-03 -0.102678E-02 0.606003E-04 0.744790E-05 0.964241E-05 61 0.111177E+03 0.926710E-04 0.687703E-03 -0.942586E-03 0.621386E-04 0.749857E-05 0.758440E-05 62 0.114347E+03 0.785350E-04 0.630724E-03 -0.867890E-03 0.610550E-04 0.746418E-05 0.945952E-05 63 0.117534E+03 0.655965E-04 0.580631E-03 -0.800856E-03 0.622777E-04 0.744447E-05 0.936262E-05 64 0.120736E+03 0.536830E-04 0.536244E-03 -0.740047E-03 0.640762E-04 0.751462E-05 0.737993E-05 65 0.123953E+03 0.428074E-04 0.496079E-03 -0.687187E-03 0.642832E-04 0.756503E-05 0.907454E-05 66 0.127181E+03 0.331323E-04 0.461596E-03 -0.639746E-03 0.651105E-04 0.754175E-05 0.835971E-05 67 0.130421E+03 0.247323E-04 0.432448E-03 -0.598313E-03 0.656616E-04 0.753273E-05 0.708238E-05 68 0.133670E+03 0.176219E-04 0.407674E-03 -0.563966E-03 0.656795E-04 0.754743E-05 0.710700E-05 69 0.136927E+03 0.118307E-04 0.386759E-03 -0.536385E-03 0.663233E-04 0.751278E-05 0.794889E-05 70 0.140190E+03 0.736547E-05 0.370199E-03 -0.514541E-03 0.674484E-04 0.745893E-05 0.780615E-05 71 0.143457E+03 0.419187E-05 0.358631E-03 -0.499117E-03 0.682983E-04 0.748120E-05 0.746226E-05 72 0.146728E+03 0.228085E-05 0.351747E-03 -0.489682E-03 0.692041E-04 0.757104E-05 0.659580E-05 73 0.150000E+03 0.163986E-05 0.349214E-03 -0.486655E-03 0.697047E-04 0.762141E-05 0.665462E-05 4.2.3 Budget for j y+ Prod. Diss. T-dp/dx Turb.Diff. Mole.Diff. 1 0.000000E+00 0.367748E-30 -0.210604E+00 0.936099E-17 -0.109062E-06 0.210604E+00 2 0.356959E-01 0.113377E-06 -0.210677E+00 -0.301692E-04 0.122788E-06 0.210705E+00 3 0.142767E+00 0.386428E-05 -0.210934E+00 -0.120568E-03 0.430051E-05 0.211041E+00 4 0.321162E+00 0.370876E-04 -0.211472E+00 -0.272116E-03 0.495015E-04 0.211645E+00 5 0.570795E+00 0.196197E-03 -0.212378E+00 -0.490092E-03 0.276220E-03 0.212373E+00 6 0.891549E+00 0.732029E-03 -0.213649E+00 -0.788497E-03 0.104199E-02 0.212626E+00 7 0.128327E+01 0.216926E-02 -0.215064E+00 -0.119381E-02 0.303642E-02 0.210996E+00 8 0.174577E+01 0.544457E-02 -0.216087E+00 -0.174668E-02 0.729838E-02 0.205010E+00 9 0.227884E+01 0.120095E-01 -0.215861E+00 -0.250039E-02 0.149364E-01 0.191304E+00 10 0.288221E+01 0.237952E-01 -0.213432E+00 -0.351543E-02 0.264221E-01 0.166575E+00 11 0.355560E+01 0.429153E-01 -0.208204E+00 -0.485035E-02 0.406631E-01 0.129267E+00 12 0.429869E+01 0.710520E-01 -0.200415E+00 -0.655086E-02 0.545100E-01 0.811364E-01 13 0.511113E+01 0.108646E+00 -0.191263E+00 -0.863838E-02 0.633399E-01 0.275807E-01 14 0.599252E+01 0.154226E+00 -0.182509E+00 -0.111011E-01 0.627442E-01 -0.237629E-01 15 0.694246E+01 0.204272E+00 -0.175753E+00 -0.138905E-01 0.504896E-01 -0.655759E-01 16 0.796048E+01 0.253825E+00 -0.171790E+00 -0.169241E-01 0.276249E-01 -0.932361E-01 17 0.904611E+01 0.297653E+00 -0.170413E+00 -0.200962E-01 -0.188267E-02 -0.105791E+00 18 0.101988E+02 0.331512E+00 -0.170669E+00 -0.232926E-01 -0.326711E-01 -0.105416E+00 19 0.114181E+02 0.352991E+00 -0.171343E+00 -0.264081E-01 -0.597826E-01 -0.959902E-01 20 0.127033E+02 0.361702E+00 -0.171395E+00 -0.293596E-01 -0.798830E-01 -0.815857E-01 21 0.140538E+02 0.358911E+00 -0.170158E+00 -0.320918E-01 -0.916280E-01 -0.655308E-01 22 0.154691E+02 0.346892E+00 -0.167365E+00 -0.345761E-01 -0.953490E-01 -0.500797E-01 23 0.169484E+02 0.328270E+00 -0.163027E+00 -0.368042E-01 -0.924196E-01 -0.364767E-01 24 0.184910E+02 0.305548E+00 -0.157322E+00 -0.387776E-01 -0.846397E-01 -0.252459E-01 25 0.200962E+02 0.280845E+00 -0.150502E+00 -0.405011E-01 -0.738210E-01 -0.164410E-01 26 0.217632E+02 0.255791E+00 -0.142864E+00 -0.419783E-01 -0.615603E-01 -0.978543E-02 27 0.234913E+02 0.231534E+00 -0.134690E+00 -0.432091E-01 -0.490998E-01 -0.490915E-02 28 0.252796E+02 0.208803E+00 -0.126200E+00 -0.441961E-01 -0.372818E-01 -0.147907E-02 29 0.271272E+02 0.187987E+00 -0.117566E+00 -0.449488E-01 -0.266373E-01 0.833361E-03 30 0.290333E+02 0.169227E+00 -0.108942E+00 -0.454777E-01 -0.174241E-01 0.229694E-02 31 0.309970E+02 0.152527E+00 -0.100492E+00 -0.457914E-01 -0.973337E-02 0.318229E-02 32 0.330173E+02 0.137794E+00 -0.923619E-01 -0.458945E-01 -0.358341E-02 0.376019E-02 33 0.350933E+02 0.124856E+00 -0.846170E-01 -0.457823E-01 0.116577E-02 0.411795E-02 34 0.372240E+02 0.113500E+00 -0.772778E-01 -0.454523E-01 0.478766E-02 0.422733E-02 35 0.394084E+02 0.103523E+00 -0.703672E-01 -0.449174E-01 0.748598E-02 0.410124E-02 36 0.416454E+02 0.947521E-01 -0.639123E-01 -0.442049E-01 0.940761E-02 0.381325E-02 37 0.439340E+02 0.870236E-01 -0.579375E-01 -0.433425E-01 0.106598E-01 0.349300E-02 38 0.462730E+02 0.801825E-01 -0.524466E-01 -0.423525E-01 0.113235E-01 0.322467E-02 39 0.486615E+02 0.740802E-01 -0.474163E-01 -0.412539E-01 0.115836E-01 0.297206E-02 40 0.510981E+02 0.685900E-01 -0.428140E-01 -0.400627E-01 0.115998E-01 0.269571E-02 41 0.535819E+02 0.636036E-01 -0.386204E-01 -0.387934E-01 0.114245E-01 0.243089E-02 42 0.561115E+02 0.590190E-01 -0.348106E-01 -0.374621E-01 0.111398E-01 0.218747E-02 43 0.586858E+02 0.547639E-01 -0.313498E-01 -0.360885E-01 0.108377E-01 0.193639E-02 44 0.613036E+02 0.508128E-01 -0.282186E-01 -0.346906E-01 0.105297E-01 0.168258E-02 45 0.639635E+02 0.471556E-01 -0.254012E-01 -0.332781E-01 0.102063E-01 0.144984E-02 46 0.666645E+02 0.437663E-01 -0.228750E-01 -0.318544E-01 0.985033E-02 0.127140E-02 47 0.694051E+02 0.406080E-01 -0.206110E-01 -0.304196E-01 0.945811E-02 0.114476E-02 48 0.721840E+02 0.376478E-01 -0.185732E-01 -0.289732E-01 0.908508E-02 0.101380E-02 49 0.750000E+02 0.348603E-01 -0.167426E-01 -0.275238E-01 0.874797E-02 0.879496E-03 50 0.778517E+02 0.322203E-01 -0.151030E-01 -0.260864E-01 0.841211E-02 0.783847E-03 51 0.807377E+02 0.296998E-01 -0.136216E-01 -0.246678E-01 0.811850E-02 0.704285E-03 52 0.836567E+02 0.272854E-01 -0.122843E-01 -0.232677E-01 0.787927E-02 0.624159E-03 53 0.866073E+02 0.249824E-01 -0.110917E-01 -0.218883E-01 0.766391E-02 0.564278E-03 54 0.895880E+02 0.227915E-01 -0.100241E-01 -0.205347E-01 0.747765E-02 0.515051E-03 55 0.925975E+02 0.207046E-01 -0.906240E-02 -0.192105E-01 0.732066E-02 0.464208E-03 56 0.956343E+02 0.187138E-01 -0.819812E-02 -0.179224E-01 0.718711E-02 0.427793E-03 57 0.986970E+02 0.168101E-01 -0.742303E-02 -0.166793E-01 0.710096E-02 0.398269E-03 58 0.101784E+03 0.149894E-01 -0.672730E-02 -0.154881E-01 0.707419E-02 0.356336E-03 59 0.104894E+03 0.132577E-01 -0.610781E-02 -0.143520E-01 0.708603E-02 0.320331E-03 60 0.108026E+03 0.116214E-01 -0.556391E-02 -0.132753E-01 0.710190E-02 0.323837E-03 61 0.111177E+03 0.100811E-01 -0.508273E-02 -0.122631E-01 0.712156E-02 0.347723E-03 62 0.114347E+03 0.863701E-02 -0.465250E-02 -0.113175E-01 0.716747E-02 0.362262E-03 63 0.117534E+03 0.728833E-02 -0.427378E-02 -0.104395E-01 0.724140E-02 0.373582E-03 64 0.120736E+03 0.603357E-02 -0.394263E-02 -0.963078E-02 0.733930E-02 0.383117E-03 65 0.123953E+03 0.487853E-02 -0.365515E-02 -0.889283E-02 0.745462E-02 0.391332E-03 66 0.127181E+03 0.383590E-02 -0.340998E-02 -0.822795E-02 0.757040E-02 0.402997E-03 67 0.130421E+03 0.291747E-02 -0.320153E-02 -0.764044E-02 0.767346E-02 0.415360E-03 68 0.133670E+03 0.213239E-02 -0.302618E-02 -0.713459E-02 0.775973E-02 0.424583E-03 69 0.136927E+03 0.148748E-02 -0.288570E-02 -0.671371E-02 0.782879E-02 0.431427E-03 70 0.140190E+03 0.985639E-03 -0.278069E-02 -0.638044E-02 0.787491E-02 0.441309E-03 71 0.143457E+03 0.626620E-03 -0.270729E-02 -0.613760E-02 0.789651E-02 0.455746E-03 72 0.146728E+03 0.410233E-03 -0.266366E-02 -0.598980E-02 0.790126E-02 0.470247E-03 73 0.150000E+03 0.337782E-03 -0.264967E-02 -0.594027E-02 0.789992E-02 0.477621E-03 4.2.4 Budget for j y+ Prod. Diss. t-dp/dy Turb.Diff. Mole.Diff. 1 0.000000E+00 -0.199725E-31 -0.279512E-18 -0.206763E-06 -0.268299E-07 0.140075E-08 2 0.356959E-01 -0.910857E-10 0.101254E-03 0.333225E-04 0.132826E-07 -0.134546E-03 3 0.142767E+00 -0.201440E-07 0.408377E-03 0.137736E-03 -0.459505E-07 -0.543426E-03 4 0.321162E+00 -0.479670E-06 0.932775E-03 0.315548E-03 -0.768195E-06 -0.124367E-02 5 0.570795E+00 -0.443023E-05 0.169509E-02 0.583882E-03 -0.714718E-05 -0.226313E-02 6 0.891549E+00 -0.240595E-04 0.271974E-02 0.979490E-03 -0.378473E-04 -0.362674E-02 7 0.128327E+01 -0.926906E-04 0.401775E-02 0.154850E-02 -0.141056E-03 -0.532311E-02 8 0.174577E+01 -0.280220E-03 0.555975E-02 0.239223E-02 -0.406827E-03 -0.725684E-02 9 0.227884E+01 -0.706283E-03 0.724964E-02 0.364142E-02 -0.960881E-03 -0.921010E-02 10 0.288221E+01 -0.154342E-02 0.891734E-02 0.540329E-02 -0.192158E-02 -0.108494E-01 11 0.355560E+01 -0.300334E-02 0.103440E-01 0.777945E-02 -0.332400E-02 -0.117970E-01 12 0.429869E+01 -0.530375E-02 0.113167E-01 0.107814E-01 -0.504357E-02 -0.117509E-01 13 0.511113E+01 -0.861997E-02 0.116918E-01 0.142863E-01 -0.677033E-02 -0.106024E-01 14 0.599252E+01 -0.130335E-01 0.114382E-01 0.181203E-01 -0.806143E-02 -0.848789E-02 15 0.694246E+01 -0.184937E-01 0.106418E-01 0.220364E-01 -0.846197E-02 -0.575072E-02 16 0.796048E+01 -0.248069E-01 0.946991E-02 0.257724E-01 -0.764320E-02 -0.283436E-02 17 0.904611E+01 -0.316572E-01 0.811912E-02 0.291411E-01 -0.549995E-02 -0.153004E-03 18 0.101988E+02 -0.386531E-01 0.676594E-02 0.319978E-01 -0.217319E-02 0.200315E-02 19 0.114181E+02 -0.453855E-01 0.553792E-02 0.342769E-01 0.199754E-02 0.350196E-02 20 0.127033E+02 -0.514848E-01 0.450656E-02 0.359773E-01 0.656317E-02 0.435308E-02 21 0.140538E+02 -0.566619E-01 0.369543E-02 0.371454E-01 0.110545E-01 0.466378E-02 22 0.154691E+02 -0.607321E-01 0.309491E-02 0.378762E-01 0.150592E-01 0.458319E-02 23 0.169484E+02 -0.636200E-01 0.267821E-02 0.382700E-01 0.182729E-01 0.425486E-02 24 0.184910E+02 -0.653487E-01 0.241277E-02 0.384599E-01 0.205147E-01 0.379836E-02 25 0.200962E+02 -0.660203E-01 0.226720E-02 0.385431E-01 0.217306E-01 0.329723E-02 26 0.217632E+02 -0.657905E-01 0.221481E-02 0.385790E-01 0.219867E-01 0.279856E-02 27 0.234913E+02 -0.648387E-01 0.223090E-02 0.386270E-01 0.214358E-01 0.233257E-02 28 0.252796E+02 -0.633414E-01 0.229389E-02 0.386251E-01 0.202811E-01 0.191053E-02 29 0.271272E+02 -0.614495E-01 0.238512E-02 0.385458E-01 0.187178E-01 0.154022E-02 30 0.290333E+02 -0.592837E-01 0.248566E-02 0.384263E-01 0.168812E-01 0.124172E-02 31 0.309970E+02 -0.569463E-01 0.258782E-02 0.382173E-01 0.148704E-01 0.100834E-02 32 0.330173E+02 -0.545233E-01 0.269303E-02 0.379687E-01 0.127761E-01 0.814087E-03 33 0.350933E+02 -0.520765E-01 0.279855E-02 0.376941E-01 0.106865E-01 0.652447E-03 34 0.372240E+02 -0.496458E-01 0.290001E-02 0.373019E-01 0.868718E-02 0.522488E-03 35 0.394084E+02 -0.472622E-01 0.299847E-02 0.367808E-01 0.684731E-02 0.414580E-03 36 0.416454E+02 -0.449499E-01 0.309590E-02 0.361250E-01 0.521428E-02 0.325196E-03 37 0.439340E+02 -0.427186E-01 0.318997E-02 0.353218E-01 0.379512E-02 0.251657E-03 38 0.462730E+02 -0.405619E-01 0.327169E-02 0.343988E-01 0.256648E-02 0.192263E-03 39 0.486615E+02 -0.384681E-01 0.333203E-02 0.333914E-01 0.148222E-02 0.154893E-03 40 0.510981E+02 -0.364341E-01 0.337423E-02 0.323193E-01 0.538523E-03 0.128558E-03 41 0.535819E+02 -0.344597E-01 0.340205E-02 0.311553E-01 -0.241400E-03 0.978407E-04 42 0.561115E+02 -0.325330E-01 0.341143E-02 0.299117E-01 -0.892637E-03 0.748029E-04 43 0.586858E+02 -0.306442E-01 0.340055E-02 0.286465E-01 -0.146113E-02 0.667002E-04 44 0.613036E+02 -0.288047E-01 0.337510E-02 0.273540E-01 -0.195148E-02 0.670793E-04 45 0.639635E+02 -0.270379E-01 0.334739E-02 0.260429E-01 -0.236072E-02 0.673817E-04 46 0.666645E+02 -0.253569E-01 0.332030E-02 0.247656E-01 -0.269361E-02 0.591109E-04 47 0.694051E+02 -0.237581E-01 0.328080E-02 0.235197E-01 -0.297212E-02 0.500187E-04 48 0.721840E+02 -0.222357E-01 0.322434E-02 0.222960E-01 -0.319997E-02 0.482986E-04 49 0.750000E+02 -0.207920E-01 0.315692E-02 0.210991E-01 -0.334456E-02 0.437595E-04 50 0.778517E+02 -0.194220E-01 0.308156E-02 0.198932E-01 -0.340453E-02 0.317895E-04 51 0.807377E+02 -0.181068E-01 0.299546E-02 0.186965E-01 -0.342498E-02 0.246356E-04 52 0.836567E+02 -0.168350E-01 0.289773E-02 0.175650E-01 -0.345050E-02 0.245456E-04 53 0.866073E+02 -0.156147E-01 0.278968E-02 0.164962E-01 -0.348651E-02 0.256589E-04 54 0.895880E+02 -0.144563E-01 0.267569E-02 0.154854E-01 -0.351371E-02 0.235949E-04 55 0.925975E+02 -0.133632E-01 0.255778E-02 0.145293E-01 -0.351858E-02 0.203199E-04 56 0.956343E+02 -0.123323E-01 0.243694E-02 0.135976E-01 -0.348595E-02 0.165863E-04 57 0.986970E+02 -0.113524E-01 0.231284E-02 0.126719E-01 -0.341564E-02 0.129060E-04 58 0.101784E+03 -0.104121E-01 0.218293E-02 0.117696E-01 -0.332174E-02 0.131135E-04 59 0.104894E+03 -0.950996E-02 0.204724E-02 0.108836E-01 -0.320742E-02 0.151052E-04 60 0.108026E+03 -0.864582E-02 0.190662E-02 0.100119E-01 -0.307466E-02 0.151786E-04 61 0.111177E+03 -0.781703E-02 0.176211E-02 0.918056E-02 -0.293468E-02 0.169126E-04 62 0.114347E+03 -0.702638E-02 0.161817E-02 0.837231E-02 -0.278237E-02 0.184652E-04 63 0.117534E+03 -0.627506E-02 0.147791E-02 0.756494E-02 -0.259928E-02 0.131238E-04 64 0.120736E+03 -0.555402E-02 0.133659E-02 0.677917E-02 -0.239800E-02 0.874043E-05 65 0.123953E+03 -0.485653E-02 0.119155E-02 0.601316E-02 -0.219674E-02 0.116193E-04 66 0.127181E+03 -0.418514E-02 0.104641E-02 0.525370E-02 -0.198742E-02 0.129649E-04 67 0.130421E+03 -0.353986E-02 0.901671E-03 0.451138E-02 -0.175700E-02 0.101089E-04 68 0.133670E+03 -0.291520E-02 0.754759E-03 0.376969E-02 -0.150666E-02 0.857620E-05 69 0.136927E+03 -0.230911E-02 0.606296E-03 0.301674E-02 -0.123776E-02 0.745760E-05 70 0.140190E+03 -0.172171E-02 0.457604E-03 0.227210E-02 -0.944545E-03 0.421645E-05 71 0.143457E+03 -0.114699E-02 0.308328E-03 0.151913E-02 -0.630731E-03 -0.327500E-06 72 0.146728E+03 -0.574755E-03 0.156109E-03 0.753470E-03 -0.312501E-03 -0.247190E-05 73 0.150000E+03 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 4.2.5 Budget for j y+ t-dp/dy p.Diff. p-dt/dy 1 0.000000E+00 -0.181399E-06 0.291964E-01 -0.291966E-01 2 0.356959E-01 0.310871E-04 0.292558E-01 -0.292248E-01 3 0.142767E+00 0.140750E-03 0.294261E-01 -0.292854E-01 4 0.321162E+00 0.313826E-03 0.296133E-01 -0.292994E-01 5 0.570795E+00 0.572618E-03 0.297397E-01 -0.291671E-01 6 0.891549E+00 0.983280E-03 0.298024E-01 -0.288192E-01 7 0.128327E+01 0.153930E-02 0.297357E-01 -0.281964E-01 8 0.174577E+01 0.235913E-02 0.295742E-01 -0.272151E-01 9 0.227884E+01 0.362221E-02 0.293506E-01 -0.257284E-01 10 0.288221E+01 0.535159E-02 0.288045E-01 -0.234528E-01 11 0.355560E+01 0.768504E-02 0.276520E-01 -0.199670E-01 12 0.429869E+01 0.107084E-01 0.255062E-01 -0.147978E-01 13 0.511113E+01 0.141905E-01 0.217395E-01 -0.754903E-02 14 0.599252E+01 0.180004E-01 0.160854E-01 0.191507E-02 15 0.694246E+01 0.219702E-01 0.863327E-02 0.133369E-01 16 0.796048E+01 0.256969E-01 -0.360908E-03 0.260578E-01 17 0.904611E+01 0.290392E-01 -0.100794E-01 0.391187E-01 18 0.101988E+02 0.319408E-01 -0.195395E-01 0.514803E-01 19 0.114181E+02 0.342216E-01 -0.280258E-01 0.622474E-01 20 0.127033E+02 0.359542E-01 -0.348817E-01 0.708358E-01 21 0.140538E+02 0.372618E-01 -0.397930E-01 0.770549E-01 22 0.154691E+02 0.381314E-01 -0.428976E-01 0.810291E-01 23 0.169484E+02 0.386916E-01 -0.443658E-01 0.830574E-01 24 0.184910E+02 0.390756E-01 -0.444244E-01 0.834999E-01 25 0.200962E+02 0.392747E-01 -0.433820E-01 0.826568E-01 26 0.217632E+02 0.393819E-01 -0.413339E-01 0.807158E-01 27 0.234913E+02 0.394753E-01 -0.383478E-01 0.778231E-01 28 0.252796E+02 0.394655E-01 -0.347133E-01 0.741788E-01 29 0.271272E+02 0.393526E-01 -0.307333E-01 0.700859E-01 30 0.290333E+02 0.391423E-01 -0.267726E-01 0.659148E-01 31 0.309970E+02 0.387964E-01 -0.230799E-01 0.618763E-01 32 0.330173E+02 0.384228E-01 -0.194993E-01 0.579222E-01 33 0.350933E+02 0.380885E-01 -0.158899E-01 0.539785E-01 34 0.372240E+02 0.377644E-01 -0.122767E-01 0.500411E-01 35 0.394084E+02 0.373851E-01 -0.874569E-02 0.461309E-01 36 0.416454E+02 0.368465E-01 -0.555185E-02 0.423984E-01 37 0.439340E+02 0.360938E-01 -0.296569E-02 0.390594E-01 38 0.462730E+02 0.351279E-01 -0.100486E-02 0.361327E-01 39 0.486615E+02 0.340199E-01 0.552634E-03 0.334672E-01 40 0.510981E+02 0.328640E-01 0.195597E-02 0.309079E-01 41 0.535819E+02 0.316620E-01 0.328593E-02 0.283760E-01 42 0.561115E+02 0.304165E-01 0.450504E-02 0.259115E-01 43 0.586858E+02 0.291303E-01 0.548919E-02 0.236412E-01 44 0.613036E+02 0.277673E-01 0.609384E-02 0.216734E-01 45 0.639635E+02 0.263637E-01 0.636861E-02 0.199951E-01 46 0.666645E+02 0.249842E-01 0.653037E-02 0.184537E-01 47 0.694051E+02 0.236659E-01 0.679217E-02 0.168737E-01 48 0.721840E+02 0.224113E-01 0.720888E-02 0.152023E-01 49 0.750000E+02 0.211624E-01 0.761268E-02 0.135497E-01 50 0.778517E+02 0.198777E-01 0.779240E-02 0.120853E-01 51 0.807377E+02 0.186180E-01 0.779348E-02 0.108245E-01 52 0.836567E+02 0.174214E-01 0.781800E-02 0.960341E-02 53 0.866073E+02 0.162915E-01 0.796657E-02 0.832489E-02 54 0.895880E+02 0.152512E-01 0.816884E-02 0.708235E-02 55 0.925975E+02 0.142526E-01 0.828900E-02 0.596366E-02 56 0.956343E+02 0.132884E-01 0.833855E-02 0.494984E-02 57 0.986970E+02 0.123560E-01 0.828773E-02 0.406826E-02 58 0.101784E+03 0.113887E-01 0.803234E-02 0.335630E-02 59 0.104894E+03 0.104389E-01 0.769487E-02 0.274405E-02 60 0.108026E+03 0.956017E-02 0.739098E-02 0.216919E-02 61 0.111177E+03 0.871057E-02 0.705025E-02 0.166033E-02 62 0.114347E+03 0.792208E-02 0.667751E-02 0.124457E-02 63 0.117534E+03 0.719031E-02 0.629459E-02 0.895718E-03 64 0.120736E+03 0.644684E-02 0.585474E-02 0.592089E-03 65 0.123953E+03 0.571758E-02 0.538383E-02 0.333748E-03 66 0.127181E+03 0.500618E-02 0.489871E-02 0.107469E-03 67 0.130421E+03 0.428091E-02 0.436903E-02 -0.881170E-04 68 0.133670E+03 0.355368E-02 0.376293E-02 -0.209243E-03 69 0.136927E+03 0.282317E-02 0.306244E-02 -0.239276E-03 70 0.140190E+03 0.208797E-02 0.230426E-02 -0.216296E-03 71 0.143457E+03 0.137038E-02 0.153505E-02 -0.164665E-03 72 0.146728E+03 0.678360E-03 0.766696E-03 -0.883383E-04 73 0.150000E+03 0.000000E+00 0.000000E+00 0.000000E+00 4.3 One-dimensional Energy Spectra at several points 4.3.1 Streamwise Power Spectra at y+ = 5.1 k_x*delta E(t+*t+) 0.000000E+00 0.314002E+00 0.400000E+00 0.453233E+00 0.800000E+00 0.238772E+00 0.120000E+01 0.175108E+00 0.160000E+01 0.116112E+00 0.200000E+01 0.869202E-01 0.240000E+01 0.611741E-01 0.280000E+01 0.476359E-01 0.320000E+01 0.372163E-01 0.360000E+01 0.281681E-01 0.400000E+01 0.227990E-01 0.440000E+01 0.186629E-01 0.480000E+01 0.148392E-01 0.520000E+01 0.121376E-01 0.560000E+01 0.100295E-01 0.600000E+01 0.811257E-02 0.640000E+01 0.646620E-02 0.680000E+01 0.533825E-02 0.720000E+01 0.450391E-02 0.760000E+01 0.378406E-02 0.800000E+01 0.309964E-02 0.840000E+01 0.259408E-02 0.880000E+01 0.216921E-02 0.920000E+01 0.182861E-02 0.960000E+01 0.155577E-02 0.100000E+02 0.131900E-02 0.104000E+02 0.111990E-02 0.108000E+02 0.975181E-03 0.112000E+02 0.836841E-03 0.116000E+02 0.724646E-03 0.120000E+02 0.622262E-03 0.124000E+02 0.555312E-03 0.128000E+02 0.482227E-03 0.132000E+02 0.421189E-03 0.136000E+02 0.366058E-03 0.140000E+02 0.322859E-03 0.144000E+02 0.284423E-03 0.148000E+02 0.250663E-03 0.152000E+02 0.220057E-03 0.156000E+02 0.199239E-03 0.160000E+02 0.178126E-03 0.164000E+02 0.159354E-03 0.168000E+02 0.144291E-03 0.172000E+02 0.129658E-03 0.176000E+02 0.116943E-03 0.180000E+02 0.106219E-03 0.184000E+02 0.970055E-04 0.188000E+02 0.893717E-04 0.192000E+02 0.832247E-04 0.196000E+02 0.753453E-04 0.200000E+02 0.698172E-04 0.204000E+02 0.645692E-04 0.208000E+02 0.600345E-04 0.212000E+02 0.559131E-04 0.216000E+02 0.517095E-04 0.220000E+02 0.484714E-04 0.224000E+02 0.450401E-04 0.228000E+02 0.420379E-04 0.232000E+02 0.386594E-04 0.236000E+02 0.355521E-04 0.240000E+02 0.325345E-04 0.244000E+02 0.295305E-04 0.248000E+02 0.275179E-04 0.252000E+02 0.270091E-04 at y+ = 12.7 k_x*delta E(t+*t+) 0.000000E+00 0.949586E+00 0.400000E+00 0.130972E+01 0.800000E+00 0.688185E+00 0.120000E+01 0.493309E+00 0.160000E+01 0.333365E+00 0.200000E+01 0.260072E+00 0.240000E+01 0.194435E+00 0.280000E+01 0.155768E+00 0.320000E+01 0.123220E+00 0.360000E+01 0.993394E-01 0.400000E+01 0.811030E-01 0.440000E+01 0.678071E-01 0.480000E+01 0.568990E-01 0.520000E+01 0.476384E-01 0.560000E+01 0.392844E-01 0.600000E+01 0.328033E-01 0.640000E+01 0.276319E-01 0.680000E+01 0.234753E-01 0.720000E+01 0.202444E-01 0.760000E+01 0.175536E-01 0.800000E+01 0.149471E-01 0.840000E+01 0.125849E-01 0.880000E+01 0.109460E-01 0.920000E+01 0.931843E-02 0.960000E+01 0.814766E-02 0.100000E+02 0.705574E-02 0.104000E+02 0.605181E-02 0.108000E+02 0.530728E-02 0.112000E+02 0.472631E-02 0.116000E+02 0.417865E-02 0.120000E+02 0.371327E-02 0.124000E+02 0.327560E-02 0.128000E+02 0.291845E-02 0.132000E+02 0.258804E-02 0.136000E+02 0.230393E-02 0.140000E+02 0.206804E-02 0.144000E+02 0.186310E-02 0.148000E+02 0.167365E-02 0.152000E+02 0.150269E-02 0.156000E+02 0.137087E-02 0.160000E+02 0.124678E-02 0.164000E+02 0.114239E-02 0.168000E+02 0.103619E-02 0.172000E+02 0.946934E-03 0.176000E+02 0.872869E-03 0.180000E+02 0.807792E-03 0.184000E+02 0.744811E-03 0.188000E+02 0.693332E-03 0.192000E+02 0.661272E-03 0.196000E+02 0.610657E-03 0.200000E+02 0.577226E-03 0.204000E+02 0.545415E-03 0.208000E+02 0.516261E-03 0.212000E+02 0.487399E-03 0.216000E+02 0.464249E-03 0.220000E+02 0.445291E-03 0.224000E+02 0.429612E-03 0.228000E+02 0.407495E-03 0.232000E+02 0.392064E-03 0.236000E+02 0.381346E-03 0.240000E+02 0.365837E-03 0.244000E+02 0.357690E-03 0.248000E+02 0.356835E-03 0.252000E+02 0.379935E-03 at y+ = 75.1 k_x*delta E(t+*t+) 0.000000E+00 0.254458E+00 0.400000E+00 0.289084E+00 0.800000E+00 0.204660E+00 0.120000E+01 0.179485E+00 0.160000E+01 0.156961E+00 0.200000E+01 0.124876E+00 0.240000E+01 0.116617E+00 0.280000E+01 0.981303E-01 0.320000E+01 0.821604E-01 0.360000E+01 0.713425E-01 0.400000E+01 0.655191E-01 0.440000E+01 0.602464E-01 0.480000E+01 0.535344E-01 0.520000E+01 0.478649E-01 0.560000E+01 0.424686E-01 0.600000E+01 0.399095E-01 0.640000E+01 0.344058E-01 0.680000E+01 0.324365E-01 0.720000E+01 0.273016E-01 0.760000E+01 0.255483E-01 0.800000E+01 0.227081E-01 0.840000E+01 0.213362E-01 0.880000E+01 0.192905E-01 0.920000E+01 0.171269E-01 0.960000E+01 0.149451E-01 0.100000E+02 0.143919E-01 0.104000E+02 0.128990E-01 0.108000E+02 0.117300E-01 0.112000E+02 0.110955E-01 0.116000E+02 0.963573E-02 0.120000E+02 0.947420E-02 0.124000E+02 0.900922E-02 0.128000E+02 0.799433E-02 0.132000E+02 0.750416E-02 0.136000E+02 0.708341E-02 0.140000E+02 0.666140E-02 0.144000E+02 0.605638E-02 0.148000E+02 0.578264E-02 0.152000E+02 0.542386E-02 0.156000E+02 0.503800E-02 0.160000E+02 0.481290E-02 0.164000E+02 0.448434E-02 0.168000E+02 0.422373E-02 0.172000E+02 0.409182E-02 0.176000E+02 0.384223E-02 0.180000E+02 0.362493E-02 0.184000E+02 0.351788E-02 0.188000E+02 0.338422E-02 0.192000E+02 0.326761E-02 0.196000E+02 0.315562E-02 0.200000E+02 0.303901E-02 0.204000E+02 0.294856E-02 0.208000E+02 0.288979E-02 0.212000E+02 0.282480E-02 0.216000E+02 0.278154E-02 0.220000E+02 0.270776E-02 0.224000E+02 0.267454E-02 0.228000E+02 0.265945E-02 0.232000E+02 0.267037E-02 0.236000E+02 0.263085E-02 0.240000E+02 0.260142E-02 0.244000E+02 0.265436E-02 0.248000E+02 0.255694E-02 0.252000E+02 0.262096E-02 at y+ = 150 k_x*delta E(t+*t+) 0.000000E+00 0.775371E-01 0.400000E+00 0.964527E-01 0.800000E+00 0.745215E-01 0.120000E+01 0.623802E-01 0.160000E+01 0.516822E-01 0.200000E+01 0.506974E-01 0.240000E+01 0.388266E-01 0.280000E+01 0.387772E-01 0.320000E+01 0.313543E-01 0.360000E+01 0.288331E-01 0.400000E+01 0.240296E-01 0.440000E+01 0.228363E-01 0.480000E+01 0.203277E-01 0.520000E+01 0.172845E-01 0.560000E+01 0.156783E-01 0.600000E+01 0.148821E-01 0.640000E+01 0.132613E-01 0.680000E+01 0.120080E-01 0.720000E+01 0.102748E-01 0.760000E+01 0.993351E-02 0.800000E+01 0.859824E-02 0.840000E+01 0.798907E-02 0.880000E+01 0.753478E-02 0.920000E+01 0.660749E-02 0.960000E+01 0.598879E-02 0.100000E+02 0.539622E-02 0.104000E+02 0.491907E-02 0.108000E+02 0.436077E-02 0.112000E+02 0.417000E-02 0.116000E+02 0.373573E-02 0.120000E+02 0.349752E-02 0.124000E+02 0.326299E-02 0.128000E+02 0.309769E-02 0.132000E+02 0.284810E-02 0.136000E+02 0.271602E-02 0.140000E+02 0.242845E-02 0.144000E+02 0.228390E-02 0.148000E+02 0.206607E-02 0.152000E+02 0.200446E-02 0.156000E+02 0.194007E-02 0.160000E+02 0.178086E-02 0.164000E+02 0.165873E-02 0.168000E+02 0.158548E-02 0.172000E+02 0.149148E-02 0.176000E+02 0.143223E-02 0.180000E+02 0.136420E-02 0.184000E+02 0.129038E-02 0.188000E+02 0.120835E-02 0.192000E+02 0.115608E-02 0.196000E+02 0.112785E-02 0.200000E+02 0.106965E-02 0.204000E+02 0.101752E-02 0.208000E+02 0.961429E-03 0.212000E+02 0.927261E-03 0.216000E+02 0.894013E-03 0.220000E+02 0.875416E-03 0.224000E+02 0.829614E-03 0.228000E+02 0.784022E-03 0.232000E+02 0.745687E-03 0.236000E+02 0.736501E-03 0.240000E+02 0.681028E-03 0.244000E+02 0.642696E-03 0.248000E+02 0.595100E-03 0.252000E+02 0.562607E-03 4.3.2 Spanwise power spectra at y+ = 5.1 k_z*delta E(t+*t+) 0.000000E+00 0.313571E-01 0.100000E+01 0.717138E-01 0.200000E+01 0.888160E-01 0.300000E+01 0.105055E+00 0.400000E+01 0.108387E+00 0.500000E+01 0.108338E+00 0.600000E+01 0.187591E+00 0.700000E+01 0.147052E+00 0.800000E+01 0.157823E+00 0.900000E+01 0.112755E+00 0.100000E+02 0.973296E-01 0.110000E+02 0.957101E-01 0.120000E+02 0.691739E-01 0.130000E+02 0.563922E-01 0.140000E+02 0.463323E-01 0.150000E+02 0.373821E-01 0.160000E+02 0.294649E-01 0.170000E+02 0.254860E-01 0.180000E+02 0.200532E-01 0.190000E+02 0.156594E-01 0.200000E+02 0.128905E-01 0.210000E+02 0.108463E-01 0.220000E+02 0.825977E-02 0.230000E+02 0.709112E-02 0.240000E+02 0.586334E-02 0.250000E+02 0.505871E-02 0.260000E+02 0.406147E-02 0.270000E+02 0.334072E-02 0.280000E+02 0.277584E-02 0.290000E+02 0.228915E-02 0.300000E+02 0.188742E-02 0.310000E+02 0.163334E-02 0.320000E+02 0.133433E-02 0.330000E+02 0.113696E-02 0.340000E+02 0.934015E-03 0.350000E+02 0.805915E-03 0.360000E+02 0.676962E-03 0.370000E+02 0.571789E-03 0.380000E+02 0.486908E-03 0.390000E+02 0.413281E-03 0.400000E+02 0.342619E-03 0.410000E+02 0.299342E-03 0.420000E+02 0.255513E-03 0.430000E+02 0.215520E-03 0.440000E+02 0.187043E-03 0.450000E+02 0.162595E-03 0.460000E+02 0.141662E-03 0.470000E+02 0.120917E-03 0.480000E+02 0.107815E-03 0.490000E+02 0.941709E-04 0.500000E+02 0.809038E-04 0.510000E+02 0.720021E-04 0.520000E+02 0.657957E-04 0.530000E+02 0.588279E-04 0.540000E+02 0.529377E-04 0.550000E+02 0.481067E-04 0.560000E+02 0.439703E-04 0.570000E+02 0.399870E-04 0.580000E+02 0.366381E-04 0.590000E+02 0.325584E-04 0.600000E+02 0.279082E-04 0.610000E+02 0.246040E-04 0.620000E+02 0.211970E-04 0.630000E+02 0.188187E-04 at y+ = 12.7 k_z*delta E(t+*t+) 0.000000E+00 0.768066E-01 0.100000E+01 0.205572E+00 0.200000E+01 0.268693E+00 0.300000E+01 0.346788E+00 0.400000E+01 0.368221E+00 0.500000E+01 0.352213E+00 0.600000E+01 0.627990E+00 0.700000E+01 0.475161E+00 0.800000E+01 0.484394E+00 0.900000E+01 0.342752E+00 0.100000E+02 0.288099E+00 0.110000E+02 0.267712E+00 0.120000E+02 0.194421E+00 0.130000E+02 0.158824E+00 0.140000E+02 0.124395E+00 0.150000E+02 0.101382E+00 0.160000E+02 0.793672E-01 0.170000E+02 0.669410E-01 0.180000E+02 0.529494E-01 0.190000E+02 0.423116E-01 0.200000E+02 0.344727E-01 0.210000E+02 0.293205E-01 0.220000E+02 0.227855E-01 0.230000E+02 0.200137E-01 0.240000E+02 0.166860E-01 0.250000E+02 0.142801E-01 0.260000E+02 0.113780E-01 0.270000E+02 0.972447E-02 0.280000E+02 0.832103E-02 0.290000E+02 0.705141E-02 0.300000E+02 0.598348E-02 0.310000E+02 0.509539E-02 0.320000E+02 0.424601E-02 0.330000E+02 0.370591E-02 0.340000E+02 0.317579E-02 0.350000E+02 0.279791E-02 0.360000E+02 0.237342E-02 0.370000E+02 0.202431E-02 0.380000E+02 0.178101E-02 0.390000E+02 0.152562E-02 0.400000E+02 0.131028E-02 0.410000E+02 0.116406E-02 0.420000E+02 0.102759E-02 0.430000E+02 0.887023E-03 0.440000E+02 0.785494E-03 0.450000E+02 0.689427E-03 0.460000E+02 0.604985E-03 0.470000E+02 0.539739E-03 0.480000E+02 0.477613E-03 0.490000E+02 0.435765E-03 0.500000E+02 0.388334E-03 0.510000E+02 0.351334E-03 0.520000E+02 0.319546E-03 0.530000E+02 0.297224E-03 0.540000E+02 0.274002E-03 0.550000E+02 0.257568E-03 0.560000E+02 0.243778E-03 0.570000E+02 0.227888E-03 0.580000E+02 0.215274E-03 0.590000E+02 0.195515E-03 0.600000E+02 0.177181E-03 0.610000E+02 0.158876E-03 0.620000E+02 0.141777E-03 0.630000E+02 0.130916E-03 at y+ = 75.1 k_z*delta E(t+*t+) 0.000000E+00 0.118899E+00 0.100000E+01 0.285297E+00 0.200000E+01 0.337129E+00 0.300000E+01 0.349289E+00 0.400000E+01 0.253820E+00 0.500000E+01 0.190920E+00 0.600000E+01 0.164534E+00 0.700000E+01 0.121222E+00 0.800000E+01 0.918037E-01 0.900000E+01 0.699691E-01 0.100000E+02 0.550630E-01 0.110000E+02 0.435525E-01 0.120000E+02 0.349109E-01 0.130000E+02 0.287886E-01 0.140000E+02 0.236994E-01 0.150000E+02 0.198830E-01 0.160000E+02 0.168526E-01 0.170000E+02 0.142028E-01 0.180000E+02 0.122394E-01 0.190000E+02 0.103238E-01 0.200000E+02 0.881832E-02 0.210000E+02 0.756741E-02 0.220000E+02 0.650654E-02 0.230000E+02 0.566215E-02 0.240000E+02 0.485690E-02 0.250000E+02 0.423057E-02 0.260000E+02 0.371636E-02 0.270000E+02 0.325126E-02 0.280000E+02 0.279563E-02 0.290000E+02 0.247932E-02 0.300000E+02 0.215769E-02 0.310000E+02 0.188973E-02 0.320000E+02 0.164625E-02 0.330000E+02 0.144982E-02 0.340000E+02 0.127635E-02 0.350000E+02 0.111784E-02 0.360000E+02 0.978592E-03 0.370000E+02 0.864736E-03 0.380000E+02 0.757873E-03 0.390000E+02 0.669567E-03 0.400000E+02 0.586122E-03 0.410000E+02 0.514227E-03 0.420000E+02 0.453641E-03 0.430000E+02 0.394793E-03 0.440000E+02 0.356468E-03 0.450000E+02 0.311792E-03 0.460000E+02 0.278326E-03 0.470000E+02 0.243890E-03 0.480000E+02 0.215258E-03 0.490000E+02 0.190864E-03 0.500000E+02 0.169933E-03 0.510000E+02 0.153100E-03 0.520000E+02 0.136859E-03 0.530000E+02 0.124274E-03 0.540000E+02 0.112184E-03 0.550000E+02 0.104373E-03 0.560000E+02 0.969618E-04 0.570000E+02 0.918180E-04 0.580000E+02 0.881702E-04 0.590000E+02 0.851740E-04 0.600000E+02 0.832077E-04 0.610000E+02 0.815620E-04 0.620000E+02 0.785868E-04 0.630000E+02 0.744503E-04 at y+ = 150 k_z*delta E(t+*t+) 0.000000E+00 0.918829E-01 0.100000E+01 0.173216E+00 0.200000E+01 0.144329E+00 0.300000E+01 0.103250E+00 0.400000E+01 0.731414E-01 0.500000E+01 0.526999E-01 0.600000E+01 0.396470E-01 0.700000E+01 0.292797E-01 0.800000E+01 0.225812E-01 0.900000E+01 0.177018E-01 0.100000E+02 0.137968E-01 0.110000E+02 0.109008E-01 0.120000E+02 0.881755E-02 0.130000E+02 0.708672E-02 0.140000E+02 0.577038E-02 0.150000E+02 0.474746E-02 0.160000E+02 0.382503E-02 0.170000E+02 0.323539E-02 0.180000E+02 0.269582E-02 0.190000E+02 0.223422E-02 0.200000E+02 0.187178E-02 0.210000E+02 0.155194E-02 0.220000E+02 0.130597E-02 0.230000E+02 0.110150E-02 0.240000E+02 0.916784E-03 0.250000E+02 0.790139E-03 0.260000E+02 0.657115E-03 0.270000E+02 0.556667E-03 0.280000E+02 0.467267E-03 0.290000E+02 0.391334E-03 0.300000E+02 0.336503E-03 0.310000E+02 0.283671E-03 0.320000E+02 0.242876E-03 0.330000E+02 0.204447E-03 0.340000E+02 0.172915E-03 0.350000E+02 0.146096E-03 0.360000E+02 0.124450E-03 0.370000E+02 0.104797E-03 0.380000E+02 0.907608E-04 0.390000E+02 0.769532E-04 0.400000E+02 0.652158E-04 0.410000E+02 0.560427E-04 0.420000E+02 0.477398E-04 0.430000E+02 0.406364E-04 0.440000E+02 0.343960E-04 0.450000E+02 0.296999E-04 0.460000E+02 0.250630E-04 0.470000E+02 0.217241E-04 0.480000E+02 0.184162E-04 0.490000E+02 0.159060E-04 0.500000E+02 0.137698E-04 0.510000E+02 0.119421E-04 0.520000E+02 0.102120E-04 0.530000E+02 0.885856E-05 0.540000E+02 0.769649E-05 0.550000E+02 0.680279E-05 0.560000E+02 0.605044E-05 0.570000E+02 0.551833E-05 0.580000E+02 0.509517E-05 0.590000E+02 0.480087E-05 0.600000E+02 0.461275E-05 0.610000E+02 0.438497E-05 0.620000E+02 0.425389E-05 0.630000E+02 0.393010E-05 4.4 Two-point Correlations at several points 4.4.1 Streamwise Separations at y+=5.1 x/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.122718E+00 0.966042E+00 0.245437E+00 0.889160E+00 0.368155E+00 0.800427E+00 0.490874E+00 0.715246E+00 0.613592E+00 0.639572E+00 0.736311E+00 0.573941E+00 0.859029E+00 0.517529E+00 0.981748E+00 0.468573E+00 0.110447E+01 0.425798E+00 0.122718E+01 0.388062E+00 0.134990E+01 0.354720E+00 0.147262E+01 0.325061E+00 0.159534E+01 0.298684E+00 0.171806E+01 0.275182E+00 0.184078E+01 0.254372E+00 0.196350E+01 0.235898E+00 0.208621E+01 0.219510E+00 0.220893E+01 0.204839E+00 0.233165E+01 0.191599E+00 0.245437E+01 0.179444E+00 0.257709E+01 0.168275E+00 0.269981E+01 0.157979E+00 0.282252E+01 0.148613E+00 0.294524E+01 0.140096E+00 0.306796E+01 0.132382E+00 0.319068E+01 0.125274E+00 0.331340E+01 0.118679E+00 0.343612E+01 0.112407E+00 0.355884E+01 0.106476E+00 0.368155E+01 0.100867E+00 0.380427E+01 0.956881E-01 0.392699E+01 0.908254E-01 0.404971E+01 0.861853E-01 0.417243E+01 0.815822E-01 0.429515E+01 0.770004E-01 0.441786E+01 0.723330E-01 0.454058E+01 0.676647E-01 0.466330E+01 0.630427E-01 0.478602E+01 0.586722E-01 0.490874E+01 0.545907E-01 0.503146E+01 0.508913E-01 0.515418E+01 0.474849E-01 0.527689E+01 0.443783E-01 0.539961E+01 0.414551E-01 0.552233E+01 0.387225E-01 0.564505E+01 0.360194E-01 0.576777E+01 0.333203E-01 0.589049E+01 0.305003E-01 0.601320E+01 0.275764E-01 0.613592E+01 0.244876E-01 0.625864E+01 0.213510E-01 0.638136E+01 0.181467E-01 0.650408E+01 0.149729E-01 0.662680E+01 0.117979E-01 0.674952E+01 0.874886E-02 0.687223E+01 0.583651E-02 0.699495E+01 0.317685E-02 0.711767E+01 0.746230E-03 0.724039E+01 -0.136517E-02 0.736311E+01 -0.317935E-02 0.748583E+01 -0.459813E-02 0.760854E+01 -0.568818E-02 0.773126E+01 -0.636257E-02 0.785398E+01 -0.662133E-02 at y+=12.7 x/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.122718E+00 0.952133E+00 0.245437E+00 0.857001E+00 0.368155E+00 0.758077E+00 0.490874E+00 0.670589E+00 0.613592E+00 0.597400E+00 0.736311E+00 0.536384E+00 0.859029E+00 0.485303E+00 0.981748E+00 0.441552E+00 0.110447E+01 0.403834E+00 0.122718E+01 0.370856E+00 0.134990E+01 0.342004E+00 0.147262E+01 0.316269E+00 0.159534E+01 0.293225E+00 0.171806E+01 0.272292E+00 0.184078E+01 0.253614E+00 0.196350E+01 0.236833E+00 0.208621E+01 0.221921E+00 0.220893E+01 0.208352E+00 0.233165E+01 0.196028E+00 0.245437E+01 0.184431E+00 0.257709E+01 0.173582E+00 0.269981E+01 0.163125E+00 0.282252E+01 0.153393E+00 0.294524E+01 0.144295E+00 0.306796E+01 0.136134E+00 0.319068E+01 0.128526E+00 0.331340E+01 0.121581E+00 0.343612E+01 0.114943E+00 0.355884E+01 0.108847E+00 0.368155E+01 0.103018E+00 0.380427E+01 0.976806E-01 0.392699E+01 0.924622E-01 0.404971E+01 0.875556E-01 0.417243E+01 0.827215E-01 0.429515E+01 0.782464E-01 0.441786E+01 0.738334E-01 0.454058E+01 0.698099E-01 0.466330E+01 0.658864E-01 0.478602E+01 0.623609E-01 0.490874E+01 0.588710E-01 0.503146E+01 0.556264E-01 0.515418E+01 0.523144E-01 0.527689E+01 0.492663E-01 0.539961E+01 0.462258E-01 0.552233E+01 0.435195E-01 0.564505E+01 0.407670E-01 0.576777E+01 0.381674E-01 0.589049E+01 0.353992E-01 0.601320E+01 0.327809E-01 0.613592E+01 0.300613E-01 0.625864E+01 0.275198E-01 0.638136E+01 0.248043E-01 0.650408E+01 0.222087E-01 0.662680E+01 0.194613E-01 0.674952E+01 0.169510E-01 0.687223E+01 0.144197E-01 0.699495E+01 0.121749E-01 0.711767E+01 0.992788E-02 0.724039E+01 0.800674E-02 0.736311E+01 0.613111E-02 0.748583E+01 0.473028E-02 0.760854E+01 0.357854E-02 0.773126E+01 0.302298E-02 0.785398E+01 0.274181E-02 at y+=75.0 x/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.122718E+00 0.812263E+00 0.245437E+00 0.599722E+00 0.368155E+00 0.447939E+00 0.490874E+00 0.348411E+00 0.613592E+00 0.283844E+00 0.736311E+00 0.239296E+00 0.859029E+00 0.208829E+00 0.981748E+00 0.182271E+00 0.110447E+01 0.161923E+00 0.122718E+01 0.143390E+00 0.134990E+01 0.130408E+00 0.147262E+01 0.117442E+00 0.159534E+01 0.108693E+00 0.171806E+01 0.997155E-01 0.184078E+01 0.954505E-01 0.196350E+01 0.907216E-01 0.208621E+01 0.891222E-01 0.220893E+01 0.855420E-01 0.233165E+01 0.843486E-01 0.245437E+01 0.810006E-01 0.257709E+01 0.801348E-01 0.269981E+01 0.772757E-01 0.282252E+01 0.767129E-01 0.294524E+01 0.734414E-01 0.306796E+01 0.709668E-01 0.319068E+01 0.656456E-01 0.331340E+01 0.632327E-01 0.343612E+01 0.602765E-01 0.355884E+01 0.609642E-01 0.368155E+01 0.592325E-01 0.380427E+01 0.595805E-01 0.392699E+01 0.584537E-01 0.404971E+01 0.601840E-01 0.417243E+01 0.593260E-01 0.429515E+01 0.602435E-01 0.441786E+01 0.587233E-01 0.454058E+01 0.588878E-01 0.466330E+01 0.561531E-01 0.478602E+01 0.551439E-01 0.490874E+01 0.526125E-01 0.503146E+01 0.523812E-01 0.515418E+01 0.488924E-01 0.527689E+01 0.469797E-01 0.539961E+01 0.440288E-01 0.552233E+01 0.437153E-01 0.564505E+01 0.405422E-01 0.576777E+01 0.388286E-01 0.589049E+01 0.349991E-01 0.601320E+01 0.346076E-01 0.613592E+01 0.333410E-01 0.625864E+01 0.342610E-01 0.638136E+01 0.322757E-01 0.650408E+01 0.326992E-01 0.662680E+01 0.312833E-01 0.674952E+01 0.321656E-01 0.687223E+01 0.305976E-01 0.699495E+01 0.323114E-01 0.711767E+01 0.329544E-01 0.724039E+01 0.366025E-01 0.736311E+01 0.370680E-01 0.748583E+01 0.385971E-01 0.760854E+01 0.364253E-01 0.773126E+01 0.362378E-01 0.785398E+01 0.343940E-01 at y+=150 x/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.122718E+00 0.809380E+00 0.245437E+00 0.577634E+00 0.368155E+00 0.422372E+00 0.490874E+00 0.316379E+00 0.613592E+00 0.252674E+00 0.736311E+00 0.206424E+00 0.859029E+00 0.175612E+00 0.981748E+00 0.148884E+00 0.110447E+01 0.130606E+00 0.122718E+01 0.115358E+00 0.134990E+01 0.106637E+00 0.147262E+01 0.974372E-01 0.159534E+01 0.909279E-01 0.171806E+01 0.843575E-01 0.184078E+01 0.817375E-01 0.196350E+01 0.780085E-01 0.208621E+01 0.750535E-01 0.220893E+01 0.703139E-01 0.233165E+01 0.676077E-01 0.245437E+01 0.637715E-01 0.257709E+01 0.620857E-01 0.269981E+01 0.599204E-01 0.282252E+01 0.592324E-01 0.294524E+01 0.553674E-01 0.306796E+01 0.525994E-01 0.319068E+01 0.489285E-01 0.331340E+01 0.464356E-01 0.343612E+01 0.436975E-01 0.355884E+01 0.433114E-01 0.368155E+01 0.424290E-01 0.380427E+01 0.430624E-01 0.392699E+01 0.424094E-01 0.404971E+01 0.424527E-01 0.417243E+01 0.398345E-01 0.429515E+01 0.376198E-01 0.441786E+01 0.336928E-01 0.454058E+01 0.311249E-01 0.466330E+01 0.281806E-01 0.478602E+01 0.286526E-01 0.490874E+01 0.284175E-01 0.503146E+01 0.292805E-01 0.515418E+01 0.283919E-01 0.527689E+01 0.287671E-01 0.539961E+01 0.284567E-01 0.552233E+01 0.303055E-01 0.564505E+01 0.306735E-01 0.576777E+01 0.314344E-01 0.589049E+01 0.308221E-01 0.601320E+01 0.321981E-01 0.613592E+01 0.328868E-01 0.625864E+01 0.354472E-01 0.638136E+01 0.373434E-01 0.650408E+01 0.397814E-01 0.662680E+01 0.391272E-01 0.674952E+01 0.381449E-01 0.687223E+01 0.348306E-01 0.699495E+01 0.324264E-01 0.711767E+01 0.289072E-01 0.724039E+01 0.267396E-01 0.736311E+01 0.224631E-01 0.748583E+01 0.183352E-01 0.760854E+01 0.130389E-01 0.773126E+01 0.112739E-01 0.785398E+01 0.986830E-02 4.4.2 Spanwise Separations at y+=5.1 z/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.490874E-01 0.883942E+00 0.981748E-01 0.613221E+00 0.147262E+00 0.317998E+00 0.196350E+00 0.773222E-01 0.245437E+00 -0.845988E-01 0.294524E+00 -0.173685E+00 0.343612E+00 -0.206521E+00 0.392699E+00 -0.201786E+00 0.441786E+00 -0.175240E+00 0.490874E+00 -0.138937E+00 0.539961E+00 -0.100510E+00 0.589049E+00 -0.644667E-01 0.638136E+00 -0.330226E-01 0.687223E+00 -0.763806E-02 0.736311E+00 0.110738E-01 0.785398E+00 0.233528E-01 0.834486E+00 0.304056E-01 0.883573E+00 0.335370E-01 0.932660E+00 0.335727E-01 0.981748E+00 0.304192E-01 0.103084E+01 0.238523E-01 0.107992E+01 0.140656E-01 0.112901E+01 0.201328E-02 0.117810E+01 -0.110988E-01 0.122718E+01 -0.238918E-01 0.127627E+01 -0.348608E-01 0.132536E+01 -0.423908E-01 0.137445E+01 -0.454539E-01 0.142353E+01 -0.438539E-01 0.147262E+01 -0.384358E-01 0.152171E+01 -0.304938E-01 0.157080E+01 -0.214296E-01 0.161988E+01 -0.122200E-01 0.166897E+01 -0.373980E-02 0.171806E+01 0.312340E-02 0.176715E+01 0.740717E-02 0.181623E+01 0.877022E-02 0.186532E+01 0.801482E-02 0.191441E+01 0.720260E-02 0.196350E+01 0.829573E-02 0.201258E+01 0.123285E-01 0.206167E+01 0.188517E-01 0.211076E+01 0.262194E-01 0.215984E+01 0.321258E-01 0.220893E+01 0.345942E-01 0.225802E+01 0.323977E-01 0.230711E+01 0.254463E-01 0.235619E+01 0.144980E-01 0.240528E+01 0.880947E-03 0.245437E+01 -0.139918E-01 0.250346E+01 -0.283029E-01 0.255254E+01 -0.399523E-01 0.260163E+01 -0.470203E-01 0.265072E+01 -0.485892E-01 0.269981E+01 -0.446849E-01 0.274889E+01 -0.361501E-01 0.279798E+01 -0.241263E-01 0.284707E+01 -0.100956E-01 0.289616E+01 0.433840E-02 0.294524E+01 0.174775E-01 0.299433E+01 0.279551E-01 0.304342E+01 0.348907E-01 0.309251E+01 0.384675E-01 0.314159E+01 0.394832E-01 at y+=12.7 z/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.490874E-01 0.888381E+00 0.981748E-01 0.631670E+00 0.147262E+00 0.348774E+00 0.196350E+00 0.108690E+00 0.245437E+00 -0.640257E-01 0.294524E+00 -0.169636E+00 0.343612E+00 -0.218964E+00 0.392699E+00 -0.227237E+00 0.441786E+00 -0.208603E+00 0.490874E+00 -0.175389E+00 0.539961E+00 -0.136110E+00 0.589049E+00 -0.967517E-01 0.638136E+00 -0.605257E-01 0.687223E+00 -0.296098E-01 0.736311E+00 -0.496468E-02 0.785398E+00 0.129910E-01 0.834486E+00 0.247967E-01 0.883573E+00 0.310441E-01 0.932660E+00 0.325423E-01 0.981748E+00 0.297574E-01 0.103084E+01 0.230255E-01 0.107992E+01 0.125510E-01 0.112901E+01 -0.537210E-03 0.117810E+01 -0.146242E-01 0.122718E+01 -0.278461E-01 0.127627E+01 -0.389031E-01 0.132536E+01 -0.466024E-01 0.137445E+01 -0.501442E-01 0.142353E+01 -0.490627E-01 0.147262E+01 -0.439896E-01 0.152171E+01 -0.360633E-01 0.157080E+01 -0.267462E-01 0.161988E+01 -0.170189E-01 0.166897E+01 -0.779657E-02 0.171806E+01 0.372330E-03 0.176715E+01 0.681203E-02 0.181623E+01 0.112273E-01 0.186532E+01 0.138664E-01 0.191441E+01 0.159982E-01 0.196350E+01 0.187172E-01 0.201258E+01 0.225908E-01 0.206167E+01 0.270948E-01 0.211076E+01 0.311910E-01 0.215984E+01 0.333794E-01 0.220893E+01 0.326212E-01 0.225802E+01 0.281598E-01 0.230711E+01 0.199021E-01 0.235619E+01 0.821262E-02 0.240528E+01 -0.579637E-02 0.245437E+01 -0.209077E-01 0.250346E+01 -0.353595E-01 0.255254E+01 -0.472285E-01 0.260163E+01 -0.544858E-01 0.265072E+01 -0.560670E-01 0.269981E+01 -0.517773E-01 0.274889E+01 -0.424583E-01 0.279798E+01 -0.291893E-01 0.284707E+01 -0.136080E-01 0.289616E+01 0.261117E-02 0.294524E+01 0.175102E-01 0.299433E+01 0.294999E-01 0.304342E+01 0.375376E-01 0.309251E+01 0.418433E-01 0.314159E+01 0.430967E-01 at y+=75.0 z/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.490874E-01 0.935618E+00 0.981748E-01 0.795857E+00 0.147262E+00 0.645897E+00 0.196350E+00 0.508998E+00 0.245437E+00 0.389635E+00 0.294524E+00 0.288195E+00 0.343612E+00 0.203699E+00 0.392699E+00 0.134603E+00 0.441786E+00 0.793528E-01 0.490874E+00 0.361487E-01 0.539961E+00 0.343359E-02 0.589049E+00 -0.207174E-01 0.638136E+00 -0.379101E-01 0.687223E+00 -0.499935E-01 0.736311E+00 -0.582100E-01 0.785398E+00 -0.637210E-01 0.834486E+00 -0.671103E-01 0.883573E+00 -0.690966E-01 0.932660E+00 -0.699205E-01 0.981748E+00 -0.700539E-01 0.103084E+01 -0.695652E-01 0.107992E+01 -0.686876E-01 0.112901E+01 -0.673410E-01 0.117810E+01 -0.656415E-01 0.122718E+01 -0.633479E-01 0.127627E+01 -0.605347E-01 0.132536E+01 -0.570154E-01 0.137445E+01 -0.529146E-01 0.142353E+01 -0.481517E-01 0.147262E+01 -0.429369E-01 0.152171E+01 -0.371813E-01 0.157080E+01 -0.310535E-01 0.161988E+01 -0.245527E-01 0.166897E+01 -0.180683E-01 0.171806E+01 -0.117424E-01 0.176715E+01 -0.586653E-02 0.181623E+01 -0.419420E-03 0.186532E+01 0.430133E-02 0.191441E+01 0.823901E-02 0.196350E+01 0.111629E-01 0.201258E+01 0.131903E-01 0.206167E+01 0.142384E-01 0.211076E+01 0.144775E-01 0.215984E+01 0.138345E-01 0.220893E+01 0.125539E-01 0.225802E+01 0.106944E-01 0.230711E+01 0.853500E-02 0.235619E+01 0.604647E-02 0.240528E+01 0.339580E-02 0.245437E+01 0.529233E-03 0.250346E+01 -0.223487E-02 0.255254E+01 -0.480625E-02 0.260163E+01 -0.692180E-02 0.265072E+01 -0.859491E-02 0.269981E+01 -0.964060E-02 0.274889E+01 -0.102718E-01 0.279798E+01 -0.104762E-01 0.284707E+01 -0.104746E-01 0.289616E+01 -0.102269E-01 0.294524E+01 -0.986308E-02 0.299433E+01 -0.933532E-02 0.304342E+01 -0.893973E-02 0.309251E+01 -0.864663E-02 0.314159E+01 -0.859284E-02 at y+=150.0 z/delta R(tt) (separation) 0.000000E+00 0.100000E+01 0.490874E-01 0.960221E+00 0.981748E-01 0.865467E+00 0.147262E+00 0.754888E+00 0.196350E+00 0.649504E+00 0.245437E+00 0.555621E+00 0.294524E+00 0.473911E+00 0.343612E+00 0.403456E+00 0.392699E+00 0.343002E+00 0.441786E+00 0.291275E+00 0.490874E+00 0.247047E+00 0.539961E+00 0.209235E+00 0.589049E+00 0.176848E+00 0.638136E+00 0.149068E+00 0.687223E+00 0.125184E+00 0.736311E+00 0.104661E+00 0.785398E+00 0.869942E-01 0.834486E+00 0.718464E-01 0.883573E+00 0.589075E-01 0.932660E+00 0.478964E-01 0.981748E+00 0.384564E-01 0.103084E+01 0.303378E-01 0.107992E+01 0.233724E-01 0.112901E+01 0.174941E-01 0.117810E+01 0.125744E-01 0.122718E+01 0.850207E-02 0.127627E+01 0.512405E-02 0.132536E+01 0.233846E-02 0.137445E+01 0.339333E-05 0.142353E+01 -0.195650E-02 0.147262E+01 -0.360554E-02 0.152171E+01 -0.492234E-02 0.157080E+01 -0.589935E-02 0.161988E+01 -0.651537E-02 0.166897E+01 -0.683588E-02 0.171806E+01 -0.689739E-02 0.176715E+01 -0.676840E-02 0.181623E+01 -0.646838E-02 0.186532E+01 -0.603401E-02 0.191441E+01 -0.545622E-02 0.196350E+01 -0.479384E-02 0.201258E+01 -0.409539E-02 0.206167E+01 -0.344471E-02 0.211076E+01 -0.288699E-02 0.215984E+01 -0.249492E-02 0.220893E+01 -0.225406E-02 0.225802E+01 -0.214947E-02 0.230711E+01 -0.209615E-02 0.235619E+01 -0.200440E-02 0.240528E+01 -0.176246E-02 0.245437E+01 -0.139773E-02 0.250346E+01 -0.992570E-03 0.255254E+01 -0.651357E-03 0.260163E+01 -0.342013E-03 0.265072E+01 -0.885667E-05 0.269981E+01 0.416693E-03 0.274889E+01 0.908883E-03 0.279798E+01 0.144290E-02 0.284707E+01 0.197812E-02 0.289616E+01 0.252768E-02 0.294524E+01 0.302344E-02 0.299433E+01 0.340755E-02 0.304342E+01 0.364454E-02 0.309251E+01 0.377625E-02 0.314159E+01 0.381006E-02 5. References 5.1 Tomita, Y., Kasagi, N., and Kuroda, A., "Direct Numerical Simulation of Turbulent Heat Transfer in a Two-Dimensional Channel," Proc. of Computational Fluid Dynamics Symposium, 1989, pp. 415-418. 5.2 Tomita, Y., Kasagi, N., and Kuroda, A., "Investigation of Turbulent Heat Flux Budget on the Wall Turbulence via Direct Numerical Simulation," Proc. of 27th National Heat Transfer Symposium of Japan, Nagoya, 1990, pp. 49-51. 5.3 Kasagi, N., Tomita, Y., and Kuroda, A., "Direct Numerical Simulation of the Passive Scalar Field in a Two-Dimensional Turbulent Channel Flow," Proc. of 3rd ASME/JSME Thermal Enginnering Joint Conference, Reno, 1991, Vol. 3, pp. 175-182. 5.4 Kasagi, N., Tomita, Y., and Kuroda, A., "Direct Numerical Simulation of Passive Scalar Field in a Turbulent Channel Flow," ASME J. Heat Transfer, Vol. 114, 1992, pp. 598-606. (EOF)