HOM03 Direct numerical simulation of forced isotropic turbulence in a periodic box From: Jimenez, J., Wray, A.A., Saffman, P.G. & Rogallo, R.S., 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech., vol. 255, 65-90. Energy spectra, normalized in Kolmogorov variables: E(k)/(eps^(2/3)*eta^(5/3)) vs. k*eta Re_lambda=97.6 eta: Kolmogorov scale (Batchelor 1953). eps: energy dissipation rate. k: wavenumber E: Three-dimensional spectrum (sums to q^2/2) E11: One-dimensional longitudinal spectrum (normalized to sum u1^2) E22: One-dimensional transverse spectrum (normalized to sum u2^2) k*eta E(k) E11(k1) E22(k1) 0.0000000e+00 0.0000000e+00 5.4069331e+02 2.9212214e+02 2.1529500e-02 6.3580000e+02 5.2448979e+02 5.6796684e+02 3.4973000e-02 5.4333000e+02 1.9566135e+02 2.4633410e+02 5.0922500e-02 2.5695000e+02 9.6720382e+01 1.2560928e+02 6.5414500e-02 1.8030000e+02 5.4311356e+01 7.6079636e+01 8.2788500e-02 1.3033000e+02 3.6105118e+01 5.4936552e+01 9.9671000e-02 9.5422000e+01 2.5755154e+01 3.9538417e+01 1.1532500e-01 7.9639000e+01 1.7892236e+01 3.0666836e+01 1.3100500e-01 6.5875000e+01 1.2876640e+01 2.2940362e+01 1.4778500e-01 5.2929000e+01 9.7402407e+00 1.7795305e+01 1.6497000e-01 4.3001000e+01 7.3373340e+00 1.4170582e+01 1.8082000e-01 3.6348000e+01 5.4702092e+00 1.0904249e+01 1.9664500e-01 3.0548000e+01 4.2068601e+00 8.7175690e+00 2.1328500e-01 2.5817000e+01 3.3084250e+00 7.0582436e+00 2.2984000e-01 2.1098000e+01 2.5373896e+00 5.6477790e+00 2.4575500e-01 1.8008000e+01 2.0235168e+00 4.6282202e+00 2.6184500e-01 1.5298000e+01 1.5962791e+00 3.7503546e+00 2.7868500e-01 1.2869000e+01 1.2770801e+00 3.0737199e+00 2.9543000e-01 1.0878000e+01 1.0234164e+00 2.5327770e+00 3.1161500e-01 9.2202000e+00 8.2958623e-01 2.0871060e+00 3.2768000e-01 7.8176000e+00 6.7111278e-01 1.7264675e+00 3.4429500e-01 6.6781000e+00 5.4794375e-01 1.4291778e+00 3.6077000e-01 5.7437000e+00 4.4991782e-01 1.2133931e+00 3.7689000e-01 4.9375000e+00 3.6955360e-01 1.0111188e+00 3.9310500e-01 4.2327000e+00 3.0426544e-01 8.4586887e-01 4.0957000e-01 3.6298000e+00 2.5280152e-01 7.1707552e-01 4.2618000e-01 3.1358000e+00 2.1013337e-01 6.0280951e-01 4.4258000e-01 2.7135000e+00 1.7553316e-01 5.1329542e-01 4.5894500e-01 2.3563000e+00 1.4662722e-01 4.3885692e-01 4.7538500e-01 2.0385000e+00 1.2382262e-01 3.7525759e-01 4.9169500e-01 1.7793000e+00 1.0353616e-01 3.1945106e-01 5.0801500e-01 1.5499000e+00 8.7646416e-02 2.7351482e-01 5.2427500e-01 1.3519000e+00 7.4478243e-02 2.3532729e-01 5.4058000e-01 1.1806000e+00 6.2926512e-02 2.0216485e-01 5.5712500e-01 1.0331000e+00 5.3254909e-02 1.7387505e-01 5.7354500e-01 9.0573000e-01 4.5583498e-02 1.5011065e-01 5.8985000e-01 7.9339000e-01 3.8810961e-02 1.2990594e-01 6.0631500e-01 6.9809000e-01 3.3301772e-02 1.1229289e-01 6.2272000e-01 6.1539000e-01 2.8509386e-02 9.7391537e-02 6.3899000e-01 5.4300000e-01 2.4410463e-02 8.4895729e-02 6.5526500e-01 4.7956000e-01 2.1005637e-02 7.3924615e-02 6.7179500e-01 4.2214000e-01 1.8045234e-02 6.4172169e-02 6.8826000e-01 3.7367000e-01 1.5539792e-02 5.5942582e-02 7.0461000e-01 3.3016000e-01 1.3422717e-02 4.8950878e-02 7.2095500e-01 2.9292000e-01 1.1632200e-02 4.2855653e-02 7.3739000e-01 2.5947000e-01 1.0069558e-02 3.7418564e-02 7.5377500e-01 2.3047000e-01 8.7329742e-03 3.2864094e-02 7.6995000e-01 2.0491000e-01 7.5922150e-03 2.8919205e-02 7.8626000e-01 1.8216000e-01 6.6151228e-03 2.5378165e-02 8.0276500e-01 1.6232000e-01 5.7485917e-03 2.2302738e-02 8.1930500e-01 1.4430000e-01 5.0142995e-03 1.9659919e-02 8.3565500e-01 1.2871000e-01 4.3671260e-03 1.7341442e-02 8.5199500e-01 1.1490000e-01 3.8173524e-03 1.5293859e-02 8.6844000e-01 1.0234000e-01 3.3445177e-03 1.3535534e-02 8.8482000e-01 9.1597000e-02 2.9224167e-03 1.1954276e-02 9.0108000e-01 8.2117000e-02 2.5608300e-03 1.0597629e-02 9.1735500e-01 7.3449000e-02 2.2453572e-03 9.3683214e-03 9.3381500e-01 6.5705000e-02 1.9750813e-03 8.3217948e-03 9.5026500e-01 5.8907000e-02 1.7311965e-03 7.3652829e-03 9.6658000e-01 5.2801000e-02 1.5262908e-03 6.5389280e-03 9.8297000e-01 4.7353000e-02 1.3415525e-03 5.8044790e-03 9.9939000e-01 4.2499000e-02 1.1835497e-03 5.1582552e-03 1.0158000e+00 3.8179000e-02 1.0430183e-03 4.5917252e-03 1.0321000e+00 3.4385000e-02 9.2016085e-04 4.0808702e-03 1.0483500e+00 3.0877000e-02 8.1201215e-04 3.6382231e-03 1.0648000e+00 2.7781000e-02 7.1793802e-04 3.2410394e-03 1.0813000e+00 2.4988000e-02 6.3578103e-04 2.8950478e-03 1.0977000e+00 2.2519000e-02 5.6180867e-04 2.5796841e-03 1.1140500e+00 2.0274000e-02 4.9866494e-04 2.3076020e-03 1.1304500e+00 1.8271000e-02 4.3977660e-04 2.0577188e-03 1.1469000e+00 1.6481000e-02 3.9119272e-04 1.8423286e-03 1.1631500e+00 1.4865000e-02 3.4716515e-04 1.6484346e-03 1.1794500e+00 1.3438000e-02 3.0818461e-04 1.4741369e-03 1.1958500e+00 1.2122000e-02 2.7434878e-04 1.3223729e-03 1.2123500e+00 1.0939000e-02 2.4434337e-04 1.1839333e-03 1.2287000e+00 9.8918000e-03 2.1724250e-04 1.0608499e-03 1.2450500e+00 8.9437000e-03 1.9341169e-04 9.5209663e-04 1.2615000e+00 8.0813000e-03 1.7242294e-04 8.5548877e-04 1.2778500e+00 7.3140000e-03 1.5372488e-04 7.6644061e-04 1.2941000e+00 6.6301000e-03 1.3715221e-04 6.8890364e-04 1.3104500e+00 5.9994000e-03 1.2240058e-04 6.1958550e-04 1.3268500e+00 5.4307000e-03 1.0927984e-04 5.5707109e-04 1.3433000e+00 4.9189000e-03 9.7643787e-05 5.0254644e-04 1.3597000e+00 4.4591000e-03 8.7291527e-05 4.5098235e-04 1.3760500e+00 4.0467000e-03 7.7905748e-05 4.0697242e-04 1.3924000e+00 3.6675000e-03 6.9830496e-05 3.6676640e-04 1.4088500e+00 3.3265000e-03 6.2520008e-05 3.3077224e-04 1.4252000e+00 3.0181000e-03 5.6010039e-05 2.9874228e-04 1.4415500e+00 2.7435000e-03 5.0114247e-05 2.6984761e-04 1.4579000e+00 2.4918000e-03 4.4947700e-05 2.4371949e-04 1.4743500e+00 2.2618000e-03 4.0100927e-05 2.1965518e-04 1.4907500e+00 2.0551000e-03 3.6038328e-05 1.9920054e-04 1.5071000e+00 1.8679000e-03 3.2220969e-05 1.8006265e-04 1.5235000e+00 1.6989000e-03 2.8826897e-05 1.6299366e-04 1.5398000e+00 1.5473000e-03 2.5856501e-05 1.4789624e-04 1.5561000e+00 1.4077000e-03 2.3126458e-05 1.3421132e-04 1.5724000e+00 1.2824000e-03 2.0697566e-05 1.2177160e-04 1.5888000e+00 1.1682000e-03 1.8455811e-05 1.1039975e-04 1.6053500e+00 1.0632000e-03 1.6522166e-05 1.0056361e-04 1.6217500e+00 9.6956000e-04 1.4651400e-05 9.1275978e-05 1.6380500e+00 8.8529000e-04 1.3091103e-05 8.3138390e-05 1.6544500e+00 8.0886000e-04 1.1609725e-05 7.5765925e-05 1.6708500e+00 7.3791000e-04 1.0283325e-05 6.8960409e-05 1.6872500e+00 6.7502000e-04 9.0453730e-06 6.2702537e-05 1.7035000e+00 6.1889000e-04 8.0040027e-06 5.7433740e-05 1.7199000e+00 5.6751000e-04 7.0821042e-06 5.2613604e-05 1.7363500e+00 5.2156000e-04 6.1130474e-06 4.7767364e-05 1.7527000e+00 4.8053000e-04 5.3018284e-06 4.3692694e-05 1.7690500e+00 4.4437000e-04 4.5846109e-06 3.9950345e-05 1.7854500e+00 4.1303000e-04 3.9186751e-06 3.6464523e-05 1.8019000e+00 3.8677000e-04 3.2953988e-06 3.3165237e-05 1.8181500e+00 3.6497000e-04 2.7496509e-06 3.0218473e-05 1.8345000e+00 3.4766000e-04 2.2467299e-06 2.7320893e-05 1.8509500e+00 3.3560000e-04 1.8144297e-06 2.4754844e-05 1.8674000e+00 3.2928000e-04 1.4205503e-06 2.2209901e-05 1.8838000e+00 3.3029000e-04 1.0565182e-06 1.9541635e-05 1.9001500e+00 3.3873000e-04 7.7408224e-07 1.7157303e-05 1.9166500e+00 3.5865000e-04 5.0727563e-07 1.4500661e-05 1.9331000e+00 3.9542000e-04 2.9607473e-07 1.1728920e-05 1.9494500e+00 4.7508000e-04 1.3163794e-07 8.5726866e-06 1.9658500e+00 6.5563000e-04 2.3875012e-08 4.2144336e-06 1.9748000e+00 7.8482000e-04 0.0000000e+00 0.0000000e+00