HOM24

Direct numerical simulation of Homogeneous shear flow. 

From Sarkar, S. 1995 J. Fluid Mech., 282, 163-186.

Three-dimensional energy spectra of the fluctuating velocity, at 
 dimensionless times   St=0,3,5,7,9,11,13,15

 S:        is the mean shear rate, 

The nondimensional viscosity is nu = 1/200.

       k            E(k)

S t = 0

   1.0000000e+00   5.8196920e-08
   2.0000000e+00   1.2328209e-04
   3.0000000e+00   5.8116573e-04
   4.0000000e+00   1.7758243e-03
   5.0000000e+00   4.0606915e-03
   6.0000000e+00   7.9652608e-03
   7.0000000e+00   1.3580007e-02
   8.0000000e+00   2.0825719e-02
   9.0000000e+00   3.0053842e-02
   1.0000000e+01   4.0992084e-02
   1.1000000e+01   5.2650197e-02
   1.2000000e+01   6.4476284e-02
   1.3000000e+01   7.6524412e-02
   1.4000000e+01   8.6956089e-02
   1.5000000e+01   9.5807609e-02
   1.6000000e+01   1.0289873e-01
   1.7000000e+01   1.0632368e-01
   1.8000000e+01   1.0788722e-01
   1.9000000e+01   1.0667189e-01
   2.0000000e+01   1.0307895e-01
   2.1000000e+01   9.7498964e-02
   2.2000000e+01   8.9784217e-02
   2.3000000e+01   8.1545500e-02
   2.4000000e+01   7.2310273e-02
   2.5000000e+01   6.3153875e-02
   2.6000000e+01   5.4050535e-02
   2.7000000e+01   4.5415071e-02
   2.8000000e+01   3.7575087e-02
   2.9000000e+01   3.0640793e-02
   3.0000000e+01   2.4490632e-02
   3.1000000e+01   1.9270811e-02
   3.2000000e+01   1.5062602e-02
   3.3000000e+01   1.1553139e-02
   3.4000000e+01   8.8267332e-03
   3.5000000e+01   6.6481376e-03
   3.6000000e+01   4.9419688e-03
   3.7000000e+01   3.7290654e-03
   3.8000000e+01   2.8009155e-03
   3.9000000e+01   2.1164110e-03
   4.0000000e+01   1.6032454e-03
   4.1000000e+01   1.2737963e-03
   4.2000000e+01   1.0228219e-03
   4.3000000e+01   8.3118941e-04
   4.4000000e+01   6.9839320e-04
   4.5000000e+01   5.9415533e-04
   4.6000000e+01   5.3345771e-04
   4.7000000e+01   4.6494331e-04
   4.8000000e+01   4.1811909e-04
   4.9000000e+01   3.9156151e-04
   5.0000000e+01   3.5776677e-04
   5.1000000e+01   3.2433962e-04
   5.2000000e+01   2.9607382e-04
   5.3000000e+01   2.7510596e-04
   5.4000000e+01   2.5433141e-04
   5.5000000e+01   2.3216674e-04
   5.6000000e+01   2.1159237e-04
   5.7000000e+01   1.9633603e-04
   5.8000000e+01   1.8361155e-04
   5.9000000e+01   1.6512012e-04
   6.0000000e+01   1.5251059e-04
   6.1000000e+01   1.4348285e-04
   6.2000000e+01   1.3103883e-04
   6.3000000e+01   1.2425103e-04
   6.4000000e+01   1.1449855e-04

S t = 3

   1.0000000e+00   4.7119427e-08
   2.0000000e+00   1.4454398e-03
   3.0000000e+00   7.2660771e-03
   4.0000000e+00   1.3316804e-02
   5.0000000e+00   2.2855988e-02
   6.0000000e+00   3.6931760e-02
   7.0000000e+00   4.4279224e-02
   8.0000000e+00   5.3579666e-02
   9.0000000e+00   5.8586830e-02
   1.0000000e+01   7.5023963e-02
   1.1000000e+01   5.8667827e-02
   1.2000000e+01   5.4626075e-02
   1.3000000e+01   5.8925055e-02
   1.4000000e+01   5.4187610e-02
   1.5000000e+01   4.8017550e-02
   1.6000000e+01   4.1667745e-02
   1.7000000e+01   4.3762286e-02
   1.8000000e+01   3.8663396e-02
   1.9000000e+01   3.5237087e-02
   2.0000000e+01   2.9621019e-02
   2.1000000e+01   2.7586716e-02
   2.2000000e+01   2.4350058e-02
   2.3000000e+01   2.0026267e-02
   2.4000000e+01   1.8297847e-02
   2.5000000e+01   1.6873299e-02
   2.6000000e+01   1.5498869e-02
   2.7000000e+01   1.3267833e-02
   2.8000000e+01   1.1441949e-02
   2.9000000e+01   1.0643881e-02
   3.0000000e+01   9.2320894e-03
   3.1000000e+01   8.3387317e-03
   3.2000000e+01   7.4524659e-03
   3.3000000e+01   6.6496686e-03
   3.4000000e+01   6.0131218e-03
   3.5000000e+01   5.3518015e-03
   3.6000000e+01   4.6838179e-03
   3.7000000e+01   4.2953643e-03
   3.8000000e+01   3.8699023e-03
   3.9000000e+01   3.4355795e-03
   4.0000000e+01   3.0619634e-03
   4.1000000e+01   2.7574015e-03
   4.2000000e+01   2.4934462e-03
   4.3000000e+01   2.1359939e-03
   4.4000000e+01   1.9006406e-03
   4.5000000e+01   1.6668634e-03
   4.6000000e+01   1.4989944e-03
   4.7000000e+01   1.2787923e-03
   4.8000000e+01   1.1199535e-03
   4.9000000e+01   1.0164827e-03
   5.0000000e+01   8.9618981e-04
   5.1000000e+01   8.0057127e-04
   5.2000000e+01   6.8817676e-04
   5.3000000e+01   6.3738230e-04
   5.4000000e+01   5.6156496e-04
   5.5000000e+01   4.8910263e-04
   5.6000000e+01   4.3711932e-04
   5.7000000e+01   3.9409416e-04
   5.8000000e+01   3.6074473e-04
   5.9000000e+01   3.1966862e-04
   6.0000000e+01   2.9241524e-04
   6.1000000e+01   2.7145635e-04
   6.2000000e+01   2.4928721e-04
   6.3000000e+01   2.2998526e-04
   6.4000000e+01   2.1242225e-04

S t = 5

   1.0000000e+00   4.4330232e-08
   2.0000000e+00   3.4260997e-03
   3.0000000e+00   2.0090928e-02
   4.0000000e+00   3.4593938e-02
   5.0000000e+00   5.0839351e-02
   6.0000000e+00   7.5335556e-02
   7.0000000e+00   6.1122344e-02
   8.0000000e+00   7.0097092e-02
   9.0000000e+00   8.6856035e-02
   1.0000000e+01   9.9655208e-02
   1.1000000e+01   7.8288866e-02
   1.2000000e+01   6.9855403e-02
   1.3000000e+01   6.9646613e-02
   1.4000000e+01   5.8089816e-02
   1.5000000e+01   5.0909637e-02
   1.6000000e+01   4.4289421e-02
   1.7000000e+01   4.2923982e-02
   1.8000000e+01   3.6982818e-02
   1.9000000e+01   3.1117163e-02
   2.0000000e+01   2.6662447e-02
   2.1000000e+01   2.3730124e-02
   2.2000000e+01   2.0806546e-02
   2.3000000e+01   1.7410049e-02
   2.4000000e+01   1.5021040e-02
   2.5000000e+01   1.3353650e-02
   2.6000000e+01   1.2170264e-02
   2.7000000e+01   1.0282530e-02
   2.8000000e+01   9.1117123e-03
   2.9000000e+01   8.5782757e-03
   3.0000000e+01   7.1137730e-03
   3.1000000e+01   6.1944108e-03
   3.2000000e+01   5.6689157e-03
   3.3000000e+01   4.8944061e-03
   3.4000000e+01   4.5196000e-03
   3.5000000e+01   4.1001524e-03
   3.6000000e+01   3.4150731e-03
   3.7000000e+01   3.1710274e-03
   3.8000000e+01   2.8307401e-03
   3.9000000e+01   2.4945947e-03
   4.0000000e+01   2.1692020e-03
   4.1000000e+01   2.0234850e-03
   4.2000000e+01   1.7852539e-03
   4.3000000e+01   1.5118197e-03
   4.4000000e+01   1.3608179e-03
   4.5000000e+01   1.1431415e-03
   4.6000000e+01   1.0522041e-03
   4.7000000e+01   8.7096359e-04
   4.8000000e+01   7.8324927e-04
   4.9000000e+01   6.9055774e-04
   5.0000000e+01   6.1616922e-04
   5.1000000e+01   5.4025650e-04
   5.2000000e+01   4.5845847e-04
   5.3000000e+01   4.1399967e-04
   5.4000000e+01   3.6957280e-04
   5.5000000e+01   3.2158812e-04
   5.6000000e+01   2.8628593e-04
   5.7000000e+01   2.5609435e-04
   5.8000000e+01   2.3420707e-04
   5.9000000e+01   2.0677594e-04
   6.0000000e+01   1.8689600e-04
   6.1000000e+01   1.7571142e-04
   6.2000000e+01   1.5787014e-04
   6.3000000e+01   1.4658853e-04
   6.4000000e+01   1.3595651e-04

S t = 7

   1.0000000e+00   4.5227231e-08
   2.0000000e+00   9.7611278e-03
   3.0000000e+00   3.1038448e-02
   4.0000000e+00   3.1798014e-02
   5.0000000e+00   7.6647854e-02
   6.0000000e+00   1.1548883e-01
   7.0000000e+00   8.8470809e-02
   8.0000000e+00   1.3390907e-01
   9.0000000e+00   1.1691763e-01
   1.0000000e+01   1.2287683e-01
   1.1000000e+01   9.5279616e-02
   1.2000000e+01   8.6976114e-02
   1.3000000e+01   7.8795243e-02
   1.4000000e+01   7.4799725e-02
   1.5000000e+01   5.8870808e-02
   1.6000000e+01   4.5877527e-02
   1.7000000e+01   4.8205878e-02
   1.8000000e+01   3.8976245e-02
   1.9000000e+01   3.1812661e-02
   2.0000000e+01   2.8170853e-02
   2.1000000e+01   2.4215866e-02
   2.2000000e+01   2.1702012e-02
   2.3000000e+01   1.7470285e-02
   2.4000000e+01   1.5617086e-02
   2.5000000e+01   1.3270888e-02
   2.6000000e+01   1.2542959e-02
   2.7000000e+01   1.0531737e-02
   2.8000000e+01   8.9351120e-03
   2.9000000e+01   7.8559733e-03
   3.0000000e+01   7.0372017e-03
   3.1000000e+01   6.1944108e-03
   3.2000000e+01   5.5195033e-03
   3.3000000e+01   4.8495339e-03
   3.4000000e+01   4.5425530e-03
   3.5000000e+01   3.9183209e-03
   3.6000000e+01   3.4601904e-03
   3.7000000e+01   3.1102837e-03
   3.8000000e+01   2.7841972e-03
   3.9000000e+01   2.4417433e-03
   4.0000000e+01   2.1577444e-03
   4.1000000e+01   1.9642646e-03
   4.2000000e+01   1.7939073e-03
   4.3000000e+01   1.4859356e-03
   4.4000000e+01   1.3721450e-03
   4.5000000e+01   1.1585106e-03
   4.6000000e+01   1.0688087e-03
   4.7000000e+01   8.8981557e-04
   4.8000000e+01   7.9396252e-04
   4.9000000e+01   7.0129380e-04
   5.0000000e+01   6.2158425e-04
   5.1000000e+01   5.4992061e-04
   5.2000000e+01   4.7162846e-04
   5.3000000e+01   4.2335042e-04
   5.4000000e+01   3.7497300e-04
   5.5000000e+01   3.3496544e-04
   5.6000000e+01   3.0067686e-04
   5.7000000e+01   2.6878189e-04
   5.8000000e+01   2.4294054e-04
   5.9000000e+01   2.1742025e-04
   6.0000000e+01   2.0081678e-04
   6.1000000e+01   1.8569491e-04
   6.2000000e+01   1.6714754e-04
   6.3000000e+01   1.6158461e-04
   6.4000000e+01   1.4842259e-04

S t = 9

   1.0000000e+00   4.9808103e-08
   2.0000000e+00   1.3170431e-02
   3.0000000e+00   5.5885611e-02
   4.0000000e+00   6.1122344e-02
   5.0000000e+00   1.1314881e-01
   6.0000000e+00   1.3766388e-01
   7.0000000e+00   1.3475659e-01
   8.0000000e+00   1.8193238e-01
   9.0000000e+00   1.6943378e-01
   1.0000000e+01   1.5316516e-01
   1.1000000e+01   1.5086205e-01
   1.2000000e+01   1.0735444e-01
   1.3000000e+01   9.8878074e-02
   1.4000000e+01   7.9909792e-02
   1.5000000e+01   6.9758960e-02
   1.6000000e+01   5.4764610e-02
   1.7000000e+01   5.2131473e-02
   1.8000000e+01   4.3351088e-02
   1.9000000e+01   3.7765914e-02
   2.0000000e+01   2.9833211e-02
   2.1000000e+01   2.6485001e-02
   2.2000000e+01   2.4171300e-02
   2.3000000e+01   2.0272159e-02
   2.4000000e+01   1.7498467e-02
   2.5000000e+01   1.5606302e-02
   2.6000000e+01   1.4308694e-02
   2.7000000e+01   1.2450879e-02
   2.8000000e+01   1.0449608e-02
   2.9000000e+01   9.1960220e-03
   3.0000000e+01   7.9781096e-03
   3.1000000e+01   7.0113234e-03
   3.2000000e+01   6.3430772e-03
   3.3000000e+01   5.3616690e-03
   3.4000000e+01   5.0049530e-03
   3.5000000e+01   4.5962114e-03
   3.6000000e+01   3.9527559e-03
   3.7000000e+01   3.5481339e-03
   3.8000000e+01   3.1702974e-03
   3.9000000e+01   2.8372656e-03
   4.0000000e+01   2.4581026e-03
   4.1000000e+01   2.2698649e-03
   4.2000000e+01   2.0104811e-03
   4.3000000e+01   1.7322078e-03
   4.4000000e+01   1.5845283e-03
   4.5000000e+01   1.3415288e-03
   4.6000000e+01   1.2229255e-03
   4.7000000e+01   1.0315731e-03
   4.8000000e+01   9.4929239e-04
   4.9000000e+01   8.3868717e-04
   5.0000000e+01   7.5700718e-04
   5.1000000e+01   6.6634631e-04
   5.2000000e+01   5.9101704e-04
   5.3000000e+01   5.2820195e-04
   5.4000000e+01   4.7435120e-04
   5.5000000e+01   4.1908296e-04
   5.6000000e+01   3.8071501e-04
   5.7000000e+01   3.4474661e-04
   5.8000000e+01   3.1550046e-04
   5.9000000e+01   2.8320440e-04
   6.0000000e+01   2.5698040e-04
   6.1000000e+01   2.4734321e-04
   6.2000000e+01   2.2945631e-04
   6.3000000e+01   2.1877616e-04
   6.4000000e+01   2.0426784e-04

S t = 11

   1.0000000e+00   5.8063071e-08
   2.0000000e+00   2.0672833e-02
   3.0000000e+00   7.3773434e-02
   4.0000000e+00   1.4510086e-01
   5.0000000e+00   1.8502482e-01
   6.0000000e+00   2.1178247e-01
   7.0000000e+00   2.1122728e-01
   8.0000000e+00   2.1849927e-01
   9.0000000e+00   2.2808147e-01
   1.0000000e+01   2.1201178e-01
   1.1000000e+01   1.5879251e-01
   1.2000000e+01   1.3384125e-01
   1.3000000e+01   1.0660314e-01
   1.4000000e+01   1.0255811e-01
   1.5000000e+01   8.6736122e-02
   1.6000000e+01   6.2618116e-02
   1.7000000e+01   6.3914589e-02
   1.8000000e+01   5.4350057e-02
   1.9000000e+01   4.8910263e-02
   2.0000000e+01   3.6124347e-02
   2.1000000e+01   3.4182199e-02
   2.2000000e+01   2.9867578e-02
   2.3000000e+01   2.4711551e-02
   2.4000000e+01   2.2156441e-02
   2.5000000e+01   1.8914724e-02
   2.6000000e+01   1.7750067e-02
   2.7000000e+01   1.5069540e-02
   2.8000000e+01   1.2708667e-02
   2.9000000e+01   1.1800489e-02
   3.0000000e+01   1.0050785e-02
   3.1000000e+01   8.9002048e-03
   3.2000000e+01   8.0112448e-03
   3.3000000e+01   6.9791093e-03
   3.4000000e+01   6.2820299e-03
   3.5000000e+01   5.7213695e-03
   3.6000000e+01   5.0991760e-03
   3.7000000e+01   4.5164790e-03
   3.8000000e+01   3.9600439e-03
   3.9000000e+01   3.5677959e-03
   4.0000000e+01   3.1746803e-03
   4.1000000e+01   2.8470822e-03
   4.2000000e+01   2.5721720e-03
   4.3000000e+01   2.2402681e-03
   4.4000000e+01   2.0639539e-03
   4.5000000e+01   1.7852539e-03
   4.6000000e+01   1.6695522e-03
   4.7000000e+01   1.4354894e-03
   4.8000000e+01   1.2891398e-03
   4.9000000e+01   1.1627866e-03
   5.0000000e+01   1.0609624e-03
   5.1000000e+01   9.3218047e-04
   5.2000000e+01   8.3004187e-04
   5.3000000e+01   7.6348411e-04
   5.4000000e+01   6.8249583e-04
   5.5000000e+01   6.0967726e-04
   5.6000000e+01   5.5795606e-04
   5.7000000e+01   5.0921361e-04
   5.8000000e+01   4.7435120e-04
   5.9000000e+01   4.2963534e-04
   6.0000000e+01   3.9382202e-04
   6.1000000e+01   3.7722459e-04
   6.2000000e+01   3.5139858e-04
   6.3000000e+01   3.4197944e-04
   6.4000000e+01   3.1790693e-04

S t = 13

   1.0000000e+00   7.0000316e-08
   2.0000000e+00   2.6478904e-02
   3.0000000e+00   9.6139088e-02
   4.0000000e+00   1.6969537e-01
   5.0000000e+00   3.5546758e-01
   6.0000000e+00   3.2894251e-01
   7.0000000e+00   3.1566033e-01
   8.0000000e+00   3.0488777e-01
   9.0000000e+00   2.7168146e-01
   1.0000000e+01   2.7652857e-01
   1.1000000e+01   2.0626712e-01
   1.2000000e+01   1.4357869e-01
   1.3000000e+01   1.5275309e-01
   1.4000000e+01   1.2083424e-01
   1.5000000e+01   1.0701385e-01
   1.6000000e+01   8.2965971e-02
   1.7000000e+01   8.0241678e-02
   1.8000000e+01   6.9071677e-02
   1.9000000e+01   5.7969559e-02
   2.0000000e+01   4.8428387e-02
   2.1000000e+01   4.2589251e-02
   2.2000000e+01   3.7774611e-02
   2.3000000e+01   3.0952804e-02
   2.4000000e+01   2.8787238e-02
   2.5000000e+01   2.5147800e-02
   2.6000000e+01   2.2615177e-02
   2.7000000e+01   1.9665274e-02
   2.8000000e+01   1.6884959e-02
   2.9000000e+01   1.4955468e-02
   3.0000000e+01   1.3505168e-02
   3.1000000e+01   1.1789625e-02
   3.2000000e+01   1.0811850e-02
   3.3000000e+01   9.4362622e-03
   3.4000000e+01   8.6357488e-03
   3.5000000e+01   7.7072598e-03
   3.6000000e+01   6.6542636e-03
   3.7000000e+01   6.1489364e-03
   3.8000000e+01   5.5335011e-03
   3.9000000e+01   4.9465226e-03
   4.0000000e+01   4.3581282e-03
   4.1000000e+01   3.9591322e-03
   4.2000000e+01   3.5497682e-03
   4.3000000e+01   3.1045596e-03
   4.4000000e+01   2.8694588e-03
   4.5000000e+01   2.4802759e-03
   4.6000000e+01   2.3545071e-03
   4.7000000e+01   2.0455024e-03
   4.8000000e+01   1.8373843e-03
   4.9000000e+01   1.6931678e-03
   5.0000000e+01   1.5484600e-03
   5.1000000e+01   1.3813381e-03
   5.2000000e+01   1.2450879e-03
   5.3000000e+01   1.1455129e-03
   5.4000000e+01   1.0490592e-03
   5.5000000e+01   9.4732718e-04
   5.6000000e+01   8.6437063e-04
   5.7000000e+01   7.8976885e-04
   5.8000000e+01   7.5648444e-04
   5.9000000e+01   6.9183097e-04
   6.0000000e+01   6.5614527e-04
   6.1000000e+01   6.2603700e-04
   6.2000000e+01   6.0117374e-04
   6.3000000e+01   5.8830156e-04
   6.4000000e+01   5.5949988e-04

S t = 15

   1.0000000e+00   8.5624885e-08
   2.0000000e+00   4.5060914e-02
   3.0000000e+00   1.7781156e-01
   4.0000000e+00   2.3919935e-01
   5.0000000e+00   5.0094495e-01
   6.0000000e+00   5.1936180e-01
   7.0000000e+00   4.0109754e-01
   8.0000000e+00   3.5150378e-01
   9.0000000e+00   3.7880003e-01
   1.0000000e+01   3.4260208e-01
   1.1000000e+01   2.3432035e-01
   1.2000000e+01   1.9421376e-01
   1.3000000e+01   1.8529342e-01
   1.4000000e+01   1.5816122e-01
   1.5000000e+01   1.3450239e-01
   1.6000000e+01   1.1241131e-01
   1.7000000e+01   9.8152191e-02
   1.8000000e+01   8.6536634e-02
   1.9000000e+01   7.3097075e-02
   2.0000000e+01   6.2921635e-02
   2.1000000e+01   5.5564831e-02
   2.2000000e+01   5.1451732e-02
   2.3000000e+01   4.4350651e-02
   2.4000000e+01   3.8556713e-02
   2.5000000e+01   3.4032982e-02
   2.6000000e+01   3.0938553e-02
   2.7000000e+01   2.7333799e-02
   2.8000000e+01   2.3463889e-02
   2.9000000e+01   2.1777098e-02
   3.0000000e+01   1.8962692e-02
   3.1000000e+01   1.6850004e-02
   3.2000000e+01   1.5027959e-02
   3.3000000e+01   1.3264778e-02
   3.4000000e+01   1.1975675e-02
   3.5000000e+01   1.0932009e-02
   3.6000000e+01   9.4232345e-03
   3.7000000e+01   8.6736122e-03
   3.8000000e+01   7.7767833e-03
   3.9000000e+01   7.0372017e-03
   4.0000000e+01   6.3197515e-03
   4.1000000e+01   5.7650091e-03
   4.2000000e+01   5.2686579e-03
   4.3000000e+01   4.6174266e-03
   4.4000000e+01   4.2795687e-03
   4.5000000e+01   3.7282068e-03
   4.6000000e+01   3.5180337e-03
   4.7000000e+01   3.0521087e-03
   4.8000000e+01   2.8144919e-03
   4.9000000e+01   2.5995609e-03
   5.0000000e+01   2.3675546e-03
   5.1000000e+01   2.1547654e-03
   5.2000000e+01   1.9413328e-03
   5.3000000e+01   1.8121744e-03
   5.4000000e+01   1.6710906e-03
   5.5000000e+01   1.5198475e-03
   5.6000000e+01   1.4118872e-03
   5.7000000e+01   1.3203832e-03
   5.8000000e+01   1.2511230e-03
   5.9000000e+01   1.1630543e-03
   6.0000000e+01   1.1225353e-03
   6.1000000e+01   1.0720129e-03
   6.2000000e+01   1.0334751e-03
   6.3000000e+01   1.0132112e-03
   6.4000000e+01   9.6894695e-04