******************************************************************************** ******************************************************************************** ********** ********** ********** "Data-Base on Turbulent Heat Transfer" ********** ********** ********** ********** Supported by the Ministry of Education, ********** ********** Science and Culture ********** ********** ********** ********** 1991 ********** ********** ********** ********** ********** ********** ********** ********** Y. Nagano (Organizer) ********** ********** ********** ********** N. Kasagi, T. Ota, H. Fujita, H. Yoshida, M. Kumada ********** ********** ********** ******************************************************************************** ******************************************************************************** ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++ << NOTICE >> ++++++++++ ++++++++++ ++++++++++ ++++++++++ All rights are reserved by the presenters 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: ++++++++++ ++++++++++ ++++++++++ ++++++++++ Y. Nagano ++++++++++ ++++++++++ Department of Mechanical Engineering ++++++++++ ++++++++++ Nagoya Institute of Technology ++++++++++ ++++++++++ Gokiso-cho, Showa-ku, Nagoya 466 ++++++++++ ++++++++++ Japan. ++++++++++ ++++++++++ ++++++++++ ++++++++++ March 1992 ++++++++++ ++++++++++ ++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1. DATA No. (FILE NAME) NW_BL008 2. KEY WORDS Natural Convection, Turbulent Boundary Layer, Reynolds Stress, Turbulent Heat Flux, Hot-Wire Measurement 3. DATA TAKERS AND ARTICLE TITLE a. T. Tsuji and Y. Nagano b. Dep. of Mech. Eng., Nagoya Institute of Technology Gokiso-cho, Showa-ku, Nagoya 466 c. Thermally Driven Turbulent Boundary Layer d. 8th Symposium on Turbulent Shear Flows Technical University of Munich (September 9-11, 1991) e. Vol. 2, 24.3.1-24.3.6 (1991) 4. ABSTRACT The budgets of turbulent energy, Reynolds shear stress, mean square scalar variance and turbulent heat fluxes have have been evaluated on the basis of velocity and temperature measurements (refs. [1] and [2]) in a thermally driven boundary layer in air along a vertical flat plate. In the near-wall region, the velocity-gradient correlation plays an important role in turbulent energy production and thermal energy is directly converted into kinetic energy through this corre- lation. Consequently, Reynolds shear stress and streamwise turbulent heat flux near the wall, which are normally considered to have close relations with the energy produc- tion process, behave differently from those in the ordinary turbulent boundary layers. On the other hand, the energy transfer in the outer region of the boundary layer becomes a process similar to that observed in the usual boundary layer. 5. INSTRUMENTATION The flat surface generating flow was a copper plate 4 m high, 1 m wide and 2 mm thick. Two V-shaped hot-wires in an X-array and a cold-wire were used to measure fluid velocity and temperature. The V-shaped hot-wire was constructed by symmetrically bending a 0.0031 mm dia. and 1.5 mm long tungsten wire at the center. The cold-wire of 0.0031 mm dia. and 3.5 mm long tungsten wire located upstream of the hot-wires for temperature compensation (refs. [1] and [2]). 6. EXPERIMENTAL PARAMETERS *** Test conditions *** Comments x [m] 2.536 : Vertical location Tw [deg.C] 60.63 : Wall temp. Ta [deg.C] 15.29 : Ambient temp. Pa [Pa] 1.017E05 : Atom. pres. Grx 8.986E10 : Grashof no. Pr 0.710 : Prandtl no. Physical properties were evaluated at the film temperature (=(Tw+Ta)/2), except that the body expansion coefficient B was defined as 1/(273.15+Ta). Ambient temperature increased at the rate of about 0.6 deg.C/m in the vertical direction. 7. NOMENCLATURE cp - Specific heat at constant pressure E - Dissipation rate of mean flow energy g - Acceleration of gravity k - Turbulent energy = (u**2+v**2+w**2)/2 p - Pressure fluctuation qw - Wall heat flux T - Mean temperature t - Temperature fluctuation t* - Friction temperature = qw/Rcpu* U - Mean streamwise velocity u - Streamwise velocity fluctuation ut - Streamwise turbulent heat flux uv - Reynolds shear stress u* - Friction velocity = (Fw/R)**(1/2) V - Mean normal-to-wall velocity v - Normal-to-wall velocity fluctuation vt - Normal-to-wall turbulent heat flux w - Spanwise velocity fluctuation x - Streamwise direction y - Normal-to-wall direction y+ - Dimensionless distance = u*y/N z - Spanwise direction a - Thermal difusivity B - Volumetric expansion coefficient = 1/(273.15+Ta) e - Dissipation rate of k eu - Dissipation rates of u**2/2 ev - Dissipation rates of v**2/2 et - Dissipation rates of t**2/2 N - Kinematic viscosity R - Density Tauu- Time-scale of velocity field, k/e Taut- Time-scale of thermal field, (t**2/2)/et Fw - Wall shear stress Abbreviations for evaluated terms of the transport equations AD - Advection BP - Buoyancy production CVP - Velocity-pressure gradient correlation CTP - Temperature-pressure gradient correlation DIS - Dissipation (destruction) MD - Molecular diffusion PD - Production TD - Turbulent diffusion 8. DATA Grx=8.986E+10, Tw=60.63 deg.C, Ta=15.29 deg.C, Pr=0.710 u*=0.07049 m/s (u*: Friction velocity) t*=2.866 deg.C (t*: Friction temperature) N=1.6727E-05 m**2/s (N: Kinematic viscosity) y+=u*y/N, U+=U/u*, V+=V/u*, T+=(Tw-T)/t* In evaluating u* and t*, the wall shear stress Fw and the wall heat flux were estimated from the following experimental formulas (ref. [1]): Fw/(RUb**2)=0.684Grx**(1/11.9) Nux=0.120(Grx.Pr)**(1/3) where Nux is the Nusselt number, R is the density and Ub is the reference velocity defined as [gB(Tw-Ta)N]**(1/3). a. Balance of mean flow energy (U**2/2) (Each term is normalized by (u*)**4/N.) y+ AD PD TD MD DIS(E) BP 1 3.870E+00 -5.008E-04 2.559E-02 -4.897E-02 3.593E-01 -5.329E-01 2.000E-01 2 4.838E+00 -9.337E-04 2.794E-02 -4.258E-02 2.542E-01 -4.692E-01 2.309E-01 3 5.805E+00 -1.581E-03 2.704E-02 -3.220E-02 1.469E-01 -3.969E-01 2.555E-01 4 6.773E+00 -2.430E-03 2.486E-02 -2.289E-02 5.833E-02 -3.306E-01 2.742E-01 5 7.740E+00 -3.471E-03 2.221E-02 -1.509E-02 -1.882E-02 -2.756E-01 2.884E-01 6 8.708E+00 -4.734E-03 1.940E-02 -1.666E-02 -7.442E-02 -2.256E-01 2.988E-01 7 9.675E+00 -6.332E-03 1.697E-02 -2.513E-02 -1.185E-01 -1.688E-01 3.059E-01 8 1.169E+01 -9.274E-03 1.522E-02 -3.466E-02 -1.753E-01 -1.072E-01 3.117E-01 9 1.372E+01 -1.279E-02 1.325E-02 -4.303E-02 -2.086E-01 -6.464E-02 3.102E-01 10 1.576E+01 -1.682E-02 1.152E-02 -6.730E-02 -1.955E-01 -3.488E-02 3.026E-01 11 1.781E+01 -2.100E-02 1.025E-02 -1.033E-01 -1.612E-01 -1.675E-02 2.906E-01 12 1.987E+01 -2.420E-02 9.841E-03 -1.340E-01 -1.113E-01 -8.672E-03 2.770E-01 13 2.298E+01 -2.722E-02 1.055E-02 -1.547E-01 -8.291E-02 -4.676E-03 2.588E-01 14 2.610E+01 -2.967E-02 1.071E-02 -1.590E-01 -6.185E-02 -2.754E-03 2.446E-01 15 3.028E+01 -3.289E-02 9.475E-03 -1.560E-01 -4.576E-02 -1.227E-03 2.276E-01 16 3.554E+01 -3.714E-02 5.129E-03 -1.449E-01 -3.223E-02 -2.155E-04 2.090E-01 17 4.083E+01 -3.966E-02 1.549E-03 -1.351E-01 -2.057E-02 -1.333E-05 1.944E-01 18 4.614E+01 -4.099E-02 -4.507E-04 -1.266E-01 -1.478E-02 -8.257E-07 1.828E-01 19 5.147E+01 -4.247E-02 -3.234E-03 -1.164E-01 -9.562E-03 -3.285E-05 1.723E-01 20 6.220E+01 -4.445E-02 -8.365E-03 -9.620E-02 -5.633E-03 -1.472E-04 1.543E-01 21 7.300E+01 -4.522E-02 -1.216E-02 -7.938E-02 -2.971E-03 -2.306E-04 1.396E-01 22 8.386E+01 -4.492E-02 -1.441E-02 -6.659E-02 -1.470E-03 -2.559E-04 1.275E-01 23 9.477E+01 -4.416E-02 -1.579E-02 -5.593E-02 -6.689E-04 -2.536E-04 1.167E-01 24 1.057E+02 -4.353E-02 -1.719E-02 -4.626E-02 -2.351E-04 -2.562E-04 1.072E-01 25 1.278E+02 -4.202E-02 -1.940E-02 -3.044E-02 7.918E-05 -2.550E-04 9.123E-02 26 1.500E+02 -4.037E-02 -2.085E-02 -1.854E-02 1.708E-04 -2.451E-04 7.956E-02 27 1.723E+02 -3.866E-02 -2.195E-02 -9.110E-03 2.635E-04 -2.359E-04 6.948E-02 28 1.947E+02 -3.701E-02 -2.274E-02 -1.079E-03 2.874E-04 -2.272E-04 6.059E-02 29 2.172E+02 -3.531E-02 -2.325E-02 5.681E-03 3.262E-04 -2.190E-04 5.255E-02 30 2.398E+02 -3.337E-02 -2.317E-02 1.077E-02 3.210E-04 -2.050E-04 4.541E-02 31 2.625E+02 -3.145E-02 -2.288E-02 1.458E-02 3.125E-04 -1.916E-04 3.951E-02 32 2.852E+02 -2.957E-02 -2.242E-02 1.743E-02 2.989E-04 -1.789E-04 3.432E-02 33 3.080E+02 -2.773E-02 -2.182E-02 1.957E-02 2.804E-04 -1.668E-04 2.976E-02 34 3.309E+02 -2.591E-02 -2.107E-02 2.097E-02 2.462E-04 -1.548E-04 2.577E-02 35 3.653E+02 -2.333E-02 -1.985E-02 2.216E-02 2.107E-04 -1.388E-04 2.085E-02 36 3.999E+02 -2.127E-02 -1.894E-02 2.305E-02 1.920E-04 -1.300E-04 1.695E-02 37 4.461E+02 -1.867E-02 -1.772E-02 2.337E-02 1.899E-04 -1.214E-04 1.269E-02 38 5.042E+02 -1.511E-02 -1.536E-02 2.171E-02 1.604E-04 -1.029E-04 8.514E-03 39 5.625E+02 -1.159E-02 -1.256E-02 1.864E-02 1.316E-04 -7.999E-05 5.480E-03 40 6.210E+02 -8.959E-03 -1.028E-02 1.572E-02 1.018E-04 -6.405E-05 3.481E-03 41 6.798E+02 -6.714E-03 -8.285E-03 1.299E-02 8.275E-05 -5.118E-05 1.981E-03 42 7.387E+02 -4.871E-03 -6.414E-03 1.026E-02 5.896E-05 -3.882E-05 1.071E-03 43 7.978E+02 -3.521E-03 -5.013E-03 8.085E-03 4.534E-05 -3.090E-05 4.713E-04 44 8.570E+02 -2.517E-03 -3.911E-03 6.273E-03 3.625E-05 -2.555E-05 1.544E-04 45 9.164E+02 -1.705E-03 -3.006E-03 4.732E-03 3.168E-05 -2.149E-05 4.808E-05 46 1.036E+03 -4.789E-04 -1.438E-03 2.179E-03 1.531E-05 -1.129E-05 1.630E-06 47 1.155E+03 0.000E+00 -4.375E-04 5.521E-04 1.664E-06 -1.664E-06 0.000E+00 b. Balance of streamwise turbulent energy component (u**2/2) (Each term is normalized by (u*)**4/N.) y+ AD PD TD CVP MD DIS(eu) BP 1 3.870E+00 -1.604E-05 -2.914E-03 0.000E+00 -9.227E-03 1.947E-02 -7.181E-03 -1.339E-04 2 4.838E+00 -3.181E-05 -6.065E-03 2.951E-04 6.502E-04 1.175E-02 -6.414E-03 -1.836E-04 3 5.805E+00 -5.492E-05 -9.720E-03 1.239E-03 9.929E-03 4.570E-03 -5.804E-03 -1.592E-04 4 6.773E+00 -8.614E-05 -1.202E-02 2.520E-03 1.615E-02 -1.165E-03 -5.330E-03 -6.294E-05 5 7.740E+00 -1.258E-04 -1.401E-02 3.397E-03 2.090E-02 -5.342E-03 -4.923E-03 1.076E-04 6 8.708E+00 -1.703E-04 -1.534E-02 3.878E-03 2.336E-02 -7.404E-03 -4.675E-03 3.514E-04 7 9.675E+00 -2.348E-04 -1.571E-02 4.394E-03 2.286E-02 -7.554E-03 -4.426E-03 6.670E-04 8 1.169E+01 -3.214E-04 -1.575E-02 4.844E-03 2.174E-02 -7.938E-03 -4.336E-03 1.762E-03 9 1.372E+01 -4.091E-04 -1.555E-02 4.908E-03 1.948E-02 -7.092E-03 -4.426E-03 3.097E-03 10 1.576E+01 -4.928E-04 -1.515E-02 4.480E-03 1.754E-02 -6.117E-03 -4.652E-03 4.390E-03 11 1.781E+01 -5.715E-04 -1.486E-02 4.145E-03 1.531E-02 -4.730E-03 -4.901E-03 5.615E-03 12 1.987E+01 -6.490E-04 -1.451E-02 3.943E-03 1.316E-02 -3.594E-03 -5.104E-03 6.746E-03 13 2.298E+01 -7.212E-04 -1.397E-02 3.817E-03 1.049E-02 -2.428E-03 -5.375E-03 8.182E-03 14 2.610E+01 -7.892E-04 -1.229E-02 3.617E-03 7.734E-03 -1.787E-03 -5.601E-03 9.114E-03 15 3.028E+01 -8.558E-04 -9.709E-03 3.507E-03 4.198E-03 -1.158E-03 -5.849E-03 9.868E-03 16 3.554E+01 -9.095E-04 -6.661E-03 3.549E-03 6.359E-04 -7.811E-04 -6.120E-03 1.029E-02 17 4.083E+01 -9.467E-04 -3.774E-03 3.773E-03 -2.655E-03 -5.197E-04 -6.301E-03 1.042E-02 18 4.614E+01 -9.723E-04 -5.906E-04 3.582E-03 -5.570E-03 -3.520E-04 -6.481E-03 1.038E-02 19 5.147E+01 -9.984E-04 2.935E-03 2.783E-03 -8.123E-03 -2.504E-04 -6.617E-03 1.027E-02 20 6.220E+01 -1.022E-03 6.461E-03 1.536E-03 -9.885E-03 -1.659E-04 -6.843E-03 9.918E-03 21 7.300E+01 -1.034E-03 9.365E-03 3.330E-04 -1.109E-02 -1.179E-04 -6.956E-03 9.502E-03 22 8.386E+01 -1.040E-03 1.171E-02 -5.683E-04 -1.200E-02 -8.778E-05 -7.069E-03 9.058E-03 23 9.477E+01 -1.048E-03 1.394E-02 -1.276E-03 -1.303E-02 -6.804E-05 -7.136E-03 8.618E-03 24 1.057E+02 -1.062E-03 1.600E-02 -1.860E-03 -1.404E-02 -5.271E-05 -7.181E-03 8.198E-03 25 1.278E+02 -1.079E-03 1.783E-02 -2.416E-03 -1.444E-02 -3.867E-05 -7.294E-03 7.447E-03 26 1.500E+02 -1.090E-03 1.907E-02 -2.815E-03 -1.458E-02 -2.946E-05 -7.340E-03 6.787E-03 27 1.723E+02 -1.097E-03 1.985E-02 -3.112E-03 -1.445E-02 -2.158E-05 -7.362E-03 6.194E-03 28 1.947E+02 -1.102E-03 2.017E-02 -3.266E-03 -1.407E-02 -2.552E-05 -7.385E-03 5.682E-03 29 2.172E+02 -1.133E-03 2.010E-02 -3.432E-03 -1.332E-02 -2.095E-05 -7.430E-03 5.234E-03 30 2.398E+02 -1.199E-03 1.974E-02 -3.649E-03 -1.227E-02 -2.525E-05 -7.430E-03 4.830E-03 31 2.625E+02 -1.263E-03 1.917E-02 -3.768E-03 -1.116E-02 -1.641E-05 -7.430E-03 4.461E-03 32 2.852E+02 -1.323E-03 1.845E-02 -3.731E-03 -1.009E-02 -1.939E-05 -7.430E-03 4.137E-03 33 3.080E+02 -1.386E-03 1.751E-02 -3.407E-03 -9.081E-03 -1.417E-05 -7.452E-03 3.835E-03 34 3.309E+02 -1.459E-03 1.640E-02 -2.906E-03 -8.124E-03 -1.406E-05 -7.452E-03 3.555E-03 35 3.653E+02 -1.539E-03 1.501E-02 -2.228E-03 -6.963E-03 -1.041E-05 -7.452E-03 3.182E-03 36 3.999E+02 -1.618E-03 1.312E-02 -1.406E-03 -5.479E-03 -7.549E-06 -7.452E-03 2.840E-03 37 4.461E+02 -1.678E-03 1.078E-02 -4.154E-04 -3.662E-03 -4.267E-06 -7.452E-03 2.430E-03 38 5.042E+02 -1.690E-03 8.245E-03 6.432E-04 -1.745E-03 -1.189E-06 -7.430E-03 1.978E-03 39 5.625E+02 -1.669E-03 6.016E-03 1.494E-03 -1.084E-04 2.688E-07 -7.317E-03 1.584E-03 40 6.210E+02 -1.618E-03 4.197E-03 1.919E-03 1.301E-03 2.572E-06 -7.046E-03 1.245E-03 41 6.798E+02 -1.524E-03 2.827E-03 1.924E-03 2.397E-03 5.209E-06 -6.572E-03 9.434E-04 42 7.387E+02 -1.371E-03 1.850E-03 1.694E-03 2.805E-03 8.375E-06 -5.646E-03 6.594E-04 43 7.978E+02 -1.149E-03 1.179E-03 1.365E-03 2.369E-03 1.044E-05 -4.178E-03 4.040E-04 44 8.570E+02 -8.842E-04 7.223E-04 1.010E-03 1.669E-03 1.036E-05 -2.710E-03 1.827E-04 45 9.164E+02 -5.697E-04 4.213E-04 6.897E-04 8.773E-04 9.596E-06 -1.468E-03 3.971E-05 46 1.036E+03 -2.644E-04 2.717E-05 2.855E-04 8.209E-05 5.196E-06 -1.355E-04 0.000E+00 47 1.155E+03 -8.958E-06 -4.440E-08 9.718E-05 -8.936E-05 1.185E-06 0.000E+00 0.000E+00 c. Balance of normal-to-wall turbulent energy component (v**2/2) (Each term is normalized by (u*)**4/N. Although the production term PD (=v**2dV/dy) can be neglected with boundary layer approximation, this term is included in the evaluation.) y+ AD PD TD CVP MD DIS(ev) 1 3.870E+00 1.429E-05 1.290E-05 -4.338E-03 6.603E-03 4.889E-03 -7.181E-03 2 4.838E+00 2.315E-05 2.448E-05 -9.189E-03 1.665E-02 -1.094E-03 -6.414E-03 3 5.805E+00 2.897E-05 4.096E-05 -1.333E-02 2.554E-02 -6.482E-03 -5.804E-03 4 6.773E+00 2.779E-05 5.908E-05 -1.542E-02 2.890E-02 -8.232E-03 -5.330E-03 5 7.740E+00 2.213E-05 7.461E-05 -1.577E-02 2.734E-02 -6.752E-03 -4.923E-03 6 8.708E+00 1.668E-05 8.788E-05 -1.476E-02 2.392E-02 -4.588E-03 -4.675E-03 7 9.675E+00 1.237E-05 1.015E-04 -1.249E-02 1.986E-02 -3.060E-03 -4.426E-03 8 1.169E+01 8.878E-06 1.181E-04 -9.028E-03 1.501E-02 -1.771E-03 -4.336E-03 9 1.372E+01 5.831E-06 1.349E-04 -5.835E-03 1.114E-02 -1.016E-03 -4.426E-03 10 1.576E+01 5.470E-06 1.502E-04 -2.914E-03 7.849E-03 -4.389E-04 -4.652E-03 11 1.781E+01 9.340E-06 1.651E-04 -5.484E-04 5.318E-03 -4.307E-05 -4.901E-03 12 1.987E+01 1.690E-05 1.780E-04 1.441E-03 3.479E-03 -1.148E-05 -5.104E-03 13 2.298E+01 2.910E-05 1.902E-04 3.059E-03 1.925E-03 1.716E-04 -5.375E-03 14 2.610E+01 4.540E-05 2.053E-04 4.137E-03 1.129E-03 8.404E-05 -5.601E-03 15 3.028E+01 6.948E-05 2.251E-04 4.915E-03 4.664E-04 1.727E-04 -5.849E-03 16 3.554E+01 1.022E-04 2.599E-04 5.274E-03 4.007E-04 8.332E-05 -6.120E-03 17 4.083E+01 1.387E-04 2.912E-04 5.227E-03 5.550E-04 8.905E-05 -6.301E-03 18 4.614E+01 1.715E-04 3.254E-04 4.926E-03 1.038E-03 1.978E-05 -6.481E-03 19 5.147E+01 2.102E-04 3.598E-04 4.470E-03 1.557E-03 1.977E-05 -6.617E-03 20 6.220E+01 2.600E-04 4.309E-04 3.978E-03 2.173E-03 8.716E-07 -6.843E-03 21 7.300E+01 3.106E-04 4.991E-04 3.501E-03 2.672E-03 -2.681E-05 -6.956E-03 22 8.386E+01 3.462E-04 5.613E-04 2.986E-03 3.212E-03 -3.745E-05 -7.069E-03 23 9.477E+01 3.522E-04 6.211E-04 2.192E-03 4.024E-03 -5.303E-05 -7.136E-03 24 1.057E+02 3.488E-04 6.678E-04 1.120E-03 5.085E-03 -4.022E-05 -7.181E-03 25 1.278E+02 3.344E-04 7.518E-04 -2.017E-05 6.272E-03 -4.336E-05 -7.294E-03 26 1.500E+02 2.861E-04 8.164E-04 -9.278E-04 7.204E-03 -3.928E-05 -7.340E-03 27 1.723E+02 2.073E-04 8.619E-04 -1.549E-03 7.877E-03 -3.525E-05 -7.362E-03 28 1.947E+02 1.134E-04 8.886E-04 -1.989E-03 8.401E-03 -2.996E-05 -7.385E-03 29 2.172E+02 1.306E-05 9.004E-04 -2.309E-03 8.847E-03 -2.198E-05 -7.430E-03 30 2.398E+02 -7.907E-05 8.959E-04 -2.506E-03 9.135E-03 -1.544E-05 -7.430E-03 31 2.625E+02 -1.406E-04 8.793E-04 -2.599E-03 9.301E-03 -1.082E-05 -7.430E-03 32 2.852E+02 -1.925E-04 8.619E-04 -2.594E-03 9.366E-03 -1.161E-05 -7.430E-03 33 3.080E+02 -2.732E-04 8.420E-04 -2.423E-03 9.318E-03 -1.105E-05 -7.452E-03 34 3.309E+02 -3.907E-04 8.136E-04 -2.035E-03 9.074E-03 -9.605E-06 -7.452E-03 35 3.653E+02 -5.208E-04 7.566E-04 -1.473E-03 8.696E-03 -6.601E-06 -7.452E-03 36 3.999E+02 -6.563E-04 7.029E-04 -9.143E-04 8.325E-03 -5.093E-06 -7.452E-03 37 4.461E+02 -8.033E-04 6.219E-04 -4.285E-04 8.065E-03 -2.363E-06 -7.452E-03 38 5.042E+02 -9.306E-04 5.015E-04 2.113E-05 7.838E-03 3.710E-08 -7.430E-03 39 5.625E+02 -9.854E-04 3.682E-04 4.387E-04 7.493E-03 2.297E-06 -7.317E-03 40 6.210E+02 -9.481E-04 2.581E-04 7.687E-04 6.963E-03 3.963E-06 -7.046E-03 41 6.798E+02 -8.419E-04 1.730E-04 9.361E-04 6.300E-03 4.480E-06 -6.572E-03 42 7.387E+02 -6.875E-04 1.063E-04 9.301E-04 5.292E-03 4.954E-06 -5.646E-03 43 7.978E+02 -5.075E-04 6.542E-05 8.037E-04 3.812E-03 4.096E-06 -4.178E-03 44 8.570E+02 -3.386E-04 4.033E-05 5.972E-04 2.408E-03 3.189E-06 -2.710E-03 45 9.164E+02 -2.119E-04 2.925E-05 3.970E-04 1.252E-03 1.899E-06 -1.468E-03 46 1.036E+03 -1.281E-04 1.420E-05 1.258E-04 1.230E-04 5.543E-07 -1.355E-04 47 1.155E+03 -6.210E-05 3.642E-06 1.791E-05 4.012E-05 4.217E-07 0.000E+00 d. Balance of Raynolds shear stress (uv) (Each term is normalized by (u*)**4/N.) y+ AD PD TD DVP MD BP 1 3.870E+00 6.580E-07 -1.103E-01 4.279E-02 6.613E-02 1.307E-03 7.286E-05 2 4.838E+00 2.143E-06 -1.584E-01 5.607E-02 1.007E-01 1.483E-03 2.077E-04 3 5.805E+00 2.703E-06 -2.029E-01 4.869E-02 1.549E-01 -1.162E-03 3.967E-04 4 6.773E+00 2.977E-06 -2.292E-01 3.098E-02 1.970E-01 4.941E-04 6.381E-04 5 7.740E+00 4.493E-06 -2.324E-01 1.475E-02 2.169E-01 -1.562E-04 9.161E-04 6 8.708E+00 5.047E-06 -2.212E-01 8.853E-03 2.122E-01 -1.052E-03 1.188E-03 7 9.675E+00 5.376E-06 -1.969E-01 6.901E-03 1.883E-01 2.166E-04 1.528E-03 8 1.169E+01 8.845E-06 -1.608E-01 1.420E-03 1.566E-01 8.851E-04 1.954E-03 9 1.372E+01 1.700E-05 -1.274E-01 0.000E+00 1.240E-01 1.168E-03 2.256E-03 10 1.576E+01 3.082E-05 -9.396E-02 -6.943E-04 9.088E-02 1.266E-03 2.477E-03 11 1.781E+01 4.738E-05 -6.538E-02 -1.389E-03 6.351E-02 5.162E-04 2.696E-03 12 1.987E+01 6.244E-05 -4.780E-02 -1.200E-03 4.562E-02 3.897E-04 2.921E-03 13 2.298E+01 7.909E-05 -3.580E-02 -9.173E-04 3.344E-02 -2.103E-05 3.213E-03 14 2.610E+01 9.531E-05 -2.867E-02 -2.323E-04 2.532E-02 7.961E-05 3.406E-03 15 3.028E+01 1.176E-04 -2.010E-02 1.343E-03 1.523E-02 -1.491E-04 3.557E-03 16 3.554E+01 1.395E-04 -9.201E-03 3.513E-03 1.954E-03 -1.220E-04 3.717E-03 17 4.083E+01 1.570E-04 -2.483E-03 4.581E-03 -5.940E-03 -1.410E-04 3.826E-03 18 4.614E+01 1.764E-04 6.752E-04 4.825E-03 -9.453E-03 -9.091E-05 3.868E-03 19 5.147E+01 1.925E-04 4.633E-03 5.077E-03 -1.367E-02 -1.082E-04 3.875E-03 20 6.220E+01 2.256E-04 1.138E-02 3.982E-03 -1.940E-02 -6.050E-05 3.869E-03 21 7.300E+01 2.610E-04 1.619E-02 3.034E-03 -2.327E-02 -5.987E-05 3.842E-03 22 8.386E+01 3.014E-04 1.903E-02 1.970E-03 -2.506E-02 -3.950E-05 3.793E-03 23 9.477E+01 3.310E-04 2.091E-02 6.555E-04 -2.556E-02 -7.736E-05 3.732E-03 24 1.057E+02 3.375E-04 2.250E-02 -4.302E-04 -2.601E-02 -7.039E-05 3.667E-03 25 1.278E+02 3.342E-04 2.510E-02 -2.253E-03 -2.663E-02 -8.337E-05 3.536E-03 26 1.500E+02 2.793E-04 2.659E-02 -3.974E-03 -2.623E-02 -7.068E-05 3.405E-03 27 1.723E+02 2.137E-04 2.741E-02 -5.741E-03 -2.509E-02 -5.417E-05 3.260E-03 28 1.947E+02 1.454E-04 2.759E-02 -6.990E-03 -2.381E-02 -4.491E-05 3.108E-03 29 2.172E+02 8.342E-05 2.731E-02 -6.837E-03 -2.347E-02 -3.007E-05 2.950E-03 30 2.398E+02 3.427E-05 2.630E-02 -6.181E-03 -2.292E-02 -2.668E-05 2.792E-03 31 2.625E+02 -1.529E-05 2.500E-02 -6.409E-03 -2.120E-02 -2.139E-05 2.641E-03 32 2.852E+02 -7.422E-05 2.375E-02 -6.892E-03 -1.925E-02 -2.035E-05 2.490E-03 33 3.080E+02 -1.364E-04 2.249E-02 -6.249E-03 -1.842E-02 -1.769E-05 2.341E-03 34 3.309E+02 -2.136E-04 2.106E-02 -5.194E-03 -1.783E-02 -1.936E-05 2.197E-03 35 3.653E+02 -3.384E-04 1.873E-02 -3.810E-03 -1.656E-02 -2.173E-05 1.994E-03 36 3.999E+02 -5.296E-04 1.684E-02 -2.463E-03 -1.564E-02 -1.524E-05 1.807E-03 37 4.461E+02 -7.592E-04 1.435E-02 -1.059E-03 -1.409E-02 -8.610E-06 1.568E-03 38 5.042E+02 -9.009E-04 1.089E-02 6.340E-04 -1.190E-02 1.873E-06 1.280E-03 39 5.625E+02 -9.198E-04 7.464E-03 2.197E-03 -9.763E-03 4.608E-06 1.017E-03 40 6.210E+02 -8.629E-04 4.919E-03 3.358E-03 -8.209E-03 7.663E-06 7.871E-04 41 6.798E+02 -7.453E-04 3.118E-03 4.004E-03 -6.959E-03 8.295E-06 5.742E-04 42 7.387E+02 -6.095E-04 1.811E-03 3.630E-03 -5.236E-03 7.142E-06 3.965E-04 43 7.978E+02 -4.799E-04 1.062E-03 2.607E-03 -3.440E-03 6.506E-06 2.444E-04 44 8.570E+02 -3.704E-04 6.279E-04 1.517E-03 -1.917E-03 4.865E-06 1.380E-04 45 9.164E+02 -2.506E-04 4.317E-04 7.848E-04 -1.055E-03 3.884E-06 8.494E-05 46 1.036E+03 -1.327E-04 1.893E-04 3.230E-04 -3.819E-04 2.263E-06 0.000E+00 47 1.155E+03 -2.316E-05 4.455E-05 1.075E-04 -1.297E-04 8.403E-07 0.000E+00 e. Balance of fluctuating temperature variance (t**2/2) (Each term is normalized by (u*)**2(t*)**2/N.) y+ AD PD TD MD DIS(et) 1 3.870E+00 4.954E-05 1.029E-02 2.735E-02 6.880E-02 -1.065E-01 2 4.838E+00 8.951E-05 2.842E-02 4.722E-02 4.187E-02 -1.176E-01 3 5.805E+00 1.386E-04 5.182E-02 5.757E-02 1.284E-02 -1.224E-01 4 6.773E+00 1.944E-04 7.845E-02 5.744E-02 -1.330E-02 -1.228E-01 5 7.740E+00 2.431E-04 1.042E-01 5.368E-02 -3.135E-02 -1.268E-01 6 8.708E+00 2.813E-04 1.246E-01 4.622E-02 -3.944E-02 -1.317E-01 7 9.675E+00 3.343E-04 1.463E-01 2.818E-02 -4.433E-02 -1.305E-01 8 1.169E+01 3.892E-04 1.563E-01 2.728E-03 -4.597E-02 -1.134E-01 9 1.372E+01 3.871E-04 1.555E-01 -1.755E-02 -4.202E-02 -9.630E-02 10 1.576E+01 3.416E-04 1.510E-01 -2.804E-02 -3.448E-02 -8.884E-02 11 1.781E+01 2.670E-04 1.431E-01 -3.116E-02 -2.587E-02 -8.630E-02 12 1.987E+01 2.000E-04 1.308E-01 -3.334E-02 -1.812E-02 -7.956E-02 13 2.298E+01 8.728E-05 1.119E-01 -3.549E-02 -1.128E-02 -6.520E-02 14 2.610E+01 -1.594E-05 9.646E-02 -3.070E-02 -5.916E-03 -5.983E-02 15 3.028E+01 -1.567E-04 8.069E-02 -2.139E-02 -2.667E-03 -5.648E-02 16 3.554E+01 -2.996E-04 6.176E-02 -1.431E-02 -8.078E-04 -4.635E-02 17 4.083E+01 -4.159E-04 4.619E-02 -9.170E-03 1.931E-04 -3.680E-02 18 4.614E+01 -5.016E-04 3.768E-02 -5.276E-03 6.703E-04 -3.258E-02 19 5.147E+01 -5.542E-04 3.259E-02 -2.529E-03 7.956E-04 -3.030E-02 20 6.220E+01 -5.897E-04 2.456E-02 -6.068E-04 7.070E-04 -2.407E-02 21 7.300E+01 -5.809E-04 1.886E-02 6.451E-04 5.594E-04 -1.948E-02 22 8.386E+01 -5.551E-04 1.556E-02 1.323E-03 4.201E-04 -1.675E-02 23 9.477E+01 -5.456E-04 1.357E-02 1.672E-03 3.147E-04 -1.501E-02 24 1.057E+02 -5.432E-04 1.172E-02 1.795E-03 2.313E-04 -1.320E-02 25 1.278E+02 -5.097E-04 8.449E-03 1.658E-03 1.614E-04 -9.759E-03 26 1.500E+02 -4.615E-04 6.308E-03 1.431E-03 1.106E-04 -7.388E-03 27 1.723E+02 -4.192E-04 5.385E-03 1.229E-03 7.640E-05 -6.272E-03 28 1.947E+02 -3.881E-04 4.746E-03 1.031E-03 5.384E-05 -5.442E-03 29 2.172E+02 -3.590E-04 4.202E-03 9.171E-04 3.862E-05 -4.798E-03 30 2.398E+02 -3.288E-04 3.507E-03 8.015E-04 2.870E-05 -4.008E-03 31 2.625E+02 -3.072E-04 2.883E-03 6.850E-04 2.225E-05 -3.283E-03 32 2.852E+02 -2.889E-04 2.489E-03 6.323E-04 1.720E-05 -2.849E-03 33 3.080E+02 -2.569E-04 2.134E-03 5.396E-04 1.275E-05 -2.430E-03 34 3.309E+02 -2.339E-04 1.793E-03 4.426E-04 9.379E-06 -2.011E-03 35 3.653E+02 -2.258E-04 1.340E-03 4.065E-04 7.297E-06 -1.528E-03 36 3.999E+02 -2.127E-04 1.033E-03 3.675E-04 5.692E-06 -1.194E-03 37 4.461E+02 -1.867E-04 7.885E-04 3.065E-04 4.292E-06 -9.125E-04 38 5.042E+02 -1.591E-04 5.620E-04 2.554E-04 3.156E-06 -6.614E-04 39 5.625E+02 -1.367E-04 3.637E-04 2.083E-04 2.416E-06 -4.377E-04 40 6.210E+02 -1.172E-04 2.361E-04 1.675E-04 1.921E-06 -2.884E-04 41 6.798E+02 -9.965E-05 1.433E-04 1.341E-04 1.594E-06 -1.794E-04 42 7.387E+02 -7.849E-05 7.750E-05 1.008E-04 1.338E-06 -1.011E-04 43 7.978E+02 -6.217E-05 3.675E-05 7.736E-05 1.113E-06 -5.305E-05 44 8.570E+02 -4.472E-05 1.176E-05 5.652E-05 9.066E-07 -2.447E-05 45 9.164E+02 -3.028E-05 3.619E-06 3.979E-05 6.620E-07 -1.379E-05 46 1.036E+03 -1.184E-05 0.000E+00 2.533E-05 3.881E-07 -1.388E-05 47 1.155E+03 -1.060E-06 0.000E+00 7.229E-06 1.140E-07 -6.283E-06 f. Balance of streamwise turbulent heat flux (ut) (Each term is normalized by (u*)**3(t*)/N.) y+ AD PD TD CTP MD BP 1 3.870E+00 -1.639E-06 -1.141E-02 1.333E-02 -1.501E-02 7.513E-03 5.574E-03 2 4.838E+00 -1.052E-06 -2.923E-02 2.332E-02 -1.475E-02 1.224E-02 8.425E-03 3 5.805E+00 5.079E-06 -4.134E-02 3.064E-02 -1.482E-02 1.402E-02 1.150E-02 4 6.773E+00 1.896E-05 -6.601E-02 3.357E-02 2.460E-03 1.528E-02 1.468E-02 5 7.740E+00 4.337E-05 -8.928E-02 3.382E-02 1.881E-02 1.882E-02 1.779E-02 6 8.708E+00 8.047E-05 -1.034E-01 3.349E-02 3.055E-02 1.885E-02 2.040E-02 7 9.675E+00 1.481E-04 -1.166E-01 3.242E-02 4.563E-02 1.561E-02 2.277E-02 8 1.169E+01 3.503E-04 -1.192E-01 3.197E-02 5.233E-02 7.732E-03 2.685E-02 9 1.372E+01 5.374E-04 -1.037E-01 3.143E-02 4.009E-02 2.151E-03 2.951E-02 10 1.576E+01 6.865E-04 -7.714E-02 2.609E-02 2.069E-02 -1.345E-03 3.102E-02 11 1.781E+01 8.177E-04 -4.836E-02 1.575E-02 4.954E-03 -4.636E-03 3.147E-02 12 1.987E+01 9.058E-04 -2.945E-02 4.385E-03 -7.921E-04 -6.365E-03 3.131E-02 13 2.298E+01 8.804E-04 -1.579E-02 -4.709E-03 -4.128E-03 -6.755E-03 3.050E-02 14 2.610E+01 7.282E-04 -7.264E-03 -9.908E-03 -7.270E-03 -5.325E-03 2.904E-02 15 3.028E+01 5.287E-04 4.921E-03 -1.153E-02 -1.691E-02 -3.975E-03 2.696E-02 16 3.554E+01 2.957E-04 1.720E-02 -1.096E-02 -2.837E-02 -2.622E-03 2.445E-02 17 4.083E+01 1.108E-04 2.175E-02 -9.892E-03 -3.240E-02 -1.721E-03 2.215E-02 18 4.614E+01 -3.481E-05 2.334E-02 -9.078E-03 -3.326E-02 -1.044E-03 2.009E-02 19 5.147E+01 -1.349E-04 2.661E-02 -8.296E-03 -3.581E-02 -6.339E-04 1.826E-02 20 6.220E+01 -2.980E-04 2.980E-02 -7.290E-03 -3.722E-02 -3.554E-04 1.536E-02 21 7.300E+01 -4.323E-04 2.994E-02 -6.292E-03 -3.620E-02 -1.900E-04 1.318E-02 22 8.386E+01 -5.404E-04 2.933E-02 -5.521E-03 -3.472E-02 -8.467E-05 1.154E-02 23 9.477E+01 -6.168E-04 2.896E-02 -4.862E-03 -3.370E-02 -2.568E-05 1.024E-02 24 1.057E+02 -6.649E-04 2.812E-02 -3.959E-03 -3.265E-02 4.578E-06 9.150E-03 25 1.278E+02 -7.224E-04 2.557E-02 -2.843E-03 -2.946E-02 1.776E-05 7.439E-03 26 1.500E+02 -7.663E-04 2.276E-02 -1.899E-03 -2.632E-02 2.326E-05 6.202E-03 27 1.723E+02 -7.831E-04 2.133E-02 -1.256E-03 -2.459E-02 2.463E-05 5.272E-03 28 1.947E+02 -7.710E-04 2.017E-02 -8.041E-04 -2.317E-02 2.190E-05 4.546E-03 29 2.172E+02 -7.618E-04 1.893E-02 -4.653E-04 -2.167E-02 1.997E-05 3.950E-03 30 2.398E+02 -7.584E-04 1.702E-02 -2.328E-04 -1.951E-02 1.703E-05 3.467E-03 31 2.625E+02 -7.371E-04 1.513E-02 -8.798E-05 -1.739E-02 1.491E-05 3.065E-03 32 2.852E+02 -7.164E-04 1.377E-02 1.159E-05 -1.580E-02 1.216E-05 2.718E-03 33 3.080E+02 -7.112E-04 1.243E-02 1.064E-04 -1.425E-02 1.052E-05 2.419E-03 34 3.309E+02 -6.921E-04 1.106E-02 1.870E-04 -1.275E-02 8.882E-06 2.184E-03 35 3.653E+02 -6.664E-04 9.105E-03 2.599E-04 -1.057E-02 6.974E-06 1.865E-03 36 3.999E+02 -6.517E-04 7.643E-03 3.721E-04 -8.957E-03 5.906E-06 1.588E-03 37 4.461E+02 -6.238E-04 6.183E-03 5.581E-04 -7.398E-03 4.895E-06 1.275E-03 38 5.042E+02 -5.851E-04 4.394E-03 7.661E-04 -5.559E-03 4.076E-06 9.806E-04 39 5.625E+02 -5.360E-04 2.899E-03 9.233E-04 -4.028E-03 3.177E-06 7.389E-04 40 6.210E+02 -4.899E-04 1.877E-03 9.916E-04 -2.932E-03 2.497E-06 5.517E-04 41 6.798E+02 -4.625E-04 1.147E-03 9.428E-04 -2.025E-03 2.137E-06 3.954E-04 42 7.387E+02 -4.371E-04 6.480E-04 7.802E-04 -1.266E-03 2.681E-06 2.725E-04 43 7.978E+02 -3.930E-04 3.356E-04 5.351E-04 -6.639E-04 3.367E-06 1.829E-04 44 8.570E+02 -3.039E-04 1.544E-04 3.014E-04 -2.663E-04 3.294E-06 1.112E-04 45 9.164E+02 -1.709E-04 7.855E-05 1.396E-04 -1.162E-04 2.442E-06 6.647E-05 46 1.036E+03 -1.655E-05 -2.145E-06 4.948E-05 -4.630E-05 6.019E-07 1.491E-05 47 1.155E+03 0.000E+00 -2.108E-08 0.000E+00 -4.296E-07 0.000E+00 4.507E-07 g. Balance of normal-to-wall turbulent heat flux (vt) (Each term is normalized by (u*)**3(t*)/N.) y+ AD PD TD CTP MD 1 3.870E+00 3.751E-06 9.950E-02 -4.719E-03 -1.068E-01 1.199E-02 2 4.838E+00 9.330E-06 1.475E-01 -1.307E-02 -1.458E-01 1.130E-02 3 5.805E+00 1.778E-05 1.961E-01 -2.202E-02 -1.826E-01 8.467E-03 4 6.773E+00 2.913E-05 2.285E-01 -2.960E-02 -2.073E-01 8.449E-03 5 7.740E+00 4.019E-05 2.349E-01 -3.649E-02 -2.006E-01 2.193E-03 6 8.708E+00 5.641E-05 2.277E-01 -3.966E-02 -1.880E-01 -1.242E-04 7 9.675E+00 6.985E-05 2.141E-01 -3.721E-02 -1.712E-01 -5.777E-03 8 1.169E+01 5.883E-05 1.832E-01 -3.260E-02 -1.473E-01 -3.385E-03 9 1.372E+01 5.626E-05 1.612E-01 -2.701E-02 -1.315E-01 -2.669E-03 10 1.576E+01 6.052E-05 1.432E-01 -1.867E-02 -1.231E-01 -1.447E-03 11 1.781E+01 7.557E-05 1.251E-01 -9.471E-03 -1.143E-01 -1.474E-03 12 1.987E+01 8.744E-05 1.074E-01 -1.933E-03 -1.040E-01 -1.579E-03 13 2.298E+01 8.470E-05 8.526E-02 3.672E-03 -8.760E-02 -1.408E-03 14 2.610E+01 6.783E-05 7.244E-02 7.827E-03 -7.930E-02 -1.031E-03 15 3.028E+01 5.634E-05 6.105E-02 1.048E-02 -7.087E-02 -7.227E-04 16 3.554E+01 5.457E-05 4.894E-02 1.147E-02 -5.988E-02 -5.856E-04 17 4.083E+01 3.727E-05 3.866E-02 1.117E-02 -4.944E-02 -4.282E-04 18 4.614E+01 1.439E-05 3.435E-02 9.844E-03 -4.394E-02 -2.726E-04 19 5.147E+01 2.760E-06 3.218E-02 7.128E-03 -3.914E-02 -1.664E-04 20 6.220E+01 -7.283E-06 2.828E-02 3.912E-03 -3.207E-02 -1.078E-04 21 7.300E+01 -1.993E-05 2.492E-02 1.663E-03 -2.650E-02 -6.806E-05 22 8.386E+01 -3.447E-05 2.329E-02 3.624E-04 -2.357E-02 -4.102E-05 23 9.477E+01 -4.577E-05 2.280E-02 -4.087E-04 -2.233E-02 -2.277E-05 24 1.057E+02 -5.339E-05 2.149E-02 -1.092E-03 -2.033E-02 -1.399E-05 25 1.278E+02 -6.712E-05 1.805E-02 -1.599E-03 -1.637E-02 -8.973E-06 26 1.500E+02 -8.438E-05 1.520E-02 -1.923E-03 -1.318E-02 -6.760E-06 27 1.723E+02 -1.057E-04 1.426E-02 -2.229E-03 -1.192E-02 -4.087E-06 28 1.947E+02 -1.264E-04 1.353E-02 -2.118E-03 -1.129E-02 -1.986E-06 29 2.172E+02 -1.448E-04 1.275E-02 -1.717E-03 -1.088E-02 -4.275E-07 30 2.398E+02 -1.574E-04 1.123E-02 -1.322E-03 -9.747E-03 3.455E-07 31 2.625E+02 -1.694E-04 9.634E-03 -9.402E-04 -8.525E-03 7.384E-07 32 2.852E+02 -1.833E-04 8.691E-03 -6.012E-04 -7.908E-03 1.469E-06 33 3.080E+02 -1.940E-04 7.796E-03 -3.000E-04 -7.304E-03 2.089E-06 34 3.309E+02 -2.001E-04 6.808E-03 -7.508E-05 -6.535E-03 2.162E-06 35 3.653E+02 -2.049E-04 5.306E-03 1.133E-04 -5.216E-03 1.861E-06 36 3.999E+02 -2.119E-04 4.229E-03 3.098E-04 -4.329E-03 1.578E-06 37 4.461E+02 -2.270E-04 3.306E-03 5.195E-04 -3.600E-03 1.614E-06 38 5.042E+02 -2.405E-04 2.408E-03 6.891E-04 -2.859E-03 1.617E-06 39 5.625E+02 -2.393E-04 1.553E-03 7.420E-04 -2.058E-03 1.739E-06 40 6.210E+02 -2.353E-04 9.811E-04 6.960E-04 -1.443E-03 1.663E-06 41 6.798E+02 -2.246E-04 5.948E-04 6.196E-04 -9.918E-04 2.009E-06 42 7.387E+02 -2.031E-04 3.207E-04 5.375E-04 -6.573E-04 2.274E-06 43 7.978E+02 -1.690E-04 1.672E-04 4.519E-04 -4.522E-04 2.159E-06 44 8.570E+02 -1.101E-04 6.418E-05 3.571E-04 -3.131E-04 1.882E-06 45 9.164E+02 -7.170E-05 2.376E-05 2.198E-04 -1.731E-04 1.151E-06 46 1.036E+03 -3.344E-05 2.396E-06 9.098E-05 -6.122E-05 1.278E-06 47 1.155E+03 0.000E+00 1.618E-07 2.938E-06 -3.100E-06 0.000E+00 h. Time scales of velocity and temperature fluctuations (k is normalized by (u*)**2, t**2/2 is normalized by (t*)**2, e is normalized by (u*)**4/N and et is normalized by (t*)**2*(u*)**2/N. Tauu is normalized by N/(u*)**2 and Taut is normalized by N/(u*)**2.) y+ k e t**2/2 et Tauu Taut Taut/tauu 1 3.870E+00 3.567E-01 2.154E-02 5.974E-01 1.064E-01 1.656E+01 5.613E+00 3.390E-01 2 4.838E+00 5.526E-01 1.924E-02 9.030E-01 1.175E-01 2.872E+01 7.682E+00 2.675E-01 3 5.805E+00 7.662E-01 1.741E-02 1.233E+00 1.223E-01 4.400E+01 1.008E+01 2.291E-01 4 6.773E+00 9.890E-01 1.599E-02 1.574E+00 1.227E-01 6.185E+01 1.282E+01 2.073E-01 5 7.740E+00 1.203E+00 1.477E-02 1.907E+00 1.267E-01 8.142E+01 1.505E+01 1.848E-01 6 8.708E+00 1.403E+00 1.402E-02 2.187E+00 1.316E-01 1.001E+02 1.662E+01 1.661E-01 7 9.675E+00 1.591E+00 1.328E-02 2.440E+00 1.305E-01 1.198E+02 1.870E+01 1.561E-01 8 1.169E+01 1.866E+00 1.301E-02 2.878E+00 1.133E-01 1.435E+02 2.539E+01 1.770E-01 9 1.372E+01 2.127E+00 1.328E-02 3.163E+00 9.624E-02 1.602E+02 3.287E+01 2.052E-01 10 1.576E+01 2.308E+00 1.396E-02 3.325E+00 8.879E-02 1.654E+02 3.745E+01 2.264E-01 11 1.781E+01 2.484E+00 1.470E-02 3.373E+00 8.625E-02 1.690E+02 3.911E+01 2.315E-01 12 1.987E+01 2.620E+00 1.531E-02 3.356E+00 7.951E-02 1.711E+02 4.221E+01 2.467E-01 13 2.298E+01 2.750E+00 1.612E-02 3.269E+00 6.516E-02 1.706E+02 5.017E+01 2.942E-01 14 2.610E+01 2.845E+00 1.680E-02 3.112E+00 5.979E-02 1.693E+02 5.205E+01 3.074E-01 15 3.028E+01 2.947E+00 1.755E-02 2.889E+00 5.645E-02 1.679E+02 5.118E+01 3.048E-01 16 3.554E+01 3.055E+00 1.836E-02 2.621E+00 4.633E-02 1.664E+02 5.658E+01 3.401E-01 17 4.083E+01 3.155E+00 1.890E-02 2.374E+00 3.678E-02 1.669E+02 6.454E+01 3.867E-01 18 4.614E+01 3.251E+00 1.944E-02 2.153E+00 3.256E-02 1.672E+02 6.612E+01 3.955E-01 19 5.147E+01 3.334E+00 1.985E-02 1.957E+00 3.028E-02 1.679E+02 6.463E+01 3.849E-01 20 6.220E+01 3.470E+00 2.053E-02 1.646E+00 2.405E-02 1.690E+02 6.844E+01 4.049E-01 21 7.300E+01 3.603E+00 2.087E-02 1.412E+00 1.947E-02 1.727E+02 7.254E+01 4.201E-01 22 8.386E+01 3.706E+00 2.121E-02 1.237E+00 1.674E-02 1.748E+02 7.388E+01 4.227E-01 23 9.477E+01 3.794E+00 2.141E-02 1.098E+00 1.500E-02 1.772E+02 7.321E+01 4.131E-01 24 1.057E+02 3.888E+00 2.154E-02 9.807E-01 1.320E-02 1.805E+02 7.432E+01 4.118E-01 25 1.278E+02 4.018E+00 2.188E-02 7.973E-01 9.753E-03 1.836E+02 8.175E+01 4.452E-01 26 1.500E+02 4.104E+00 2.202E-02 6.647E-01 7.384E-03 1.864E+02 9.002E+01 4.830E-01 27 1.723E+02 4.156E+00 2.209E-02 5.651E-01 6.268E-03 1.882E+02 9.015E+01 4.791E-01 28 1.947E+02 4.173E+00 2.215E-02 4.872E-01 5.439E-03 1.884E+02 8.958E+01 4.756E-01 29 2.172E+02 4.156E+00 2.229E-02 4.234E-01 4.796E-03 1.864E+02 8.828E+01 4.735E-01 30 2.398E+02 4.110E+00 2.229E-02 3.716E-01 4.006E-03 1.844E+02 9.276E+01 5.031E-01 31 2.625E+02 4.052E+00 2.229E-02 3.285E-01 3.282E-03 1.818E+02 1.001E+02 5.507E-01 32 2.852E+02 3.978E+00 2.229E-02 2.913E-01 2.848E-03 1.785E+02 1.023E+02 5.731E-01 33 3.080E+02 3.883E+00 2.236E-02 2.593E-01 2.428E-03 1.737E+02 1.068E+02 6.149E-01 34 3.309E+02 3.744E+00 2.236E-02 2.341E-01 2.010E-03 1.675E+02 1.165E+02 6.954E-01 35 3.653E+02 3.496E+00 2.236E-02 1.999E-01 1.527E-03 1.564E+02 1.309E+02 8.373E-01 36 3.999E+02 3.221E+00 2.236E-02 1.702E-01 1.193E-03 1.440E+02 1.426E+02 9.900E-01 37 4.461E+02 2.802E+00 2.236E-02 1.367E-01 9.120E-04 1.253E+02 1.499E+02 1.196E+00 38 5.042E+02 2.210E+00 2.229E-02 1.051E-01 6.610E-04 9.917E+01 1.590E+02 1.603E+00 39 5.625E+02 1.786E+00 2.195E-02 7.919E-02 4.375E-04 8.136E+01 1.810E+02 2.225E+00 40 6.210E+02 1.366E+00 2.114E-02 5.913E-02 2.882E-04 6.465E+01 2.052E+02 3.174E+00 41 6.798E+02 1.058E+00 1.972E-02 4.238E-02 1.793E-04 5.366E+01 2.364E+02 4.405E+00 42 7.387E+02 7.988E-01 1.694E-02 2.921E-02 1.011E-04 4.716E+01 2.890E+02 6.127E+00 9. GRAPH File name Contents BMUU BALANCE OF MEAN FLOW ENERGY U**2/2 BNHFVT BALANCE OF NORMAL-TO-WALL HEAT FLUX vt BRSUV BALANCE OF REYNOLDS SHEAR STRESS uv BSHFUT BALANCE OF STREAMWISE HEAT FLUX ut BTEU BALANCE OF TURBULENT ENERGY OOMPONENT u**2/2 BTEV BALANCE OF TURBULENT ENERGY COMPONENT v**2/2 BTVT2 BALANCE OF TEMPERATURE VARIANCE t**2/2 10. REFERENCES 1. T. Tsuji and Y. Nagano, Characteristics of a Turbulent Natural Convection Boundary Layer along a Vertical Flat Plate, Int. J. Heat Mass Transfer 31, 1723-1734 (1988). 2. T. Tsuji and Y. Nagano, Turbulent Measurements in a Natural Convection Boundary Layer along a Vertical Flat Plate, Int. J. Heat Mass Transfer 31, 2101-2111 (1988). 11. DISCUSSION