******************************************************************************* ******************************************************************************* ********** *********** ********** "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: Homogeneous Isotropic Flow with a Mean Temperature Gradient Code Number: IS__2_UT.HM1 Date of Release: March 1, 1992 Computors: O. Iida and N. Kasagi Department of Mechanical Engineering The University of Tokyo Bunkyo-ku, Tokyo 113 Nomenclature D = dissipation for K D_ij = (i,j) component of dissipation tensor D_tt = dissipation of tt D_vt = dissipation of vt E(k) = 3 dimensional spectral distribution of turbulent kinetic energy E_tt(k) = 3 dimensional spectral distribution of tt E_ii(k_1) = 1 dimensional spectral distribution of (i,i) component of Reynolds stress tensor E_tt(k_1) = 1 dimensional spectral distribution of tt K = turbulent kinetic energy (1/2(u**2+v**2+w**2)) k = 3 dimensional wave number ((k_1**2+k_2**2+k_3**2)**1/2) k_i = wave number in the i_th direction Lamda_ii(x1)= integral scale of u_i component (2*pi*E_ii(k_1 = 0)/(u_i**2)) Lamda_tt(x1)= integral scale of t (2*pi*E_tt(k_1 = 0)/(u_i**2)) OMG_ij = (i,j) component of vorticity tensor P_tt = production of tt P_vt = production of vt phi_vt = pressure temperature gradient correlation of vt Pr= Prandtl number PS_ij = (i,j) component of pressure strain tensor R_ii(x1) = two point correlation coefficient of u_i R_tt(x1) = two point correlation coefficient of t Re_t= turbulent Reynolds number (K**2/D/Ve) RS_ij = (i,j) component of Reynolds stress tensor St = mean temperature gradient in the y direction t = temperature fluctuation tt = temperature fluctuation covariance (t**2) tau= non-dimensional time u_i = i-th component of velocity fluctuation u, v, w = velocity fluctuations in the x-, y- and z-directions vt = turbulent heat flux in the y direction Ve = Nondimensional kinematic viscosity x, y, z = x_1, x_2 and x_3 directions 1. Description of Flow Field The flow field simulated is homogeneus isotropic turbulence with scalar transport. A linear mean temperature gradient is imposed in the x_2 (y) direction. Four simulations have been carried out at the Prandtl numbers of 0.20, 0.71 and 1.5 without initial temperature fluctuations and at the Prandtl number of 0.71 with initial temperature fluctuations. 2. Numerical Method Governing equations: three-dimensional Navier-Stokes equations (rotational form) and the energy conservation equation. Discretization method: spectral method = 96 x 96 x 96 Fourier series. Aliasing treatment: nonlinear terms computed with collocation grids 1.5 times finer in each direction. Time integration: second order Adams-Bashforth for the nonlinear terms and Crank-Nicolson for the diffusion terms. Size of computational box: 2*pai x 2*pi x 2*pi. Initial spectral distribution: E(k) = (0.49/5.0**2) * k * exp(-k/5.0) with Et(k) = (0.49/5.0**2) * k * exp(-k/5.0) or Et(k) = 0. Error in continuity equation: not applicable. Computer: HITAC-S820/80 at the Computer Center of the University of Tokyo. Computation time: 2.5 sec CPU time per one time step. 3. Flow Conditions Ve = 1/300 Pr = 0.2, 0.71, 1.5 St = -1.0 4. Numerical Data 4.1 Velocity Field 4.1.1 Reynolds Strss Tensor tau RS_11 RS_22 RS_33 0.200000E+00 0.261687E+00 0.263467E+00 0.276813E+00 0.400000E+00 0.219159E+00 0.217766E+00 0.225315E+00 0.600000E+00 0.185595E+00 0.182805E+00 0.186819E+00 0.800000E+00 0.159147E+00 0.156073E+00 0.158170E+00 0.100000E+01 0.138021E+00 0.135236E+00 0.136513E+00 0.120000E+01 0.121267E+00 0.118613E+00 0.119440E+00 0.140000E+01 0.107901E+00 0.105073E+00 0.105534E+00 0.160000E+01 0.970981E-01 0.938294E-01 0.940699E-01 0.180000E+01 0.881949E-01 0.843484E-01 0.846045E-01 0.200000E+01 0.806688E-01 0.763056E-01 0.767590E-01 0.220000E+01 0.741865E-01 0.694457E-01 0.701972E-01 0.240000E+01 0.685298E-01 0.635411E-01 0.646676E-01 0.260000E+01 0.635417E-01 0.584201E-01 0.599720E-01 0.280000E+01 0.591052E-01 0.539546E-01 0.559545E-01 0.300000E+01 0.551463E-01 0.500393E-01 0.524798E-01 0.320000E+01 0.516197E-01 0.465907E-01 0.494244E-01 0.340000E+01 0.484823E-01 0.435484E-01 0.466884E-01 0.360000E+01 0.456883E-01 0.408608E-01 0.442030E-01 0.380000E+01 0.431952E-01 0.384766E-01 0.419255E-01 0.400000E+01 0.409631E-01 0.363499E-01 0.398291E-01 0.420000E+01 0.389530E-01 0.344453E-01 0.378952E-01 0.440000E+01 0.371296E-01 0.327350E-01 0.361091E-01 0.460000E+01 0.354639E-01 0.311934E-01 0.344590E-01 0.480000E+01 0.339335E-01 0.297961E-01 0.329355E-01 0.500000E+01 0.325201E-01 0.285212E-01 0.315315E-01 0.520000E+01 0.312086E-01 0.273497E-01 0.302407E-01 0.540000E+01 0.299870E-01 0.262663E-01 0.290564E-01 tau RS_12 RS_13 RS_23 0.200000E+00 0.199526E-02 -0.422021E-02 -0.524566E-02 0.400000E+00 0.122202E-02 -0.392306E-02 -0.522052E-02 0.600000E+00 0.122219E-02 -0.416557E-02 -0.524015E-02 0.800000E+00 0.156897E-02 -0.439465E-02 -0.518171E-02 0.100000E+01 0.165979E-02 -0.443364E-02 -0.492557E-02 0.120000E+01 0.143764E-02 -0.402277E-02 -0.446787E-02 0.140000E+01 0.119364E-02 -0.329882E-02 -0.400776E-02 0.160000E+01 0.111608E-02 -0.257034E-02 -0.361250E-02 0.180000E+01 0.118338E-02 -0.199530E-02 -0.329726E-02 0.200000E+01 0.124852E-02 -0.159871E-02 -0.303494E-02 0.220000E+01 0.122711E-02 -0.135944E-02 -0.277689E-02 0.240000E+01 0.113994E-02 -0.124581E-02 -0.251295E-02 0.260000E+01 0.104770E-02 -0.122017E-02 -0.224665E-02 0.280000E+01 0.992352E-03 -0.124166E-02 -0.197799E-02 0.300000E+01 0.983273E-03 -0.126821E-02 -0.170324E-02 0.320000E+01 0.101256E-02 -0.126865E-02 -0.142523E-02 0.340000E+01 0.106638E-02 -0.123053E-02 -0.115684E-02 0.360000E+01 0.113061E-02 -0.115762E-02 -0.913231E-03 0.380000E+01 0.119521E-02 -0.106231E-02 -0.704009E-03 0.400000E+01 0.125563E-02 -0.957265E-03 -0.530874E-03 0.420000E+01 0.130942E-02 -0.849450E-03 -0.389799E-03 0.440000E+01 0.135372E-02 -0.739082E-03 -0.274872E-03 0.460000E+01 0.138724E-02 -0.623606E-03 -0.180939E-03 0.480000E+01 0.141150E-02 -0.502815E-03 -0.104463E-03 0.500000E+01 0.142946E-02 -0.380662E-03 -0.430576E-04 0.520000E+01 0.144354E-02 -0.263459E-03 0.529697E-05 0.540000E+01 0.145503E-02 -0.157147E-03 0.425650E-04 4.1.2 Dissipation Tensor tau D_11 D_22 D_33 0.200000E+00 0.249996E+00 0.261060E+00 0.271686E+00 0.400000E+00 0.199072E+00 0.203043E+00 0.209879E+00 0.600000E+00 0.152792E+00 0.153978E+00 0.158452E+00 0.800000E+00 0.118936E+00 0.118414E+00 0.121379E+00 0.100000E+01 0.935653E-01 0.931292E-01 0.948741E-01 0.120000E+01 0.747176E-01 0.750269E-01 0.760343E-01 0.140000E+01 0.606897E-01 0.614208E-01 0.620867E-01 0.160000E+01 0.500138E-01 0.508780E-01 0.513293E-01 0.180000E+01 0.418309E-01 0.426116E-01 0.428258E-01 0.200000E+01 0.354537E-01 0.360915E-01 0.360803E-01 0.220000E+01 0.303529E-01 0.308893E-01 0.307377E-01 0.240000E+01 0.262101E-01 0.266659E-01 0.264801E-01 0.260000E+01 0.228044E-01 0.231816E-01 0.230290E-01 0.280000E+01 0.199709E-01 0.202748E-01 0.201890E-01 0.300000E+01 0.175848E-01 0.178334E-01 0.178413E-01 0.320000E+01 0.155573E-01 0.157695E-01 0.158851E-01 0.340000E+01 0.138279E-01 0.140197E-01 0.142325E-01 0.360000E+01 0.123473E-01 0.125350E-01 0.128185E-01 0.380000E+01 0.110753E-01 0.112684E-01 0.115958E-01 0.400000E+01 0.998415E-02 0.101747E-01 0.105291E-01 0.420000E+01 0.904989E-02 0.921986E-02 0.959111E-02 0.440000E+01 0.824805E-02 0.838375E-02 0.876014E-02 0.460000E+01 0.755521E-02 0.765262E-02 0.801994E-02 0.480000E+01 0.695037E-02 0.701408E-02 0.735751E-02 0.500000E+01 0.641652E-02 0.645511E-02 0.676254E-02 0.520000E+01 0.594084E-02 0.596250E-02 0.622778E-02 0.540000E+01 0.551337E-02 0.552427E-02 0.574843E-02 tau D_12 D_13 D_23 0.200000E+00 0.367780E-04 -0.672225E-03 -0.438978E-03 0.400000E+00 -0.121439E-02 -0.241433E-04 0.685364E-04 0.600000E+00 -0.148445E-02 -0.338171E-03 0.984568E-04 0.800000E+00 -0.103619E-02 -0.532345E-03 -0.291972E-03 0.100000E+01 -0.366484E-03 -0.865936E-03 -0.621889E-03 0.120000E+01 -0.106644E-03 -0.980936E-03 -0.548031E-03 0.140000E+01 0.331775E-05 -0.774036E-03 -0.374044E-03 0.160000E+01 -0.415909E-05 -0.462679E-03 -0.219518E-03 0.180000E+01 -0.112094E-05 -0.237239E-03 -0.798893E-04 0.200000E+01 0.538337E-04 -0.910946E-04 -0.352153E-04 0.220000E+01 0.759313E-04 0.227766E-04 -0.549091E-04 0.240000E+01 0.496573E-04 0.939006E-04 -0.100141E-03 0.260000E+01 -0.743018E-05 0.123483E-03 -0.142218E-03 0.280000E+01 -0.722579E-04 0.112130E-03 -0.180166E-03 0.300000E+01 -0.119060E-03 0.673641E-04 -0.204702E-03 0.320000E+01 -0.132175E-03 0.122238E-04 -0.201597E-03 0.340000E+01 -0.118602E-03 -0.325093E-04 -0.171177E-03 0.360000E+01 -0.952656E-04 -0.593819E-04 -0.125641E-03 0.380000E+01 -0.730218E-04 -0.696739E-04 -0.770806E-04 0.400000E+01 -0.521350E-04 -0.708958E-04 -0.336750E-04 0.420000E+01 -0.302417E-04 -0.719132E-04 0.774076E-06 0.440000E+01 -0.911680E-05 -0.761141E-04 0.262669E-04 0.460000E+01 0.725113E-05 -0.808438E-04 0.442540E-04 0.480000E+01 0.168501E-04 -0.820292E-04 0.555130E-04 0.500000E+01 0.204528E-04 -0.776301E-04 0.602605E-04 0.520000E+01 0.201625E-04 -0.683582E-04 0.596721E-04 0.540000E+01 0.177324E-04 -0.565762E-04 0.561696E-04 4.1.3 Pressure Strain Correlation tau PS_11 PS_22 PS_33 0.200000E+00 0.172558E-01 0.302844E-02 -0.202843E-01 0.400000E+00 0.939482E-02 0.351463E-02 -0.129095E-01 0.600000E+00 0.519819E-02 0.184303E-02 -0.704121E-02 0.800000E+00 0.804931E-03 0.128977E-02 -0.209470E-02 0.100000E+01 -0.252345E-03 0.633174E-03 -0.380829E-03 0.120000E+01 0.184956E-03 0.424385E-03 -0.609341E-03 0.140000E+01 0.842281E-03 0.449244E-04 -0.887205E-03 0.160000E+01 0.123894E-02 -0.564298E-03 -0.674640E-03 0.180000E+01 0.109583E-02 -0.960953E-03 -0.134875E-03 0.200000E+01 0.642973E-03 -0.947676E-03 0.304703E-03 0.220000E+01 0.157351E-03 -0.846833E-03 0.689482E-03 0.240000E+01 -0.286335E-03 -0.771004E-03 0.105734E-02 0.260000E+01 -0.673728E-03 -0.683199E-03 0.135693E-02 0.280000E+01 -0.970638E-03 -0.591345E-03 0.156198E-02 0.300000E+01 -0.109332E-02 -0.514000E-03 0.160732E-02 0.320000E+01 -0.106304E-02 -0.411275E-03 0.147431E-02 0.340000E+01 -0.962391E-03 -0.261180E-03 0.122357E-02 0.360000E+01 -0.836704E-03 -0.101976E-03 0.938680E-03 0.380000E+01 -0.704832E-03 0.256347E-04 0.679198E-03 0.400000E+01 -0.589292E-03 0.121727E-03 0.467565E-03 0.420000E+01 -0.506526E-03 0.204103E-03 0.302423E-03 0.440000E+01 -0.452804E-03 0.274372E-03 0.178432E-03 0.460000E+01 -0.417362E-03 0.324779E-03 0.925837E-04 0.480000E+01 -0.394632E-03 0.350944E-03 0.436880E-04 0.500000E+01 -0.383758E-03 0.353632E-03 0.301257E-04 0.520000E+01 -0.382784E-03 0.337037E-03 0.457472E-04 0.540000E+01 -0.386045E-03 0.307145E-03 0.788998E-04 tau PS_12 PS_13 PS_23 0.200000E+00 -0.541541E-02 0.376175E-02 0.975906E-03 0.400000E+00 -0.297312E-02 -0.282849E-03 -0.330867E-03 0.600000E+00 0.883313E-04 -0.176782E-02 0.222412E-03 0.800000E+00 0.420558E-03 -0.143165E-02 0.362753E-03 0.100000E+01 -0.856349E-03 -0.618079E-04 0.132623E-02 0.120000E+01 -0.151601E-02 0.210528E-02 0.189695E-02 0.140000E+01 -0.890589E-03 0.306470E-02 0.176473E-02 0.160000E+01 0.544672E-04 0.286898E-02 0.157483E-02 0.180000E+01 0.448807E-03 0.218653E-02 0.130169E-02 0.200000E+01 0.184012E-03 0.148301E-02 0.123551E-02 0.220000E+01 -0.238029E-03 0.878528E-03 0.124482E-02 0.240000E+01 -0.449015E-03 0.414352E-03 0.122572E-02 0.260000E+01 -0.398998E-03 0.995214E-04 0.119136E-02 0.280000E+01 -0.236126E-03 -0.408321E-04 0.117651E-02 0.300000E+01 -0.634778E-04 -0.208950E-04 0.118495E-02 0.320000E+01 0.828245E-04 0.100723E-03 0.117882E-02 0.340000E+01 0.182669E-03 0.249929E-03 0.112146E-02 0.360000E+01 0.228514E-03 0.370416E-03 0.101276E-02 0.380000E+01 0.237746E-03 0.438646E-03 0.878795E-03 0.400000E+01 0.231918E-03 0.463500E-03 0.748567E-03 0.420000E+01 0.213846E-03 0.471788E-03 0.637244E-03 0.440000E+01 0.182388E-03 0.487228E-03 0.546157E-03 0.460000E+01 0.147008E-03 0.512419E-03 0.469397E-03 0.480000E+01 0.117841E-03 0.531575E-03 0.400000E-03 0.500000E+01 0.972940E-04 0.528313E-03 0.334519E-03 0.520000E+01 0.820858E-04 0.497179E-03 0.273541E-03 0.540000E+01 0.688256E-04 0.442944E-03 0.219202E-03 4.1.4 Vorticity Tensor tau OMG_11 OMG_22 OMG_33 0.200000E+00 0.402989E+02 0.393717E+02 0.377406E+02 0.400000E+00 0.308416E+02 0.309436E+02 0.300139E+02 0.600000E+00 0.232461E+02 0.234997E+02 0.230375E+02 0.800000E+00 0.178469E+02 0.181294E+02 0.178330E+02 0.100000E+01 0.140232E+02 0.142202E+02 0.139919E+02 0.120000E+01 0.112708E+02 0.113823E+02 0.112137E+02 0.140000E+01 0.920671E+01 0.926589E+01 0.915697E+01 0.160000E+01 0.762876E+01 0.763296E+01 0.757145E+01 0.180000E+01 0.639209E+01 0.635509E+01 0.634307E+01 0.200000E+01 0.540834E+01 0.535054E+01 0.538494E+01 0.220000E+01 0.462329E+01 0.455887E+01 0.461482E+01 0.240000E+01 0.399073E+01 0.392706E+01 0.398562E+01 0.260000E+01 0.347279E+01 0.341209E+01 0.346736E+01 0.280000E+01 0.304205E+01 0.298652E+01 0.303663E+01 0.300000E+01 0.268114E+01 0.263195E+01 0.267583E+01 0.320000E+01 0.237835E+01 0.233225E+01 0.237118E+01 0.340000E+01 0.212370E+01 0.207562E+01 0.211271E+01 0.360000E+01 0.190772E+01 0.185503E+01 0.189238E+01 0.380000E+01 0.172203E+01 0.166562E+01 0.170328E+01 0.400000E+01 0.156012E+01 0.150305E+01 0.154002E+01 0.420000E+01 0.141768E+01 0.136292E+01 0.139852E+01 0.440000E+01 0.129185E+01 0.124135E+01 0.127559E+01 0.460000E+01 0.118037E+01 0.113530E+01 0.116850E+01 0.480000E+01 0.108128E+01 0.104224E+01 0.107477E+01 0.500000E+01 0.992939E+00 0.960075E+00 0.992113E+00 0.520000E+01 0.914106E+00 0.887046E+00 0.918517E+00 tau OMG_12 OMG_13 OMG_23 0.200000E+00 0.121262E+00 0.718921E-01 0.961702E-01 0.400000E+00 0.119772E+00 -0.134112E+00 -0.528899E-01 0.600000E+00 0.887430E-01 -0.101413E+00 -0.652585E-01 0.800000E+00 0.121369E+00 -0.733911E-01 -0.308450E-01 0.100000E+01 0.813011E-01 -0.420279E-01 0.218231E-01 0.120000E+01 0.348209E-01 -0.419913E-01 0.479465E-01 0.140000E+01 -0.736839E-02 -0.640368E-01 0.771447E-01 0.160000E+01 -0.276412E-01 -0.770727E-01 0.881196E-01 0.180000E+01 -0.338122E-01 -0.730408E-01 0.767024E-01 0.200000E+01 -0.348214E-01 -0.640502E-01 0.563890E-01 0.220000E+01 -0.373411E-01 -0.563587E-01 0.389518E-01 0.240000E+01 -0.423883E-01 -0.506911E-01 0.297666E-01 0.260000E+01 -0.469016E-01 -0.443681E-01 0.263887E-01 0.280000E+01 -0.482908E-01 -0.349419E-01 0.268828E-01 0.300000E+01 -0.483670E-01 -0.236175E-01 0.283968E-01 0.320000E+01 -0.495733E-01 -0.135285E-01 0.290012E-01 0.340000E+01 -0.515501E-01 -0.659464E-02 0.283705E-01 0.360000E+01 -0.529951E-01 -0.308477E-02 0.268470E-01 0.380000E+01 -0.531841E-01 -0.236282E-02 0.247527E-01 0.400000E+01 -0.520572E-01 -0.330874E-02 0.223187E-01 0.420000E+01 -0.498973E-01 -0.454234E-02 0.196558E-01 0.440000E+01 -0.470376E-01 -0.516008E-02 0.168670E-01 0.460000E+01 -0.437402E-01 -0.504913E-02 0.141684E-01 0.480000E+01 -0.402674E-01 -0.441651E-02 0.118918E-01 0.500000E+01 -0.368841E-01 -0.347075E-02 0.103038E-01 0.520000E+01 -0.338119E-01 -0.241455E-02 0.937357E-02 0.540000E+01 -0.311846E-01 -0.141373E-02 0.881425E-02 4.1.5 Skewness Factor of du/dx tau SF du/dx 0.200000E+00 -0.465077E+00 0.400000E+00 -0.464715E+00 0.600000E+00 -0.469586E+00 0.800000E+00 -0.495606E+00 0.100000E+01 -0.502174E+00 0.120000E+01 -0.501206E+00 0.140000E+01 -0.507355E+00 0.160000E+01 -0.504072E+00 0.180000E+01 -0.501976E+00 0.200000E+01 -0.498927E+00 0.220000E+01 -0.490696E+00 0.240000E+01 -0.487916E+00 0.260000E+01 -0.489835E+00 0.280000E+01 -0.496655E+00 0.300000E+01 -0.510955E+00 0.320000E+01 -0.529905E+00 0.340000E+01 -0.547139E+00 0.360000E+01 -0.559776E+00 0.380000E+01 -0.567015E+00 0.400000E+01 -0.569112E+00 0.420000E+01 -0.568033E+00 0.440000E+01 -0.563190E+00 0.460000E+01 -0.552583E+00 0.480000E+01 -0.536680E+00 0.500000E+01 -0.519280E+00 0.520000E+01 -0.505168E+00 0.540000E+01 -0.496848E+00 4.1.6 Budget of Turbulent Kinetic Energy tau K D 0.200000E+00 0.400983E+00 0.391371E+00 0.400000E+00 0.331120E+00 0.305997E+00 0.600000E+00 0.277609E+00 0.232611E+00 0.800000E+00 0.236695E+00 0.179364E+00 0.100000E+01 0.204885E+00 0.140784E+00 0.120000E+01 0.179660E+00 0.112889E+00 0.140000E+01 0.159254E+00 0.920986E-01 0.160000E+01 0.142499E+00 0.761106E-01 0.180000E+01 0.128574E+00 0.636341E-01 0.200000E+01 0.116867E+00 0.538127E-01 0.220000E+01 0.106915E+00 0.459899E-01 0.240000E+01 0.983692E-01 0.396781E-01 0.260000E+01 0.909669E-01 0.345075E-01 0.280000E+01 0.845072E-01 0.302173E-01 0.300000E+01 0.788327E-01 0.266297E-01 0.320000E+01 0.738174E-01 0.236059E-01 0.340000E+01 0.693596E-01 0.210401E-01 0.360000E+01 0.653761E-01 0.188504E-01 0.380000E+01 0.617986E-01 0.169697E-01 0.400000E+01 0.585710E-01 0.153440E-01 0.420000E+01 0.556468E-01 0.139304E-01 0.440000E+01 0.529868E-01 0.126960E-01 0.460000E+01 0.505581E-01 0.116139E-01 0.480000E+01 0.483326E-01 0.106610E-01 0.500000E+01 0.462864E-01 0.981709E-02 0.520000E+01 0.443995E-01 0.906556E-02 0.540000E+01 0.426549E-01 0.839304E-02 4.1.7 Turbulent Reynolds Number tau RE_t 0.200000E+00 0.123250E+03 0.400000E+00 0.107492E+03 0.600000E+00 0.993937E+02 0.800000E+00 0.937053E+02 0.100000E+01 0.894512E+02 0.120000E+01 0.857768E+02 0.140000E+01 0.826129E+02 0.160000E+01 0.800383E+02 0.180000E+01 0.779357E+02 0.200000E+01 0.761409E+02 0.220000E+01 0.745647E+02 0.240000E+01 0.731627E+02 0.260000E+01 0.719407E+02 0.280000E+01 0.709009E+02 0.300000E+01 0.700111E+02 0.320000E+01 0.692496E+02 0.340000E+01 0.685940E+02 0.360000E+01 0.680202E+02 0.380000E+01 0.675155E+02 0.400000E+01 0.670733E+02 0.420000E+01 0.666863E+02 0.440000E+01 0.663424E+02 0.460000E+01 0.660276E+02 0.480000E+01 0.657361E+02 0.500000E+01 0.654705E+02 0.520000E+01 0.652354E+02 0.540000E+01 0.650338E+02 4.1.8 Integral Scales tau Lamda_11(x_1) Lamda_22(x_1) Lamda_33(x_1) 0.200000E+00 0.971830E+00 0.374309E+00 0.436610E+00 0.400000E+00 0.104462E+01 0.376248E+00 0.447933E+00 0.600000E+00 0.110455E+01 0.383055E+00 0.462805E+00 0.800000E+00 0.114875E+01 0.395825E+00 0.474236E+00 0.100000E+01 0.120277E+01 0.418623E+00 0.488510E+00 0.120000E+01 0.126359E+01 0.441037E+00 0.513223E+00 0.140000E+01 0.132414E+01 0.456280E+00 0.537969E+00 0.160000E+01 0.138766E+01 0.469972E+00 0.562685E+00 0.180000E+01 0.144681E+01 0.483264E+00 0.584122E+00 0.200000E+01 0.149788E+01 0.494791E+00 0.600198E+00 0.220000E+01 0.155166E+01 0.503020E+00 0.609099E+00 0.240000E+01 0.161278E+01 0.509484E+00 0.613137E+00 0.260000E+01 0.168161E+01 0.516688E+00 0.617895E+00 0.280000E+01 0.175315E+01 0.526139E+00 0.625912E+00 0.300000E+01 0.182124E+01 0.539745E+00 0.635675E+00 0.320000E+01 0.188425E+01 0.557808E+00 0.645488E+00 0.340000E+01 0.194101E+01 0.579242E+00 0.655256E+00 0.360000E+01 0.199135E+01 0.602589E+00 0.665195E+00 0.380000E+01 0.203758E+01 0.626638E+00 0.675342E+00 0.400000E+01 0.208078E+01 0.650592E+00 0.686038E+00 0.420000E+01 0.212117E+01 0.674025E+00 0.697661E+00 0.440000E+01 0.215984E+01 0.696968E+00 0.710362E+00 0.460000E+01 0.219684E+01 0.719403E+00 0.724276E+00 0.400000E+01 0.208078E+01 0.650592E+00 0.686038E+00 0.420000E+01 0.212117E+01 0.674025E+00 0.697661E+00 0.440000E+01 0.215984E+01 0.696968E+00 0.710362E+00 0.460000E+01 0.219684E+01 0.719403E+00 0.724276E+00 0.480000E+01 0.223177E+01 0.741170E+00 0.739439E+00 0.500000E+01 0.226523E+01 0.762231E+00 0.755758E+00 0.520000E+01 0.229882E+01 0.782585E+00 0.773165E+00 0.540000E+01 0.233379E+01 0.802071E+00 0.791748E+00 4.1.9 Two Point Correlations tau 0.200000E+01 x_1 R_11(x_1) R_22(x_1) R_33(x_1) 0.0 0.100000E+01 0.100000E+01 0.100000E+01 0.872665E-01 0.953697E+00 0.902615E+00 0.904112E+00 0.174533E+00 0.847016E+00 0.701823E+00 0.707167E+00 0.261799E+00 0.728578E+00 0.511418E+00 0.521312E+00 0.349066E+00 0.622669E+00 0.367243E+00 0.381835E+00 0.436332E+00 0.534935E+00 0.265430E+00 0.285408E+00 0.523599E+00 0.463812E+00 0.193891E+00 0.219163E+00 0.610865E+00 0.406161E+00 0.143027E+00 0.172155E+00 0.698132E+00 0.358873E+00 0.107048E+00 0.137875E+00 0.785398E+00 0.319238E+00 0.815245E-01 0.111609E+00 0.872665E+00 0.285221E+00 0.617122E-01 0.895554E-01 0.959931E+00 0.255525E+00 0.434259E-01 0.695791E-01 0.104720E+01 0.229415E+00 0.251190E-01 0.509140E-01 0.113446E+01 0.206622E+00 0.875518E-02 0.336233E-01 0.122173E+01 0.187114E+00 -0.270871E-02 0.174510E-01 0.130900E+01 0.170625E+00 -0.846019E-02 0.208187E-02 0.139626E+01 0.156399E+00 -0.109612E-01 -0.121706E-01 0.148353E+01 0.143562E+00 -0.141247E-01 -0.251041E-01 0.157080E+01 0.131618E+00 -0.195679E-01 -0.367206E-01 0.165806E+01 0.120458E+00 -0.258813E-01 -0.471083E-01 0.174533E+01 0.110078E+00 -0.315208E-01 -0.553145E-01 0.183260E+01 0.100506E+00 -0.362034E-01 -0.591049E-01 0.191986E+01 0.916996E-01 -0.401122E-01 -0.575314E-01 0.200713E+01 0.836187E-01 -0.436917E-01 -0.519172E-01 0.209440E+01 0.763007E-01 -0.482827E-01 -0.447026E-01 0.218166E+01 0.695128E-01 -0.551761E-01 -0.385057E-01 0.226893E+01 0.628899E-01 -0.631138E-01 -0.352284E-01 0.235619E+01 0.564170E-01 -0.695064E-01 -0.351791E-01 0.244346E+01 0.504592E-01 -0.730924E-01 -0.371090E-01 0.253073E+01 0.453977E-01 -0.743297E-01 -0.389744E-01 0.261799E+01 0.412453E-01 -0.739206E-01 -0.393076E-01 0.270526E+01 0.376233E-01 -0.723399E-01 -0.376697E-01 0.279253E+01 0.342166E-01 -0.703838E-01 -0.342098E-01 0.287979E+01 0.311418E-01 -0.693312E-01 -0.291994E-01 0.296706E+01 0.287668E-01 -0.695720E-01 -0.233298E-01 0.305433E+01 0.273495E-01 -0.703946E-01 -0.183614E-01 tau 0.500000E+01 x_1 R_11(x_1) R_22(x_1) R_33(x_1) 0.0 0.100000E+01 0.100000E+01 0.100000E+01 0.872665E-01 0.978349E+00 0.949856E+00 0.954178E+00 0.174533E+00 0.921626E+00 0.826776E+00 0.841352E+00 0.261799E+00 0.846694E+00 0.680946E+00 0.706453E+00 0.349066E+00 0.767868E+00 0.546717E+00 0.579553E+00 0.436332E+00 0.693385E+00 0.437210E+00 0.471965E+00 0.523599E+00 0.626654E+00 0.352407E+00 0.384489E+00 0.610865E+00 0.568293E+00 0.286859E+00 0.314050E+00 0.698132E+00 0.517634E+00 0.234460E+00 0.256888E+00 0.785398E+00 0.473601E+00 0.190557E+00 0.209520E+00 0.872665E+00 0.435194E+00 0.152356E+00 0.169139E+00 0.959931E+00 0.401673E+00 0.118529E+00 0.133836E+00 0.104720E+01 0.372511E+00 0.887857E-01 0.102464E+00 0.113446E+01 0.347250E+00 0.634139E-01 0.743790E-01 0.122173E+01 0.325379E+00 0.425895E-01 0.491982E-01 0.130900E+01 0.306317E+00 0.257008E-01 0.266006E-01 0.139626E+01 0.289511E+00 0.112332E-01 0.636077E-02 0.148353E+01 0.274499E+00 -0.237697E-02 -0.115842E-01 0.157080E+01 0.260862E+00 -0.157371E-01 -0.273319E-01 0.165806E+01 0.248197E+00 -0.284069E-01 -0.412851E-01 0.174533E+01 0.236182E+00 -0.396720E-01 -0.540498E-01 0.183260E+01 0.224644E+00 -0.494071E-01 -0.658219E-01 0.191986E+01 0.213571E+00 -0.582645E-01 -0.761477E-01 0.200713E+01 0.203048E+00 -0.670459E-01 -0.844621E-01 0.209440E+01 0.193206E+00 -0.757945E-01 -0.905950E-01 0.218166E+01 0.184199E+00 -0.833362E-01 -0.946007E-01 0.226893E+01 0.176133E+00 -0.878839E-01 -0.963891E-01 0.235619E+01 0.168976E+00 -0.883098E-01 -0.959369E-01 0.244346E+01 0.162532E+00 -0.848450E-01 -0.936484E-01 0.253073E+01 0.156545E+00 -0.788689E-01 -0.902261E-01 0.261799E+01 0.150868E+00 -0.721485E-01 -0.863825E-01 0.270526E+01 0.145548E+00 -0.659740E-01 -0.828668E-01 0.279253E+01 0.140749E+00 -0.607143E-01 -0.804476E-01 0.287979E+01 0.136664E+00 -0.561784E-01 -0.794337E-01 0.296706E+01 0.133515E+00 -0.523345E-01 -0.794115E-01 0.305433E+01 0.131527E+00 -0.495713E-01 -0.797061E-01 4.1.10 One Dimensional Energy Spectrum tau 0.200000E+01 k_1 E_11(k_1) E_22(k_1) E_33(k_1) 0.0 0.192310E-01 0.600895E-02 0.733237E-02 0.100000E+01 0.121342E-01 0.936378E-02 0.911251E-02 0.200000E+01 0.606879E-02 0.616955E-02 0.693242E-02 0.300000E+01 0.395981E-02 0.469352E-02 0.413791E-02 0.400000E+01 0.253308E-02 0.364989E-02 0.315944E-02 0.500000E+01 0.172223E-02 0.254153E-02 0.267859E-02 0.600000E+01 0.119746E-02 0.207528E-02 0.218392E-02 0.700000E+01 0.867264E-03 0.160254E-02 0.139127E-02 0.800000E+01 0.620902E-03 0.120118E-02 0.126627E-02 0.900000E+01 0.444322E-03 0.943704E-03 0.904558E-03 0.100000E+02 0.298311E-03 0.607903E-03 0.652211E-03 0.110000E+02 0.223637E-03 0.484502E-03 0.522817E-03 0.120000E+02 0.165507E-03 0.419388E-03 0.413094E-03 0.130000E+02 0.121270E-03 0.333531E-03 0.295915E-03 0.140000E+02 0.933870E-04 0.242139E-03 0.238609E-03 0.150000E+02 0.637882E-04 0.183079E-03 0.181733E-03 0.160000E+02 0.498238E-04 0.129684E-03 0.142752E-03 0.170000E+02 0.375819E-04 0.108776E-03 0.103132E-03 0.180000E+02 0.279542E-04 0.875901E-04 0.803613E-04 0.190000E+02 0.209531E-04 0.619624E-04 0.649358E-04 0.200000E+02 0.157017E-04 0.512073E-04 0.507666E-04 0.210000E+02 0.117202E-04 0.412641E-04 0.396920E-04 0.220000E+02 0.908879E-05 0.317404E-04 0.320671E-04 0.230000E+02 0.720334E-05 0.248505E-04 0.261052E-04 0.240000E+02 0.538086E-05 0.198450E-04 0.201919E-04 0.250000E+02 0.411121E-05 0.155597E-04 0.160984E-04 0.260000E+02 0.333404E-05 0.125551E-04 0.131705E-04 0.270000E+02 0.252805E-05 0.101134E-04 0.105297E-04 0.280000E+02 0.194391E-05 0.764347E-05 0.785620E-05 0.290000E+02 0.156239E-05 0.631440E-05 0.633728E-05 0.300000E+02 0.124004E-05 0.510911E-05 0.516718E-05 0.310000E+02 0.959129E-06 0.415982E-05 0.429354E-05 0.320000E+02 0.754952E-06 0.332943E-05 0.342903E-05 0.330000E+02 0.622765E-06 0.280130E-05 0.275858E-05 0.340000E+02 0.482260E-06 0.221884E-05 0.225145E-05 0.350000E+02 0.388155E-06 0.172558E-05 0.186206E-05 0.360000E+02 0.303891E-06 0.151612E-05 0.146320E-05 0.370000E+02 0.246401E-06 0.122084E-05 0.120806E-05 0.380000E+02 0.201293E-06 0.987027E-06 0.970057E-06 0.390000E+02 0.162523E-06 0.828495E-06 0.813530E-06 0.400000E+02 0.137379E-06 0.662746E-06 0.694198E-06 0.410000E+02 0.109063E-06 0.570307E-06 0.565045E-06 0.420000E+02 0.945059E-07 0.498183E-06 0.493004E-06 0.430000E+02 0.842964E-07 0.436437E-06 0.448064E-06 0.440000E+02 0.731338E-07 0.406494E-06 0.393376E-06 0.450000E+02 0.661049E-07 0.361888E-06 0.368075E-06 0.460000E+02 0.625916E-07 0.359944E-06 0.366070E-06 0.470000E+02 0.565654E-07 0.358896E-06 0.353871E-06 tau 0.500000E+01 k_1 E_11(k_1) E_22(k_1) E_33(k_1) 0.0 0.117243E-01 0.345998E-02 0.379269E-02 0.100000E+01 0.503655E-02 0.452078E-02 0.536693E-02 0.200000E+01 0.217363E-02 0.281824E-02 0.317065E-02 0.300000E+01 0.131156E-02 0.149607E-02 0.162957E-02 0.400000E+01 0.728829E-03 0.121260E-02 0.120010E-02 0.500000E+01 0.430952E-03 0.720180E-03 0.797684E-03 0.600000E+01 0.249709E-03 0.526271E-03 0.521367E-03 0.700000E+01 0.173656E-03 0.401649E-03 0.390491E-03 0.800000E+01 0.105186E-03 0.261076E-03 0.243029E-03 0.900000E+01 0.660227E-04 0.193674E-03 0.170983E-03 0.100000E+02 0.430612E-04 0.125436E-03 0.113234E-03 0.110000E+02 0.262617E-04 0.692004E-04 0.814792E-04 0.120000E+02 0.171096E-04 0.593170E-04 0.542830E-04 0.130000E+02 0.113800E-04 0.391162E-04 0.373020E-04 0.140000E+02 0.754613E-05 0.254472E-04 0.273977E-04 0.150000E+02 0.539320E-05 0.172099E-04 0.194655E-04 0.160000E+02 0.342758E-05 0.123711E-04 0.129174E-04 0.170000E+02 0.227897E-05 0.879836E-05 0.876229E-05 0.180000E+02 0.163844E-05 0.645223E-05 0.707857E-05 0.190000E+02 0.109499E-05 0.459048E-05 0.447978E-05 0.200000E+02 0.791212E-06 0.319931E-05 0.328143E-05 0.210000E+02 0.519581E-06 0.237732E-05 0.242545E-05 0.220000E+02 0.385502E-06 0.175786E-05 0.172892E-05 0.230000E+02 0.262096E-06 0.123205E-05 0.129771E-05 0.240000E+02 0.197890E-06 0.951145E-06 0.927923E-06 0.250000E+02 0.139990E-06 0.655573E-06 0.697805E-06 0.260000E+02 0.972807E-07 0.505579E-06 0.490737E-06 0.270000E+02 0.698578E-07 0.370792E-06 0.360332E-06 0.280000E+02 0.507123E-07 0.285124E-06 0.250663E-06 0.290000E+02 0.372126E-07 0.193561E-06 0.193622E-06 0.300000E+02 0.264424E-07 0.150280E-06 0.144315E-06 0.310000E+02 0.192967E-07 0.107988E-06 0.100172E-06 0.320000E+02 0.141061E-07 0.819430E-07 0.741916E-07 0.330000E+02 0.103257E-07 0.637519E-07 0.560303E-07 0.340000E+02 0.783349E-08 0.466426E-07 0.427260E-07 0.350000E+02 0.560577E-08 0.357159E-07 0.312569E-07 0.360000E+02 0.423584E-08 0.262749E-07 0.241826E-07 0.370000E+02 0.315377E-08 0.197840E-07 0.178542E-07 0.380000E+02 0.228915E-08 0.145361E-07 0.135483E-07 0.390000E+02 0.173265E-08 0.114200E-07 0.100246E-07 0.400000E+02 0.125768E-08 0.817590E-08 0.749084E-08 0.410000E+02 0.964661E-09 0.657238E-08 0.606024E-08 0.420000E+02 0.728554E-09 0.490014E-08 0.455115E-08 0.430000E+02 0.550233E-09 0.382801E-08 0.346692E-08 0.440000E+02 0.430063E-09 0.307919E-08 0.280015E-08 0.450000E+02 0.379207E-09 0.262843E-08 0.239803E-08 0.460000E+02 0.328865E-09 0.252361E-08 0.216663E-08 0.470000E+02 0.302189E-09 0.236831E-08 0.214624E-08 4.2 Thermal Field 4.2.1 Pr=0.71 Without Initial Temperature Fluctuations 4.2.1.1 Temperature Variance and Heat Flux tau tt vt 0.200000E+00 0.101079E-01 0.496246E-01 0.400000E+00 0.301417E-01 0.736427E-01 0.600000E+00 0.523198E-01 0.851810E-01 0.800000E+00 0.742285E-01 0.911545E-01 0.100000E+01 0.953365E-01 0.943699E-01 0.120000E+01 0.115505E+00 0.960929E-01 0.140000E+01 0.134752E+00 0.969552E-01 0.160000E+01 0.153189E+00 0.971480E-01 0.180000E+01 0.170875E+00 0.968320E-01 0.200000E+01 0.187801E+00 0.962241E-01 0.220000E+01 0.204029E+00 0.954937E-01 0.240000E+01 0.219694E+00 0.946840E-01 0.260000E+01 0.234892E+00 0.937942E-01 0.280000E+01 0.249656E+00 0.928567E-01 0.300000E+01 0.264015E+00 0.919192E-01 0.320000E+01 0.278025E+00 0.910155E-01 0.340000E+01 0.291769E+00 0.901631E-01 0.360000E+01 0.305332E+00 0.893664E-01 0.380000E+01 0.318759E+00 0.886197E-01 0.400000E+01 0.332046E+00 0.879144E-01 0.420000E+01 0.345169E+00 0.872474E-01 0.440000E+01 0.358104E+00 0.866221E-01 0.460000E+01 0.370853E+00 0.860436E-01 0.480000E+01 0.383446E+00 0.855147E-01 0.500000E+01 0.395940E+00 0.850328E-01 0.520000E+01 0.408393E+00 0.845888E-01 0.540000E+01 0.420844E+00 0.841685E-01 4.2.1.2 vt Budget tau P_vt fai_vt D_vt 0.200000E+00 0.263467E+00 -0.391314E-01 0.537244E-01 0.400000E+00 0.217766E+00 -0.716120E-01 0.661521E-01 0.600000E+00 0.182805E+00 -0.799650E-01 0.632050E-01 0.800000E+00 0.156073E+00 -0.773858E-01 0.576288E-01 0.100000E+01 0.135236E+00 -0.718619E-01 0.522984E-01 0.120000E+01 0.118613E+00 -0.650367E-01 0.477588E-01 0.140000E+01 0.105073E+00 -0.588669E-01 0.439921E-01 0.160000E+01 0.938294E-01 -0.539135E-01 0.406371E-01 0.180000E+01 0.843484E-01 -0.494723E-01 0.375938E-01 0.200000E+01 0.763056E-01 -0.450575E-01 0.348779E-01 0.220000E+01 0.694457E-01 -0.409293E-01 0.325363E-01 0.240000E+01 0.635411E-01 -0.374747E-01 0.304705E-01 0.260000E+01 0.584201E-01 -0.345767E-01 0.285774E-01 0.280000E+01 0.539546E-01 -0.319966E-01 0.267909E-01 0.300000E+01 0.500393E-01 -0.296673E-01 0.250917E-01 0.320000E+01 0.465907E-01 -0.275669E-01 0.235083E-01 0.340000E+01 0.435484E-01 -0.256769E-01 0.220693E-01 0.360000E+01 0.408608E-01 -0.240079E-01 0.207712E-01 0.380000E+01 0.384766E-01 -0.225621E-01 0.195979E-01 0.400000E+01 0.363499E-01 -0.212957E-01 0.185382E-01 0.420000E+01 0.344453E-01 -0.201494E-01 0.175784E-01 0.440000E+01 0.327350E-01 -0.190890E-01 0.167029E-01 0.460000E+01 0.311934E-01 -0.181006E-01 0.159015E-01 0.480000E+01 0.297961E-01 -0.171845E-01 0.151701E-01 0.500000E+01 0.285212E-01 -0.163542E-01 0.145053E-01 0.520000E+01 0.273497E-01 -0.156272E-01 0.139014E-01 0.540000E+01 0.262663E-01 -0.150123E-01 0.133511E-01 4.2.1.3 tt Budget tau P_tt D_tt 0.200000E+00 0.992492E-01 0.139296E-01 0.400000E+00 0.147285E+00 0.385136E-01 0.600000E+00 0.170362E+00 0.594082E-01 0.800000E+00 0.182309E+00 0.747256E-01 0.100000E+01 0.188740E+00 0.855654E-01 0.120000E+01 0.192186E+00 0.937888E-01 0.140000E+01 0.193910E+00 0.998410E-01 0.160000E+01 0.194296E+00 0.104019E+00 0.180000E+01 0.193664E+00 0.107161E+00 0.200000E+01 0.192448E+00 0.109687E+00 0.220000E+01 0.190987E+00 0.111380E+00 0.240000E+01 0.189368E+00 0.112273E+00 0.260000E+01 0.187588E+00 0.112709E+00 0.280000E+01 0.185713E+00 0.112948E+00 0.300000E+01 0.183838E+00 0.112984E+00 0.320000E+01 0.182031E+00 0.112727E+00 0.340000E+01 0.180326E+00 0.112124E+00 0.360000E+01 0.178733E+00 0.111280E+00 0.380000E+01 0.177239E+00 0.110441E+00 0.400000E+01 0.175829E+00 0.109784E+00 0.420000E+01 0.174495E+00 0.109340E+00 0.440000E+01 0.173244E+00 0.109048E+00 0.460000E+01 0.172087E+00 0.108774E+00 0.480000E+01 0.171029E+00 0.108366E+00 0.500000E+01 0.170066E+00 0.107744E+00 0.520000E+01 0.169178E+00 0.106940E+00 0.540000E+01 0.168337E+00 0.106058E+00 4.2.1.4 Thermal Integreal Scale tau Lamda_tt(x_1) 0.200000E+00 0.379771E+00 0.400000E+00 0.399920E+00 0.600000E+00 0.424845E+00 0.800000E+00 0.454236E+00 0.100000E+01 0.487015E+00 0.120000E+01 0.516698E+00 0.140000E+01 0.540935E+00 0.160000E+01 0.567490E+00 0.180000E+01 0.597852E+00 0.200000E+01 0.628418E+00 0.220000E+01 0.653510E+00 0.240000E+01 0.673721E+00 0.260000E+01 0.688843E+00 0.280000E+01 0.699703E+00 0.300000E+01 0.709970E+00 0.320000E+01 0.723209E+00 0.340000E+01 0.739802E+00 0.360000E+01 0.758035E+00 0.380000E+01 0.775975E+00 0.400000E+01 0.792959E+00 0.420000E+01 0.809147E+00 0.440000E+01 0.824508E+00 0.460000E+01 0.839352E+00 0.480000E+01 0.854490E+00 0.500000E+01 0.870726E+00 0.520000E+01 0.888649E+00 0.540000E+01 0.908467E+00 4.2.1.5 Thermal Two Point Correlation tau = 0.200000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.930882E+00 0.174533E+00 0.783930E+00 0.261799E+00 0.632776E+00 0.349066E+00 0.503228E+00 0.436332E+00 0.398893E+00 0.523599E+00 0.317131E+00 0.610865E+00 0.253498E+00 0.698132E+00 0.203400E+00 0.785398E+00 0.162670E+00 0.872665E+00 0.127735E+00 0.959931E+00 0.967278E-01 0.104720E+01 0.696860E-01 0.113446E+01 0.468592E-01 0.122173E+01 0.281884E-01 0.130900E+01 0.136378E-01 0.139626E+01 0.217270E-02 0.148353E+01 -0.821961E-02 0.157080E+01 -0.190580E-01 0.165806E+01 -0.304937E-01 0.174533E+01 -0.416665E-01 0.183260E+01 -0.516029E-01 0.191986E+01 -0.598716E-01 0.200713E+01 -0.670553E-01 0.209440E+01 -0.740290E-01 0.218166E+01 -0.808889E-01 0.226893E+01 -0.871273E-01 0.235619E+01 -0.921305E-01 0.244346E+01 -0.956028E-01 0.253073E+01 -0.979693E-01 0.261799E+01 -0.998463E-01 0.270526E+01 -0.101499E+00 0.279253E+01 -0.102818E+00 0.287979E+01 -0.103526E+00 0.296706E+01 -0.103427E+00 0.305433E+01 -0.102797E+00 tau = 0.500000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.966129E+00 0.174533E+00 0.881730E+00 0.261799E+00 0.777706E+00 0.349066E+00 0.674740E+00 0.436332E+00 0.581483E+00 0.523599E+00 0.499835E+00 0.610865E+00 0.428755E+00 0.698132E+00 0.366199E+00 0.785398E+00 0.310188E+00 0.872665E+00 0.259407E+00 0.959931E+00 0.213339E+00 0.104720E+01 0.172040E+00 0.113446E+01 0.135649E+00 0.122173E+01 0.103867E+00 0.130900E+01 0.757960E-01 0.139626E+01 0.502401E-01 0.148353E+01 0.262358E-01 0.157080E+01 0.332977E-02 0.165806E+01 -0.184730E-01 0.174533E+01 -0.389530E-01 0.183260E+01 -0.579590E-01 0.191986E+01 -0.754142E-01 0.200713E+01 -0.911767E-01 0.209440E+01 -0.105003E+00 0.218166E+01 -0.116598E+00 0.226893E+01 -0.125747E+00 0.235619E+01 -0.132496E+00 0.244346E+01 -0.137256E+00 0.253073E+01 -0.140782E+00 0.261799E+01 -0.143980E+00 0.270526E+01 -0.147533E+00 0.279253E+01 -0.151510E+00 0.287979E+01 -0.155379E+00 0.296706E+01 -0.158493E+00 0.305433E+01 -0.160458E+00 4.2.1.6 One Dimensinal Energy Spectrum tau 0.200000E+01 k_1 E_tt(k_1) 0.0 0.187830E-01 0.100000E+01 0.295465E-01 0.200000E+01 0.166656E-01 0.300000E+01 0.108988E-01 0.400000E+01 0.770154E-02 0.500000E+01 0.513460E-02 0.600000E+01 0.371022E-02 0.700000E+01 0.277262E-02 0.800000E+01 0.208993E-02 0.900000E+01 0.148770E-02 0.100000E+02 0.101179E-02 0.110000E+02 0.725717E-03 0.120000E+02 0.629862E-03 0.130000E+02 0.456894E-03 0.140000E+02 0.350628E-03 0.150000E+02 0.276731E-03 0.160000E+02 0.221259E-03 0.170000E+02 0.169591E-03 0.180000E+02 0.133003E-03 0.190000E+02 0.101854E-03 0.200000E+02 0.826749E-04 0.210000E+02 0.672730E-04 0.220000E+02 0.562536E-04 0.230000E+02 0.433510E-04 0.240000E+02 0.333950E-04 0.250000E+02 0.266516E-04 0.260000E+02 0.211194E-04 0.270000E+02 0.171597E-04 0.280000E+02 0.143615E-04 0.290000E+02 0.114554E-04 0.300000E+02 0.908496E-05 0.310000E+02 0.753359E-05 0.320000E+02 0.610763E-05 0.330000E+02 0.505930E-05 0.340000E+02 0.407499E-05 0.350000E+02 0.328292E-05 0.360000E+02 0.272306E-05 0.370000E+02 0.226978E-05 0.380000E+02 0.180054E-05 0.390000E+02 0.152207E-05 0.400000E+02 0.123773E-05 0.410000E+02 0.104400E-05 0.420000E+02 0.911044E-06 0.430000E+02 0.803190E-06 0.440000E+02 0.715262E-06 0.450000E+02 0.676462E-06 0.460000E+02 0.636544E-06 0.470000E+02 0.597816E-06 tau 0.500000E+01 k_1 E_tt(k_1) 0.0 0.548695E-01 0.100000E+01 0.833126E-01 0.200000E+01 0.357462E-01 0.300000E+01 0.183085E-01 0.400000E+01 0.116368E-01 0.500000E+01 0.718628E-02 0.600000E+01 0.413906E-02 0.700000E+01 0.334212E-02 0.800000E+01 0.215786E-02 0.900000E+01 0.153430E-02 0.100000E+02 0.983704E-03 0.110000E+02 0.597599E-03 0.120000E+02 0.458457E-03 0.130000E+02 0.316181E-03 0.140000E+02 0.236984E-03 0.150000E+02 0.158702E-03 0.160000E+02 0.115634E-03 0.170000E+02 0.832773E-04 0.180000E+02 0.593887E-04 0.190000E+02 0.440866E-04 0.200000E+02 0.311475E-04 0.210000E+02 0.233483E-04 0.220000E+02 0.162276E-04 0.230000E+02 0.122242E-04 0.240000E+02 0.909001E-05 0.250000E+02 0.661242E-05 0.260000E+02 0.485306E-05 0.270000E+02 0.362090E-05 0.280000E+02 0.279731E-05 0.290000E+02 0.198051E-05 0.300000E+02 0.146540E-05 0.310000E+02 0.107645E-05 0.320000E+02 0.818283E-06 0.330000E+02 0.610250E-06 0.340000E+02 0.432283E-06 0.350000E+02 0.329764E-06 0.360000E+02 0.250814E-06 0.370000E+02 0.181960E-06 0.380000E+02 0.137855E-06 0.390000E+02 0.103102E-06 0.400000E+02 0.780351E-07 0.410000E+02 0.602080E-07 0.420000E+02 0.439553E-07 0.430000E+02 0.341441E-07 0.440000E+02 0.274260E-07 0.450000E+02 0.233804E-07 0.460000E+02 0.204045E-07 0.470000E+02 0.192816E-07 4.2.2 Pr=0.71 With Initial Temperature Fluctuations 4.2.2.1 Temperature Variance and Heat Flux tau tt vt 0.200000E+00 0.731224E+00 0.384283E-01 0.400000E+00 0.541246E+00 0.636461E-01 0.600000E+00 0.422320E+00 0.747979E-01 0.800000E+00 0.350988E+00 0.809139E-01 0.100000E+01 0.308802E+00 0.851098E-01 0.120000E+01 0.285074E+00 0.882324E-01 0.140000E+01 0.273046E+00 0.904143E-01 0.160000E+01 0.268409E+00 0.915546E-01 0.180000E+01 0.268455E+00 0.918206E-01 0.200000E+01 0.271417E+00 0.915385E-01 0.220000E+01 0.276138E+00 0.909991E-01 0.240000E+01 0.282002E+00 0.903136E-01 0.260000E+01 0.288738E+00 0.895058E-01 0.280000E+01 0.296177E+00 0.886205E-01 0.300000E+01 0.304163E+00 0.877195E-01 0.320000E+01 0.312571E+00 0.868513E-01 0.340000E+01 0.321331E+00 0.860438E-01 0.360000E+01 0.330419E+00 0.853070E-01 0.380000E+01 0.339799E+00 0.846360E-01 0.400000E+01 0.349408E+00 0.840200E-01 0.420000E+01 0.359181E+00 0.834539E-01 0.440000E+01 0.369067E+00 0.829392E-01 0.460000E+01 0.379041E+00 0.824791E-01 0.480000E+01 0.389109E+00 0.820742E-01 0.500000E+01 0.399303E+00 0.817192E-01 0.520000E+01 0.409654E+00 0.814029E-01 0.540000E+01 0.420182E+00 0.811099E-01 4.2.2.2 vt Budget tau P_vt phi_vt D_vt 0.200000E+00 0.263467E+00 -0.312295E-01 0.471879E-01 0.400000E+00 0.217766E+00 -0.733931E-01 0.643566E-01 0.600000E+00 0.182805E+00 -0.834750E-01 0.615161E-01 0.800000E+00 0.156073E+00 -0.766748E-01 0.551707E-01 0.100000E+01 0.135236E+00 -0.680948E-01 0.497780E-01 0.120000E+01 0.118613E+00 -0.596998E-01 0.458812E-01 0.140000E+01 0.105073E+00 -0.541694E-01 0.429288E-01 0.160000E+01 0.938294E-01 -0.507443E-01 0.400360E-01 0.180000E+01 0.843484E-01 -0.477584E-01 0.371434E-01 0.200000E+01 0.763056E-01 -0.443261E-01 0.343960E-01 0.220000E+01 0.694457E-01 -0.406570E-01 0.320504E-01 0.240000E+01 0.635411E-01 -0.373607E-01 0.300799E-01 0.260000E+01 0.584201E-01 -0.345366E-01 0.282930E-01 0.280000E+01 0.539546E-01 -0.320053E-01 0.265744E-01 0.300000E+01 0.500393E-01 -0.296820E-01 0.249089E-01 0.320000E+01 0.465907E-01 -0.275321E-01 0.233491E-01 0.340000E+01 0.435484E-01 -0.255537E-01 0.219331E-01 0.360000E+01 0.408608E-01 -0.237879E-01 0.206511E-01 0.380000E+01 0.384766E-01 -0.222581E-01 0.194868E-01 0.400000E+01 0.363499E-01 -0.209231E-01 0.184339E-01 0.420000E+01 0.344453E-01 -0.197170E-01 0.174813E-01 0.440000E+01 0.327350E-01 -0.186033E-01 0.166145E-01 0.460000E+01 0.311934E-01 -0.175707E-01 0.158237E-01 0.480000E+01 0.297961E-01 -0.166214E-01 0.151047E-01 0.500000E+01 0.285212E-01 -0.157694E-01 0.144527E-01 0.520000E+01 0.273497E-01 -0.150305E-01 0.138600E-01 0.540000E+01 0.262663E-01 -0.144110E-01 0.133179E-01 4.2.2.3 tt Budget tau P_tt D_tt 0.200000E+00 0.768565E-01 0.121471E+01 0.400000E+00 0.127292E+00 0.886982E+00 0.600000E+00 0.149596E+00 0.606753E+00 0.800000E+00 0.161828E+00 0.434663E+00 0.100000E+01 0.170220E+00 0.328356E+00 0.120000E+01 0.176465E+00 0.261483E+00 0.140000E+01 0.180829E+00 0.219761E+00 0.160000E+01 0.183109E+00 0.192841E+00 0.180000E+01 0.183641E+00 0.174957E+00 0.200000E+01 0.183077E+00 0.163160E+00 0.220000E+01 0.181998E+00 0.155237E+00 0.240000E+01 0.180627E+00 0.148989E+00 0.260000E+01 0.179012E+00 0.143447E+00 0.280000E+01 0.177241E+00 0.138568E+00 0.300000E+01 0.175439E+00 0.134374E+00 0.320000E+01 0.173703E+00 0.130759E+00 0.340000E+01 0.172088E+00 0.127458E+00 0.360000E+01 0.170614E+00 0.124405E+00 0.380000E+01 0.169272E+00 0.121744E+00 0.400000E+01 0.168040E+00 0.119537E+00 0.420000E+01 0.166908E+00 0.117732E+00 0.440000E+01 0.165878E+00 0.116224E+00 0.460000E+01 0.164958E+00 0.114872E+00 0.480000E+01 0.164148E+00 0.113526E+00 0.500000E+01 0.163438E+00 0.112103E+00 0.520000E+01 0.162806E+00 0.110614E+00 0.540000E+01 0.162220E+00 0.109140E+00 4.2.2.4 Thermal Integral scale tau Lamda_tt(x_1) 0.200000E+00 0.602171E+00 0.400000E+00 0.626168E+00 0.600000E+00 0.628967E+00 0.800000E+00 0.624814E+00 0.100000E+01 0.618943E+00 0.120000E+01 0.613361E+00 0.140000E+01 0.602031E+00 0.160000E+01 0.596568E+00 0.180000E+01 0.599008E+00 0.200000E+01 0.599850E+00 0.220000E+01 0.598473E+00 0.240000E+01 0.598778E+00 0.260000E+01 0.600890E+00 0.280000E+01 0.602770E+00 0.300000E+01 0.605653E+00 0.320000E+01 0.613520E+00 0.340000E+01 0.626698E+00 0.360000E+01 0.643041E+00 0.380000E+01 0.660317E+00 0.400000E+01 0.677341E+00 0.420000E+01 0.694102E+00 0.440000E+01 0.710443E+00 0.460000E+01 0.726176E+00 0.480000E+01 0.741692E+00 0.500000E+01 0.757787E+00 0.520000E+01 0.775254E+00 0.540000E+01 0.794563E+00 4.2.2.5 Thermal Two Point Correlation tau 0.200000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.928873E+00 0.174533E+00 0.781891E+00 0.261799E+00 0.636672E+00 0.349066E+00 0.516339E+00 0.436332E+00 0.420702E+00 0.523599E+00 0.344625E+00 0.610865E+00 0.283237E+00 0.698132E+00 0.232844E+00 0.785398E+00 0.190654E+00 0.872665E+00 0.154916E+00 0.959931E+00 0.124768E+00 0.104720E+01 0.995990E-01 0.113446E+01 0.788366E-01 0.122173E+01 0.621403E-01 0.130900E+01 0.488866E-01 0.139626E+01 0.371674E-01 0.148353E+01 0.245555E-01 0.157080E+01 0.971955E-02 0.165806E+01 -0.728442E-02 0.174533E+01 -0.254472E-01 0.183260E+01 -0.438874E-01 0.191986E+01 -0.621206E-01 0.200713E+01 -0.799623E-01 0.209440E+01 -0.974267E-01 0.218166E+01 -0.114060E+00 0.226893E+01 -0.129093E+00 0.235619E+01 -0.141331E+00 0.244346E+01 -0.149967E+00 0.253073E+01 -0.155564E+00 0.261799E+01 -0.158929E+00 0.270526E+01 -0.160676E+00 0.279253E+01 -0.161074E+00 0.287979E+01 -0.159980E+00 0.296706E+01 -0.158059E+00 0.305433E+01 -0.156605E+00 tau 0.500000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.964568E+00 0.174533E+00 0.876557E+00 0.261799E+00 0.768662E+00 0.349066E+00 0.662641E+00 0.436332E+00 0.567555E+00 0.523599E+00 0.485315E+00 0.610865E+00 0.414616E+00 0.698132E+00 0.353045E+00 0.785398E+00 0.298323E+00 0.872665E+00 0.248970E+00 0.959931E+00 0.204383E+00 0.104720E+01 0.164500E+00 0.113446E+01 0.129212E+00 0.122173E+01 0.979254E-01 0.130900E+01 0.695749E-01 0.139626E+01 0.430314E-01 0.148353E+01 0.175869E-01 0.157080E+01 -0.691911E-02 0.165806E+01 -0.303215E-01 0.174533E+01 -0.524221E-01 0.183260E+01 -0.731860E-01 0.191986E+01 -0.926438E-01 0.200713E+01 -0.110708E+00 0.209440E+01 -0.127107E+00 0.218166E+01 -0.141403E+00 0.226893E+01 -0.153128E+00 0.235619E+01 -0.162077E+00 0.244346E+01 -0.168555E+00 0.253073E+01 -0.173387E+00 0.261799E+01 -0.177641E+00 0.270526E+01 -0.182159E+00 0.279253E+01 -0.187099E+00 0.287979E+01 -0.191918E+00 0.296706E+01 -0.195877E+00 0.305433E+01 -0.198447E+00 4.2.2.6 One Dimensional Energy Spectrum tau 0.200000E+01 k_1 E_tt(k_1) 0.0 0.259119E-01 0.100000E+01 0.483040E-01 0.200000E+01 0.205154E-01 0.300000E+01 0.144268E-01 0.400000E+01 0.118112E-01 0.500000E+01 0.662795E-02 0.600000E+01 0.493813E-02 0.700000E+01 0.375731E-02 0.800000E+01 0.295188E-02 0.900000E+01 0.221785E-02 0.100000E+02 0.158506E-02 0.110000E+02 0.116071E-02 0.120000E+02 0.996293E-03 0.130000E+02 0.738994E-03 0.140000E+02 0.564465E-03 0.150000E+02 0.441908E-03 0.160000E+02 0.342325E-03 0.170000E+02 0.286640E-03 0.180000E+02 0.217702E-03 0.190000E+02 0.172474E-03 0.200000E+02 0.133132E-03 0.210000E+02 0.109809E-03 0.220000E+02 0.860563E-04 0.230000E+02 0.731100E-04 0.240000E+02 0.550220E-04 0.250000E+02 0.457322E-04 0.260000E+02 0.357890E-04 0.270000E+02 0.286487E-04 0.280000E+02 0.247834E-04 0.290000E+02 0.186121E-04 0.300000E+02 0.150689E-04 0.310000E+02 0.128510E-04 0.320000E+02 0.102757E-04 0.330000E+02 0.842030E-05 0.340000E+02 0.692500E-05 0.350000E+02 0.556426E-05 0.360000E+02 0.460075E-05 0.370000E+02 0.383740E-05 0.380000E+02 0.300425E-05 0.390000E+02 0.246474E-05 0.400000E+02 0.212074E-05 0.410000E+02 0.178200E-05 0.420000E+02 0.155031E-05 0.430000E+02 0.135239E-05 0.440000E+02 0.118945E-05 0.450000E+02 0.108799E-05 0.460000E+02 0.108556E-05 0.470000E+02 0.101796E-05 tau 0.500000E+01 k_1 E_tt(k_1) 0.0 0.481581E-01 0.100000E+01 0.868262E-01 0.200000E+01 0.347494E-01 0.300000E+01 0.186310E-01 0.400000E+01 0.123150E-01 0.500000E+01 0.767986E-02 0.600000E+01 0.449166E-02 0.700000E+01 0.358179E-02 0.800000E+01 0.222344E-02 0.900000E+01 0.166808E-02 0.100000E+02 0.107216E-02 0.110000E+02 0.641879E-03 0.120000E+02 0.483879E-03 0.130000E+02 0.331148E-03 0.140000E+02 0.251225E-03 0.150000E+02 0.172167E-03 0.160000E+02 0.123492E-03 0.170000E+02 0.896850E-04 0.180000E+02 0.644156E-04 0.190000E+02 0.476097E-04 0.200000E+02 0.337002E-04 0.210000E+02 0.255443E-04 0.220000E+02 0.177693E-04 0.230000E+02 0.134772E-04 0.240000E+02 0.986120E-05 0.250000E+02 0.721562E-05 0.260000E+02 0.528065E-05 0.270000E+02 0.394960E-05 0.280000E+02 0.305277E-05 0.290000E+02 0.215292E-05 0.300000E+02 0.158838E-05 0.310000E+02 0.116034E-05 0.320000E+02 0.878117E-06 0.330000E+02 0.661067E-06 0.340000E+02 0.470818E-06 0.350000E+02 0.361340E-06 0.360000E+02 0.269783E-06 0.370000E+02 0.198215E-06 0.380000E+02 0.149421E-06 0.390000E+02 0.111082E-06 0.400000E+02 0.844339E-07 0.410000E+02 0.658548E-07 0.420000E+02 0.473380E-07 0.430000E+02 0.371096E-07 0.440000E+02 0.294538E-07 0.450000E+02 0.248473E-07 0.460000E+02 0.217755E-07 0.470000E+02 0.204970E-07 4.2.3 Pr=1.5 Without Initial Temperature Fluctuations 4.2.3.1 Temperature Variance and Turbulent Heat Flux tau tt vt 0.200000E+00 0.107663E-01 0.509837E-01 0.400000E+00 0.332896E-01 0.762770E-01 0.600000E+00 0.588770E-01 0.883410E-01 0.800000E+00 0.844239E-01 0.945521E-01 0.100000E+01 0.109154E+00 0.979260E-01 0.120000E+01 0.132934E+00 0.997914E-01 0.140000E+01 0.155756E+00 0.100789E+00 0.160000E+01 0.177680E+00 0.101080E+00 0.180000E+01 0.198778E+00 0.100825E+00 0.200000E+01 0.219066E+00 0.100261E+00 0.220000E+01 0.238572E+00 0.995767E-01 0.240000E+01 0.257403E+00 0.988072E-01 0.260000E+01 0.275673E+00 0.979436E-01 0.280000E+01 0.293443E+00 0.970179E-01 0.300000E+01 0.310732E+00 0.960780E-01 0.320000E+01 0.327569E+00 0.951598E-01 0.340000E+01 0.344022E+00 0.942877E-01 0.360000E+01 0.360188E+00 0.934711E-01 0.380000E+01 0.376157E+00 0.927046E-01 0.400000E+01 0.391968E+00 0.919781E-01 0.420000E+01 0.407611E+00 0.912890E-01 0.440000E+01 0.423054E+00 0.906420E-01 0.460000E+01 0.438272E+00 0.900436E-01 0.480000E+01 0.453271E+00 0.894991E-01 0.500000E+01 0.468091E+00 0.890082E-01 0.520000E+01 0.482793E+00 0.885630E-01 0.540000E+01 0.497440E+00 0.881486E-01 4.2.3.2 vt Budget tau P_vt phi_vt D_vt 0.200000E+00 0.263467E+00 -0.429015E-01 0.413248E-01 0.400000E+00 0.217766E+00 -0.806377E-01 0.531500E-01 0.600000E+00 0.182805E+00 -0.904315E-01 0.511806E-01 0.800000E+00 0.156073E+00 -0.874612E-01 0.467105E-01 0.100000E+01 0.135236E+00 -0.810882E-01 0.424188E-01 0.120000E+01 0.118613E+00 -0.733946E-01 0.387284E-01 0.140000E+01 0.105073E+00 -0.665976E-01 0.357055E-01 0.160000E+01 0.938294E-01 -0.611759E-01 0.330245E-01 0.180000E+01 0.843484E-01 -0.562611E-01 0.305976E-01 0.200000E+01 0.763056E-01 -0.513318E-01 0.284109E-01 0.220000E+01 0.694457E-01 -0.467182E-01 0.265474E-01 0.240000E+01 0.635411E-01 -0.428734E-01 0.249256E-01 0.260000E+01 0.584201E-01 -0.396336E-01 0.234457E-01 0.280000E+01 0.539546E-01 -0.367315E-01 0.220499E-01 0.300000E+01 0.500393E-01 -0.341193E-01 0.207020E-01 0.320000E+01 0.465907E-01 -0.317680E-01 0.194137E-01 0.340000E+01 0.435484E-01 -0.296363E-01 0.182247E-01 0.360000E+01 0.408608E-01 -0.277351E-01 0.171544E-01 0.380000E+01 0.384766E-01 -0.260812E-01 0.161920E-01 0.400000E+01 0.363499E-01 -0.246304E-01 0.153230E-01 0.420000E+01 0.344453E-01 -0.233131E-01 0.145346E-01 0.440000E+01 0.327350E-01 -0.220920E-01 0.138130E-01 0.460000E+01 0.311934E-01 -0.209503E-01 0.131494E-01 0.480000E+01 0.297961E-01 -0.198831E-01 0.125411E-01 0.500000E+01 0.285212E-01 -0.189035E-01 0.119872E-01 0.520000E+01 0.273497E-01 -0.180356E-01 0.114850E-01 0.540000E+01 0.262663E-01 -0.172961E-01 0.110283E-01 4.2.3.3 tt Budget tau P_tt D_tt 0.200000E+00 0.101967E+00 0.856482E-02 0.400000E+00 0.152554E+00 0.284289E-01 0.600000E+00 0.176682E+00 0.479993E-01 0.800000E+00 0.189104E+00 0.635614E-01 0.100000E+01 0.195852E+00 0.747932E-01 0.120000E+01 0.199583E+00 0.833260E-01 0.140000E+01 0.201579E+00 0.899413E-01 0.160000E+01 0.202161E+00 0.947594E-01 0.180000E+01 0.201650E+00 0.982826E-01 0.200000E+01 0.200523E+00 0.101164E+00 0.220000E+01 0.199153E+00 0.103486E+00 0.240000E+01 0.197614E+00 0.104991E+00 0.260000E+01 0.195887E+00 0.105853E+00 0.280000E+01 0.194036E+00 0.106423E+00 0.300000E+01 0.192156E+00 0.106901E+00 0.320000E+01 0.190320E+00 0.107184E+00 0.340000E+01 0.188575E+00 0.107129E+00 0.360000E+01 0.186942E+00 0.106673E+00 0.380000E+01 0.185409E+00 0.105975E+00 0.400000E+01 0.183956E+00 0.105308E+00 0.420000E+01 0.182578E+00 0.104843E+00 0.440000E+01 0.181284E+00 0.104625E+00 0.460000E+01 0.180087E+00 0.104570E+00 0.480000E+01 0.178998E+00 0.104504E+00 0.500000E+01 0.178016E+00 0.104269E+00 0.520000E+01 0.177126E+00 0.103802E+00 0.540000E+01 0.176297E+00 0.103122E+00 4.2.3.4 Thermal Integral Scale tau lamda_tt(x_1) 0.200000E+00 0.367289E+00 0.400000E+00 0.380026E+00 0.600000E+00 0.400071E+00 0.800000E+00 0.424670E+00 0.100000E+01 0.453621E+00 0.120000E+01 0.480407E+00 0.140000E+01 0.501075E+00 0.160000E+01 0.524682E+00 0.180000E+01 0.552549E+00 0.200000E+01 0.581221E+00 0.220000E+01 0.604067E+00 0.240000E+01 0.622591E+00 0.260000E+01 0.636540E+00 0.280000E+01 0.646282E+00 0.300000E+01 0.655493E+00 0.320000E+01 0.668023E+00 0.340000E+01 0.683932E+00 0.360000E+01 0.701689E+00 0.380000E+01 0.718966E+00 0.400000E+01 0.734635E+00 0.420000E+01 0.749068E+00 0.440000E+01 0.762323E+00 0.460000E+01 0.774637E+00 0.480000E+01 0.786756E+00 0.500000E+01 0.799629E+00 0.520000E+01 0.814290E+00 0.540000E+01 0.831515E+00 4.2.3.5 Thermal Two Point Correlation tau 0.200000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.896683E+00 0.174533E+00 0.719412E+00 0.261799E+00 0.562900E+00 0.349066E+00 0.438517E+00 0.436332E+00 0.342982E+00 0.523599E+00 0.270108E+00 0.610865E+00 0.214643E+00 0.698132E+00 0.172070E+00 0.785398E+00 0.137916E+00 0.872665E+00 0.108620E+00 0.959931E+00 0.823022E-01 0.104720E+01 0.589786E-01 0.113446E+01 0.394765E-01 0.122173E+01 0.236047E-01 0.130900E+01 0.114861E-01 0.139626E+01 0.241992E-02 0.148353E+01 -0.586759E-02 0.157080E+01 -0.152804E-01 0.165806E+01 -0.258128E-01 0.174533E+01 -0.362066E-01 0.183260E+01 -0.453140E-01 0.191986E+01 -0.523032E-01 0.200713E+01 -0.580421E-01 0.209440E+01 -0.640471E-01 0.218166E+01 -0.700376E-01 0.226893E+01 -0.752428E-01 0.235619E+01 -0.792520E-01 0.244346E+01 -0.816238E-01 0.253073E+01 -0.830519E-01 0.261799E+01 -0.843884E-01 0.270526E+01 -0.857990E-01 0.279253E+01 -0.871585E-01 0.287979E+01 -0.878505E-01 0.296706E+01 -0.871235E-01 0.305433E+01 -0.853502E-01 tau 0.500000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.945636E+00 0.174533E+00 0.828478E+00 0.261799E+00 0.705523E+00 0.349066E+00 0.597027E+00 0.436332E+00 0.505900E+00 0.523599E+00 0.430078E+00 0.610865E+00 0.366407E+00 0.698132E+00 0.311616E+00 0.785398E+00 0.262972E+00 0.872665E+00 0.218905E+00 0.959931E+00 0.178948E+00 0.104720E+01 0.143434E+00 0.113446E+01 0.112725E+00 0.122173E+01 0.865209E-01 0.130900E+01 0.637497E-01 0.139626E+01 0.429177E-01 0.148353E+01 0.228893E-01 0.157080E+01 0.324218E-02 0.165806E+01 -0.158000E-01 0.174533E+01 -0.336460E-01 0.183260E+01 -0.500877E-01 0.191986E+01 -0.652779E-01 0.200713E+01 -0.791772E-01 0.209440E+01 -0.914874E-01 0.218166E+01 -0.101801E+00 0.226893E+01 -0.109802E+00 0.235619E+01 -0.115380E+00 0.244346E+01 -0.118738E+00 0.253073E+01 -0.120621E+00 0.261799E+01 -0.122161E+00 0.270526E+01 -0.124427E+00 0.279253E+01 -0.127700E+00 0.287979E+01 -0.131248E+00 0.296706E+01 -0.134105E+00 0.305433E+01 -0.135803E+00 4.2.3.6 One Dimensional Energy Spectrum tau 0.200000E+01 k_1 E_tt(k_1) 0.0 0.202646E-01 0.100000E+01 0.309256E-01 0.200000E+01 0.181605E-01 0.300000E+01 0.122421E-01 0.400000E+01 0.908686E-02 0.500000E+01 0.636377E-02 0.600000E+01 0.477491E-02 0.700000E+01 0.371068E-02 0.800000E+01 0.294411E-02 0.900000E+01 0.218182E-02 0.100000E+02 0.160501E-02 0.110000E+02 0.120305E-02 0.120000E+02 0.110654E-02 0.130000E+02 0.838069E-03 0.140000E+02 0.688058E-03 0.150000E+02 0.564610E-03 0.160000E+02 0.483744E-03 0.170000E+02 0.383961E-03 0.180000E+02 0.324506E-03 0.190000E+02 0.264914E-03 0.200000E+02 0.227550E-03 0.210000E+02 0.194266E-03 0.220000E+02 0.171000E-03 0.230000E+02 0.139735E-03 0.240000E+02 0.114480E-03 0.250000E+02 0.980748E-04 0.260000E+02 0.822598E-04 0.270000E+02 0.709935E-04 0.280000E+02 0.624475E-04 0.290000E+02 0.519394E-04 0.300000E+02 0.441589E-04 0.310000E+02 0.391257E-04 0.320000E+02 0.337320E-04 0.330000E+02 0.296027E-04 0.340000E+02 0.250216E-04 0.350000E+02 0.214701E-04 0.360000E+02 0.186472E-04 0.370000E+02 0.165627E-04 0.380000E+02 0.142210E-04 0.390000E+02 0.127560E-04 0.400000E+02 0.112173E-04 0.410000E+02 0.101363E-04 0.420000E+02 0.954757E-05 0.430000E+02 0.919757E-05 0.440000E+02 0.878265E-05 0.450000E+02 0.885338E-05 0.460000E+02 0.900808E-05 0.470000E+02 0.923350E-05 tau 0.500000E+01 k_1 E_tt(k_1) 0.0 0.595715E-01 0.100000E+01 0.883825E-01 0.200000E+01 0.405097E-01 0.300000E+01 0.223438E-01 0.400000E+01 0.154751E-01 0.500000E+01 0.101680E-01 0.600000E+01 0.646326E-02 0.700000E+01 0.544795E-02 0.800000E+01 0.381207E-02 0.900000E+01 0.296839E-02 0.100000E+02 0.205813E-02 0.110000E+02 0.140854E-02 0.120000E+02 0.115393E-02 0.130000E+02 0.868870E-03 0.140000E+02 0.703866E-03 0.150000E+02 0.515136E-03 0.160000E+02 0.417573E-03 0.170000E+02 0.324842E-03 0.180000E+02 0.251912E-03 0.190000E+02 0.200374E-03 0.200000E+02 0.158905E-03 0.210000E+02 0.126224E-03 0.220000E+02 0.981803E-04 0.230000E+02 0.798829E-04 0.240000E+02 0.636397E-04 0.250000E+02 0.500337E-04 0.260000E+02 0.398976E-04 0.270000E+02 0.326159E-04 0.280000E+02 0.270976E-04 0.290000E+02 0.210450E-04 0.300000E+02 0.168165E-04 0.310000E+02 0.135259E-04 0.320000E+02 0.108938E-04 0.330000E+02 0.886327E-05 0.340000E+02 0.716395E-05 0.350000E+02 0.571027E-05 0.360000E+02 0.471429E-05 0.370000E+02 0.378901E-05 0.380000E+02 0.300767E-05 0.390000E+02 0.245170E-05 0.400000E+02 0.204660E-05 0.410000E+02 0.171362E-05 0.420000E+02 0.137769E-05 0.430000E+02 0.118496E-05 0.440000E+02 0.107482E-05 0.450000E+02 0.104025E-05 0.460000E+02 0.108237E-05 0.470000E+02 0.118914E-05 4.2.4 Pr=0.2 Without Initial Temperature Fluctuations 4.2.4.1 Temperature Variance and Turbulent Het Flux tau tt vt 0.200000E+00 0.785341E-02 0.437130E-01 0.400000E+00 0.222800E-01 0.638576E-01 0.600000E+00 0.377608E-01 0.736300E-01 0.800000E+00 0.529142E-01 0.787363E-01 0.100000E+01 0.673675E-01 0.814083E-01 0.120000E+01 0.810157E-01 0.826975E-01 0.140000E+01 0.939448E-01 0.831653E-01 0.160000E+01 0.106251E+00 0.830702E-01 0.180000E+01 0.117969E+00 0.825886E-01 0.200000E+01 0.129157E+00 0.818869E-01 0.220000E+01 0.139910E+00 0.810871E-01 0.240000E+01 0.150305E+00 0.802336E-01 0.260000E+01 0.160392E+00 0.793417E-01 0.280000E+01 0.170209E+00 0.784450E-01 0.300000E+01 0.179804E+00 0.775790E-01 0.320000E+01 0.189223E+00 0.767612E-01 0.340000E+01 0.198504E+00 0.759969E-01 0.360000E+01 0.207666E+00 0.752854E-01 0.380000E+01 0.216716E+00 0.746204E-01 0.400000E+01 0.225648E+00 0.739943E-01 0.420000E+01 0.234464E+00 0.734039E-01 0.440000E+01 0.243171E+00 0.728503E-01 0.460000E+01 0.251789E+00 0.723346E-01 0.480000E+01 0.260334E+00 0.718545E-01 0.500000E+01 0.268810E+00 0.714038E-01 0.520000E+01 0.277204E+00 0.709730E-01 0.540000E+01 0.285488E+00 0.705519E-01 4.2.4.2 vt Budget tau P_vt phi_vt D_tt 0.200000E+00 0.263467E+00 -0.265364E-01 0.925704E-01 0.400000E+00 0.217766E+00 -0.456064E-01 0.104804E+00 0.600000E+00 0.182805E+00 -0.501243E-01 0.986554E-01 0.800000E+00 0.156073E+00 -0.483749E-01 0.897076E-01 0.100000E+01 0.135236E+00 -0.449048E-01 0.813655E-01 0.120000E+01 0.118613E+00 -0.405132E-01 0.742267E-01 0.140000E+01 0.105073E+00 -0.364722E-01 0.680098E-01 0.160000E+01 0.938294E-01 -0.331545E-01 0.623994E-01 0.180000E+01 0.843484E-01 -0.301813E-01 0.573834E-01 0.200000E+01 0.763056E-01 -0.272868E-01 0.529514E-01 0.220000E+01 0.694457E-01 -0.246249E-01 0.490622E-01 0.240000E+01 0.635411E-01 -0.223946E-01 0.456095E-01 0.260000E+01 0.584201E-01 -0.205381E-01 0.424563E-01 0.280000E+01 0.539546E-01 -0.189019E-01 0.395412E-01 0.300000E+01 0.500393E-01 -0.174202E-01 0.368880E-01 0.320000E+01 0.465907E-01 -0.160821E-01 0.345107E-01 0.340000E+01 0.435484E-01 -0.148943E-01 0.323800E-01 0.360000E+01 0.408608E-01 -0.138698E-01 0.304593E-01 0.380000E+01 0.384766E-01 -0.130032E-01 0.287254E-01 0.400000E+01 0.363499E-01 -0.122607E-01 0.271561E-01 0.420000E+01 0.344453E-01 -0.116027E-01 0.257280E-01 0.440000E+01 0.327350E-01 -0.110039E-01 0.244261E-01 0.460000E+01 0.311934E-01 -0.104554E-01 0.232438E-01 0.480000E+01 0.297961E-01 -0.995874E-02 0.221759E-01 0.500000E+01 0.285212E-01 -0.952031E-02 0.212132E-01 0.520000E+01 0.273497E-01 -0.914420E-02 0.203429E-01 0.540000E+01 0.262663E-01 -0.882800E-02 0.195500E-01 4.2.4.3 tt Budget tau P_tt D_tt 0.200000E+00 0.874259E-01 0.237290E-01 0.400000E+00 0.127715E+00 0.509638E-01 0.600000E+00 0.147260E+00 0.702144E-01 0.800000E+00 0.157473E+00 0.832927E-01 0.100000E+01 0.162817E+00 0.925873E-01 0.120000E+01 0.165395E+00 0.990722E-01 0.140000E+01 0.166331E+00 0.103296E+00 0.160000E+01 0.166140E+00 0.106111E+00 0.180000E+01 0.165177E+00 0.107987E+00 0.200000E+01 0.163774E+00 0.109007E+00 0.220000E+01 0.162174E+00 0.109359E+00 0.240000E+01 0.160467E+00 0.109296E+00 0.260000E+01 0.158683E+00 0.108961E+00 0.280000E+01 0.156890E+00 0.108404E+00 0.300000E+01 0.155158E+00 0.107664E+00 0.320000E+01 0.153522E+00 0.106799E+00 0.340000E+01 0.151994E+00 0.105896E+00 0.360000E+01 0.150571E+00 0.105041E+00 0.380000E+01 0.149241E+00 0.104284E+00 0.400000E+01 0.147989E+00 0.103622E+00 0.420000E+01 0.146808E+00 0.103014E+00 0.440000E+01 0.145701E+00 0.102405E+00 0.460000E+01 0.144669E+00 0.101773E+00 0.480000E+01 0.143709E+00 0.101153E+00 0.500000E+01 0.142808E+00 0.100616E+00 0.520000E+01 0.141946E+00 0.100225E+00 0.540000E+01 0.141104E+00 0.100005E+00 4.2.4.4 Thermal Integral Scale tau Lamda_tt(x_1) 0.200000E+00 0.414261E+00 0.400000E+00 0.447871E+00 0.600000E+00 0.481770E+00 0.800000E+00 0.518679E+00 0.100000E+01 0.557321E+00 0.120000E+01 0.592218E+00 0.140000E+01 0.623438E+00 0.160000E+01 0.655217E+00 0.180000E+01 0.688910E+00 0.200000E+01 0.721037E+00 0.220000E+01 0.748031E+00 0.240000E+01 0.769571E+00 0.260000E+01 0.786418E+00 0.280000E+01 0.800389E+00 0.300000E+01 0.814328E+00 0.320000E+01 0.830186E+00 0.340000E+01 0.848240E+00 0.360000E+01 0.867798E+00 0.380000E+01 0.888200E+00 0.400000E+01 0.909209E+00 0.420000E+01 0.930735E+00 0.440000E+01 0.952703E+00 0.460000E+01 0.975264E+00 0.480000E+01 0.998744E+00 0.500000E+01 0.102337E+01 0.520000E+01 0.104917E+01 0.540000E+01 0.107598E+01 4.2.4.5 Thermal Two Point Correlation tau 0.200000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.967729E+00 0.174533E+00 0.883171E+00 0.261799E+00 0.771780E+00 0.349066E+00 0.655384E+00 0.436332E+00 0.546561E+00 0.523599E+00 0.450512E+00 0.610865E+00 0.368126E+00 0.698132E+00 0.298157E+00 0.785398E+00 0.238521E+00 0.872665E+00 0.187145E+00 0.959931E+00 0.142541E+00 0.104720E+01 0.103960E+00 0.113446E+01 0.711057E-01 0.122173E+01 0.437251E-01 0.130900E+01 0.212350E-01 0.139626E+01 0.251888E-02 0.148353E+01 -0.138270E-01 0.157080E+01 -0.289335E-01 0.165806E+01 -0.433006E-01 0.174533E+01 -0.569052E-01 0.183260E+01 -0.695846E-01 0.191986E+01 -0.813445E-01 0.200713E+01 -0.923876E-01 0.209440E+01 -0.102905E+00 0.218166E+01 -0.112889E+00 0.226893E+01 -0.122100E+00 0.235619E+01 -0.130190E+00 0.244346E+01 -0.136919E+00 0.253073E+01 -0.142258E+00 0.261799E+01 -0.146327E+00 0.270526E+01 -0.149325E+00 0.279253E+01 -0.151502E+00 0.287979E+01 -0.153109E+00 0.296706E+01 -0.154312E+00 0.305433E+01 -0.155113E+00 tau 0.500000E+01 x_1 R_tt(x_1) 0.0 0.100000E+01 0.872665E-01 0.985245E+00 0.174533E+00 0.943755E+00 0.261799E+00 0.882421E+00 0.349066E+00 0.809278E+00 0.436332E+00 0.731161E+00 0.523599E+00 0.652792E+00 0.610865E+00 0.576897E+00 0.698132E+00 0.504777E+00 0.785398E+00 0.436908E+00 0.872665E+00 0.373408E+00 0.959931E+00 0.314310E+00 0.104720E+01 0.259647E+00 0.113446E+01 0.209406E+00 0.122173E+01 0.163435E+00 0.130900E+01 0.121404E+00 0.139626E+01 0.828558E-01 0.148353E+01 0.473337E-01 0.157080E+01 0.144742E-01 0.165806E+01 -0.159574E-01 0.174533E+01 -0.440855E-01 0.183260E+01 -0.699574E-01 0.191986E+01 -0.935647E-01 0.200713E+01 -0.114853E+00 0.209440E+01 -0.133748E+00 0.218166E+01 -0.150208E+00 0.226893E+01 -0.164294E+00 0.235619E+01 -0.176212E+00 0.244346E+01 -0.186290E+00 0.253073E+01 -0.194899E+00 0.261799E+01 -0.202347E+00 0.270526E+01 -0.208802E+00 0.279253E+01 -0.214269E+00 0.287979E+01 -0.218655E+00 0.296706E+01 -0.221851E+00 0.305433E+01 -0.223789E+00 4.2.4.6 One Dimensional Energy Spectrum tau 0.200000E+01 k_1 E_tt(k_1) 0.0 0.148217E-01 0.100000E+01 0.255668E-01 0.200000E+01 0.127028E-01 0.300000E+01 0.752974E-02 0.400000E+01 0.448997E-02 0.500000E+01 0.247621E-02 0.600000E+01 0.158477E-02 0.700000E+01 0.103918E-02 0.800000E+01 0.667534E-03 0.900000E+01 0.419074E-03 0.100000E+02 0.226494E-03 0.110000E+02 0.147267E-03 0.120000E+02 0.107367E-03 0.130000E+02 0.723995E-04 0.140000E+02 0.440679E-04 0.150000E+02 0.305265E-04 0.160000E+02 0.203331E-04 0.170000E+02 0.141233E-04 0.180000E+02 0.915366E-05 0.190000E+02 0.604476E-05 0.200000E+02 0.420984E-05 0.210000E+02 0.297675E-05 0.220000E+02 0.211253E-05 0.230000E+02 0.148773E-05 0.240000E+02 0.956846E-06 0.250000E+02 0.657413E-06 0.260000E+02 0.476691E-06 0.270000E+02 0.318267E-06 0.280000E+02 0.241645E-06 0.290000E+02 0.170251E-06 0.300000E+02 0.116765E-06 0.310000E+02 0.839634E-07 0.320000E+02 0.617651E-07 0.330000E+02 0.439151E-07 0.340000E+02 0.322826E-07 0.350000E+02 0.230711E-07 0.360000E+02 0.177231E-07 0.370000E+02 0.127243E-07 0.380000E+02 0.900476E-08 0.390000E+02 0.684902E-08 0.400000E+02 0.501632E-08 0.410000E+02 0.381887E-08 0.420000E+02 0.293870E-08 0.430000E+02 0.252375E-08 0.440000E+02 0.191465E-08 0.450000E+02 0.163666E-08 0.460000E+02 0.143691E-08 0.470000E+02 0.118657E-08 tau 0.500000E+01 k_1 E_tt(k_1) 0.0 0.437825E-01 0.100000E+01 0.693554E-01 0.200000E+01 0.238761E-01 0.300000E+01 0.959958E-02 0.400000E+01 0.472608E-02 0.500000E+01 0.234293E-02 0.600000E+01 0.109127E-02 0.700000E+01 0.716470E-03 0.800000E+01 0.381653E-03 0.900000E+01 0.198381E-03 0.100000E+02 0.108568E-03 0.110000E+02 0.466190E-04 0.120000E+02 0.301633E-04 0.130000E+02 0.174563E-04 0.140000E+02 0.100611E-04 0.150000E+02 0.544464E-05 0.160000E+02 0.303150E-05 0.170000E+02 0.182689E-05 0.180000E+02 0.103611E-05 0.190000E+02 0.703357E-06 0.200000E+02 0.365584E-06 0.210000E+02 0.232450E-06 0.220000E+02 0.129763E-06 0.230000E+02 0.824247E-07 0.240000E+02 0.549608E-07 0.250000E+02 0.322825E-07 0.260000E+02 0.196745E-07 0.270000E+02 0.121291E-07 0.280000E+02 0.785428E-08 0.290000E+02 0.478346E-08 0.300000E+02 0.307275E-08 0.310000E+02 0.188117E-08 0.320000E+02 0.126240E-08 0.330000E+02 0.790091E-09 0.340000E+02 0.492545E-09 0.350000E+02 0.331678E-09 0.360000E+02 0.219689E-09 0.370000E+02 0.135258E-09 0.380000E+02 0.921948E-10 0.390000E+02 0.616987E-10 0.400000E+02 0.399294E-10 0.410000E+02 0.278110E-10 0.420000E+02 0.188854E-10 0.430000E+02 0.126663E-10 0.440000E+02 0.896347E-11 0.450000E+02 0.722703E-11 0.460000E+02 0.535594E-11 0.470000E+02 0.505562E-11 5. References 5.1 Iida, O., and Kasagi, N., "Direct Numerical Simulation of Homogeneous Isotropic Turbulence with Scalar Transport," Preprint of the 69th JSME Ann. Meeting, Nagoya, 1991, Vol. B, pp. 425-427. 5.2 Iida, O., and Kasagi, N., "Plandtl Number Effect on Scalar Transport in Homogeneous Isotropic Turbulence," Proc. of the 5th Symposium of Numeical Fluid Dynamics, Tokyo, 1991, pp. 307-310. (EOF)