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. Pdf of transversal velocity diferences at various separations = dx. Only positive part is included, using the symmetry of the pdf. Re_lambda=142. Field filtered with the Gaussian filter with transfer function F = exp(-k^2 H^2), H=4*eta eta: Kolmogorov scale (Batchelor 1953). L: integral scale (Batchelor 1953). u': one-component rms velocity du : velocity difference at centre of the histogram box pdfs ____________________________________________________________________________ du/u' dx/L =4/3 dx/L=4/6 dx/L=4/9 dx/L=4/12 dx/L=4/15 2.0000000e-002 2.8942585e-001 3.6101895e-001 4.2580185e-001 4.8492985e-001 5.4400900e-001 6.0000000e-002 2.8918265e-001 3.6040855e-001 4.2469910e-001 4.8371185e-001 5.4168600e-001 1.0000000e-001 2.8870740e-001 3.5903170e-001 4.2302060e-001 4.8102560e-001 5.3718500e-001 1.4000000e-001 2.8807335e-001 3.5712935e-001 4.1991780e-001 4.7697080e-001 5.3046900e-001 1.8000000e-001 2.8731315e-001 3.5474895e-001 4.1574020e-001 4.7145205e-001 5.2213500e-001 2.2000000e-001 2.8604760e-001 3.5186340e-001 4.1069830e-001 4.6450750e-001 5.1209500e-001 2.6000000e-001 2.8446575e-001 3.4818340e-001 4.0495290e-001 4.5609225e-001 5.0049750e-001 3.0000000e-001 2.8269425e-001 3.4394265e-001 3.9860450e-001 4.4634940e-001 4.8729010e-001 3.4000000e-001 2.8083565e-001 3.3922360e-001 3.9147305e-001 4.3545935e-001 4.7274605e-001 3.8000000e-001 2.7865735e-001 3.3428455e-001 3.8366940e-001 4.2378645e-001 4.5713525e-001 4.2000000e-001 2.7648135e-001 3.2855870e-001 3.7529255e-001 4.1161485e-001 4.4065340e-001 4.6000000e-001 2.7374850e-001 3.2249930e-001 3.6610045e-001 3.9854165e-001 4.2381490e-001 5.0000000e-001 2.7086495e-001 3.1625635e-001 3.5631810e-001 3.8517215e-001 4.0622355e-001 5.4000000e-001 2.6778620e-001 3.0976935e-001 3.4667340e-001 3.7183105e-001 3.8848900e-001 5.8000000e-001 2.6435695e-001 3.0300495e-001 3.3665405e-001 3.5776795e-001 3.7054975e-001 6.2000000e-001 2.6099335e-001 2.9607945e-001 3.2616215e-001 3.4377625e-001 3.5292245e-001 6.6000000e-001 2.5716100e-001 2.8905330e-001 3.1567825e-001 3.2960265e-001 3.3550725e-001 7.0000000e-001 2.5323715e-001 2.8185460e-001 3.0496620e-001 3.1549605e-001 3.1826905e-001 7.4000000e-001 2.4924920e-001 2.7466225e-001 2.9411935e-001 3.0156555e-001 3.0130120e-001 7.8000000e-001 2.4515555e-001 2.6740515e-001 2.8335170e-001 2.8784715e-001 2.8463745e-001 8.2000000e-001 2.4093920e-001 2.6012395e-001 2.7290725e-001 2.7407475e-001 2.6848185e-001 8.6000000e-001 2.3682555e-001 2.5268475e-001 2.6232255e-001 2.6075215e-001 2.5283205e-001 9.0000000e-001 2.3240070e-001 2.4520395e-001 2.5202730e-001 2.4756935e-001 2.3793835e-001 9.4000000e-001 2.2806040e-001 2.3783790e-001 2.4170840e-001 2.3470390e-001 2.2344080e-001 9.8000000e-001 2.2341705e-001 2.3050660e-001 2.3130525e-001 2.2228260e-001 2.0969790e-001 1.0200000e+000 2.1885130e-001 2.2320030e-001 2.2105465e-001 2.1029980e-001 1.9636990e-001 1.0600000e+000 2.1414145e-001 2.1582370e-001 2.1115350e-001 1.9868690e-001 1.8353790e-001 1.1000000e+000 2.0931720e-001 2.0862255e-001 2.0145895e-001 1.8761725e-001 1.7123935e-001 1.1400000e+000 2.0429045e-001 2.0157400e-001 1.9194325e-001 1.7685725e-001 1.5952680e-001 1.1800000e+000 1.9908380e-001 1.9441660e-001 1.8281420e-001 1.6636800e-001 1.4831115e-001 1.2200000e+000 1.9401030e-001 1.8744645e-001 1.7405175e-001 1.5625185e-001 1.3779060e-001 1.2600000e+000 1.8896290e-001 1.8044280e-001 1.6547090e-001 1.4668655e-001 1.2793485e-001 1.3000000e+000 1.8396155e-001 1.7375470e-001 1.5705185e-001 1.3750965e-001 1.1882810e-001 1.3400000e+000 1.7884860e-001 1.6713130e-001 1.4878160e-001 1.2878405e-001 1.0999565e-001 1.3800000e+000 1.7359370e-001 1.6071800e-001 1.4088915e-001 1.2048425e-001 1.0175370e-001 1.4200000e+000 1.6849655e-001 1.5448950e-001 1.3317215e-001 1.1259950e-001 9.3977750e-002 1.4600000e+000 1.6331000e-001 1.4837740e-001 1.2587210e-001 1.0518980e-001 8.6849450e-002 1.5000000e+000 1.5835105e-001 1.4217235e-001 1.1889650e-001 9.8299300e-002 8.0145500e-002 1.5400000e+000 1.5342295e-001 1.3610100e-001 1.1229390e-001 9.1701250e-002 7.4055000e-002 1.5800000e+000 1.4857035e-001 1.3029515e-001 1.0578415e-001 8.5495350e-002 6.8356000e-002 1.6200000e+000 1.4364875e-001 1.2443625e-001 9.9795000e-002 7.9558000e-002 6.2913750e-002 1.6600000e+000 1.3875640e-001 1.1884550e-001 9.4069050e-002 7.3926100e-002 5.7904250e-002 1.7000000e+000 1.3403540e-001 1.1338230e-001 8.8527900e-002 6.8697000e-002 5.3159600e-002 1.7400000e+000 1.2951290e-001 1.0815625e-001 8.3075050e-002 6.3799100e-002 4.8767610e-002 1.7800000e+000 1.2502575e-001 1.0284595e-001 7.8009000e-002 5.9202500e-002 4.4850960e-002 1.8200000e+000 1.2063410e-001 9.7796750e-002 7.3119550e-002 5.4831050e-002 4.1200960e-002 1.8600000e+000 1.1644395e-001 9.2966650e-002 6.8438500e-002 5.0836800e-002 3.7823440e-002 1.9000000e+000 1.1228275e-001 8.8168200e-002 6.3943300e-002 4.6893330e-002 3.4678790e-002 1.9400000e+000 1.0822780e-001 8.3660450e-002 5.9858500e-002 4.3322695e-002 3.1774560e-002 1.9800000e+000 1.0409130e-001 7.9198300e-002 5.5988800e-002 4.0059850e-002 2.9045455e-002 2.0200000e+000 1.0007655e-001 7.4881200e-002 5.2287750e-002 3.7068830e-002 2.6544965e-002 2.0600000e+000 9.6198350e-002 7.0757050e-002 4.8744360e-002 3.4257855e-002 2.4119765e-002 2.1000000e+000 9.2377700e-002 6.6836950e-002 4.5401765e-002 3.1671170e-002 2.1858900e-002 2.1400000e+000 8.8636300e-002 6.3118800e-002 4.2245150e-002 2.9179230e-002 1.9857030e-002 2.1800000e+000 8.5135200e-002 5.9519600e-002 3.9253790e-002 2.6824285e-002 1.8053930e-002 2.2200000e+000 8.1431050e-002 5.6087850e-002 3.6425860e-002 2.4576735e-002 1.6340505e-002 2.2600000e+000 7.7774850e-002 5.2808000e-002 3.3840450e-002 2.2486220e-002 1.4865925e-002 2.3000000e+000 7.4187200e-002 4.9711975e-002 3.1427235e-002 2.0553780e-002 1.3487600e-002 2.3400000e+000 7.0768300e-002 4.6825225e-002 2.9123320e-002 1.8753055e-002 1.2230430e-002 2.3800000e+000 6.7480450e-002 4.4056400e-002 2.6996745e-002 1.7110250e-002 1.1067710e-002 2.4200000e+000 6.4356600e-002 4.1370675e-002 2.5011995e-002 1.5560685e-002 9.9892850e-003 2.4600000e+000 6.1260300e-002 3.8778600e-002 2.3102835e-002 1.4204510e-002 9.0305800e-003 2.5000000e+000 5.8298600e-002 3.6316875e-002 2.1363725e-002 1.2956995e-002 8.1621100e-003 2.5400000e+000 5.5355100e-002 3.4017240e-002 1.9679440e-002 1.1749535e-002 7.3889500e-003 2.5800000e+000 5.2595650e-002 3.1831410e-002 1.8154360e-002 1.0630760e-002 6.6913450e-003 2.6200000e+000 4.9905045e-002 2.9735100e-002 1.6719485e-002 9.6783950e-003 6.0738950e-003 2.6600000e+000 4.7134320e-002 2.7783955e-002 1.5435675e-002 8.7985300e-003 5.4899200e-003 2.7000000e+000 4.4550685e-002 2.5924930e-002 1.4184090e-002 8.0237050e-003 4.9686485e-003 2.7400000e+000 4.2237205e-002 2.4184410e-002 1.3077870e-002 7.3403350e-003 4.4667305e-003 2.7800000e+000 3.9846990e-002 2.2555560e-002 1.2041620e-002 6.6397100e-003 4.0169235e-003 2.8200000e+000 3.7460330e-002 2.0900250e-002 1.1091565e-002 6.0608100e-003 3.6102140e-003 2.8600000e+000 3.5233210e-002 1.9383310e-002 1.0137880e-002 5.5173800e-003 3.2525860e-003 2.9000000e+000 3.3033325e-002 1.7867685e-002 9.2900450e-003 5.0252000e-003 2.9419430e-003 2.9400000e+000 3.0983525e-002 1.6453300e-002 8.5105100e-003 4.5576580e-003 2.6600965e-003 2.9800000e+000 2.9045835e-002 1.5193970e-002 7.7750600e-003 4.1463130e-003 2.3807025e-003 3.0200000e+000 2.7219335e-002 1.4005535e-002 7.1065900e-003 3.7513645e-003 2.1529540e-003 3.0600000e+000 2.5478580e-002 1.2857235e-002 6.4416900e-003 3.3835080e-003 1.9402540e-003 3.1000000e+000 2.3854390e-002 1.1824825e-002 5.8414000e-003 3.0543455e-003 1.7314905e-003 3.1400000e+000 2.2280030e-002 1.0900940e-002 5.3284950e-003 2.7749640e-003 1.5619730e-003 3.1800000e+000 2.0746035e-002 1.0046300e-002 4.8414175e-003 2.4922100e-003 1.3834290e-003 3.2200000e+000 1.9312065e-002 9.2142150e-003 4.3631210e-003 2.2325740e-003 1.2298670e-003 3.2600000e+000 1.8002330e-002 8.3926750e-003 3.9262415e-003 2.0019800e-003 1.0940275e-003 3.3000000e+000 1.6782620e-002 7.6328650e-003 3.5274545e-003 1.8134650e-003 9.7432750e-004 3.3400000e+000 1.5547980e-002 6.9539600e-003 3.1783995e-003 1.6274395e-003 8.7039950e-004 3.3800000e+000 1.4407425e-002 6.3082950e-003 2.8597350e-003 1.4720385e-003 7.7879750e-004 3.4200000e+000 1.3364700e-002 5.6956400e-003 2.5873200e-003 1.3348865e-003 6.9459050e-004 3.4600000e+000 1.2391550e-002 5.1605600e-003 2.3439220e-003 1.1979800e-003 6.1826950e-004 3.5000000e+000 1.1436510e-002 4.7069025e-003 2.0996290e-003 1.0683580e-003 5.5444600e-004 3.5400000e+000 1.0576585e-002 4.2786200e-003 1.8718435e-003 9.5721850e-004 4.9148075e-004 3.5800000e+000 9.7250500e-003 3.8937405e-003 1.6555865e-003 8.4525750e-004 4.3290630e-004 3.6200000e+000 8.9392500e-003 3.5298580e-003 1.4559600e-003 7.5550750e-004 3.8368955e-004 3.6600000e+000 8.2160700e-003 3.1707710e-003 1.2743255e-003 6.6780500e-004 3.4303330e-004 3.7000000e+000 7.5474700e-003 2.8654505e-003 1.1066105e-003 5.8548700e-004 3.0934320e-004 3.7400000e+000 6.9237400e-003 2.5656610e-003 9.6205100e-004 5.1022050e-004 2.7530965e-004 3.7800000e+000 6.3632750e-003 2.2810185e-003 8.4242450e-004 4.4173665e-004 2.4344695e-004 3.8200000e+000 5.8213500e-003 2.0319050e-003 7.2976450e-004 3.8484240e-004 2.1986265e-004 3.8600000e+000 5.3387250e-003 1.8212650e-003 6.4005100e-004 3.3481620e-004 1.9170375e-004 3.9000000e+000 4.8411230e-003 1.6411515e-003 5.6441650e-004 3.0037800e-004 1.6824210e-004 3.9400000e+000 4.3938675e-003 1.4719405e-003 4.9766200e-004 2.6546140e-004 1.4686535e-004 3.9800000e+000 3.9802900e-003 1.2995775e-003 4.3983565e-004 2.3222510e-004 1.2676410e-004 4.0200000e+000 3.5982195e-003 1.1508235e-003 3.7316675e-004 2.0368600e-004 1.1052615e-004 4.0600000e+000 3.2120775e-003 1.0268800e-003 3.2068770e-004 1.7802900e-004 9.6115550e-005 4.1000000e+000 2.8787200e-003 9.0778100e-004 2.7389930e-004 1.5021355e-004 8.5126700e-005 4.1400000e+000 2.5885710e-003 8.0005150e-004 2.3906860e-004 1.2469145e-004 7.4836950e-005 4.1800000e+000 2.3193195e-003 7.0662150e-004 2.0345295e-004 1.0348640e-004 6.4117900e-005 4.2200000e+000 2.0931040e-003 6.2079600e-004 1.7253460e-004 8.7812600e-005 5.6060250e-005 4.2600000e+000 1.8998920e-003 5.4793350e-004 1.4384830e-004 7.6014300e-005 4.5132735e-005 4.3000000e+000 1.7142955e-003 4.7705790e-004 1.2570940e-004 6.4044350e-005 3.6731670e-005 4.3400000e+000 1.5617400e-003 4.2341370e-004 1.0524020e-004 5.1301700e-005 2.7840030e-005 4.3800000e+000 1.4138935e-003 3.7197715e-004 9.3110800e-005 4.1514755e-005 2.3400340e-005 4.4200000e+000 1.2533410e-003 3.3008225e-004 7.8467200e-005 3.2230660e-005 1.7832335e-005 4.4600000e+000 1.1313720e-003 2.8130695e-004 6.7637750e-005 2.5890000e-005 1.5183240e-005 4.5000000e+000 1.0201590e-003 2.4518850e-004 5.7421600e-005 2.0788040e-005 1.2840755e-005 4.5400000e+000 9.1582650e-004 2.1348520e-004 4.4924240e-005 1.7954980e-005 1.1602055e-005 4.5800000e+000 8.0620800e-004 1.8527725e-004 3.7320355e-005 1.7047420e-005 1.0596380e-005 4.6200000e+000 6.9706750e-004 1.5288715e-004 3.1433480e-005 1.4778520e-005 8.9406950e-006 4.6600000e+000 5.9968900e-004 1.2546410e-004 2.4038090e-005 1.4619080e-005 8.0454000e-006 4.7000000e+000 5.3181800e-004 1.0212510e-004 2.0039915e-005 1.3220950e-005 7.1869000e-006 4.7400000e+000 4.7294935e-004 8.7788050e-005 1.7206855e-005 1.2436030e-005 6.4265100e-006 4.7800000e+000 4.2959500e-004 7.3868050e-005 1.4337005e-005 1.1050160e-005 5.6170650e-006 4.8200000e+000 3.8562730e-004 6.2928300e-005 1.2705845e-005 9.8727850e-006 3.7406205e-006 4.8600000e+000 3.4776735e-004 5.2932850e-005 1.0510530e-005 7.8859650e-006 2.5755090e-006 4.9000000e+000 3.1101115e-004 4.5451610e-005 8.2906850e-006 6.8312300e-006 1.9990855e-006 4.9400000e+000 2.8411545e-004 3.8914715e-005 7.1991600e-006 5.6048000e-006 1.1405825e-006 4.9800000e+000 2.6513030e-004 3.2181600e-005 6.1199000e-006 4.1821365e-006 3.6792995e-008 5.0200000e+000 2.5686415e-004 2.7508890e-005 5.2981900e-006 3.1764615e-006 5.0000000e-015 5.0600000e+000 2.3758460e-004 2.3473925e-005 4.5991235e-006 2.2321080e-006 5.0000000e-015 5.1000000e+000 2.1883245e-004 2.0861625e-005 3.7528850e-006 8.0944600e-007 5.0000000e-015 5.1400000e+000 1.9040375e-004 1.7292705e-005 3.2745765e-006 5.0000000e-015 5.0000000e-015 5.1800000e+000 1.7165155e-004 1.3870960e-005 2.8330605e-006 5.0000000e-015 5.0000000e-015 5.2200000e+000 1.4979655e-004 9.7501400e-006 1.9255000e-006 5.0000000e-015 5.0000000e-015 5.2600000e+000 1.3330100e-004 5.7029150e-006 1.4717195e-006 5.0000000e-015 5.0000000e-015 5.3000000e+000 1.1988385e-004 3.2132545e-006 1.1283185e-006 5.0000000e-015 5.0000000e-015 5.3400000e+000 1.0918935e-004 2.3915445e-006 6.3774500e-007 5.0000000e-015 5.0000000e-015 5.3800000e+000 9.7280650e-005 1.7415350e-006 2.8207960e-007 5.0000000e-015 5.0000000e-015 5.4200000e+000 8.7003150e-005 1.1405825e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.4600000e+000 7.9129450e-005 2.2075795e-007 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.5000000e+000 7.3046350e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.5400000e+000 6.5822650e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.5800000e+000 6.0352750e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.6200000e+000 5.5152700e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.6600000e+000 5.1436600e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.7000000e+000 4.7708240e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.7400000e+000 4.1110035e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.7800000e+000 3.7504320e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.8200000e+000 3.3125955e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.8600000e+000 2.5141875e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.9000000e+000 2.1303140e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.9400000e+000 1.9733310e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.9800000e+000 1.6152120e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.0200000e+000 1.2693580e-005 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.0600000e+000 9.9831650e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.1000000e+000 9.1737200e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.1400000e+000 7.8001150e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.1800000e+000 6.2670750e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.2200000e+000 5.3717750e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.2600000e+000 3.9368500e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.3000000e+000 3.7406205e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.3400000e+000 3.1151395e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.3800000e+000 2.0604075e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.4200000e+000 1.3122835e-006 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015 6.4600000e+000 3.6792995e-008 5.0000000e-015 5.0000000e-015 5.0000000e-015 5.0000000e-015