3D Unsteady Flow: approximation to Ekman layer (P.R. Spalart, J.Fluid Mech. 205, 319) Free-stream velocity components are U,inf = U,0 cos(ft) and W,inf = U,0 sin(ft). U and W (and all six Reynolds stresses) are non-zero, but are functions of y and t only, not of x and z (so V = 0 by continuity). A program capable of computing steady flow over infinite swept wings (z coordinate along generators and d[ ]/dz=0) could be adapted: Ud[ ]/x becomes d[ ]/dt; Vd[ ]/dy and Wd[ ]/dz are zero - for different reasons - and the program can be stepped in time instead of marching in x. Notation is explained in the JFM paper, especially para. 3.1: the defining Reynolds number, Rl, is U,0 [2/(f*nu)]^(1/2) where f is in rad/sec not Hz: it is independent of time. The length scale,delta = (Utau)/f, is quite close to the physical thickness: y- = y/delta. Rt = (Utau)*(delta)/nu. Phi0 (phi* in the JFM paper, eq. 18) is related to the direction of the surface shear stress, alpha = lim tan^1 (W/U) by eq. 18: it is not relevant to the computations. Rl Utau Phi0 Rt 766.51428 0.05580 0.30867 914.74451 === Part 3 === RMS, FIG 12: U+, V+, W+ 0.0000e+00 0.7613e-11 0.8396e-11 0.4266e-11 0.1426e-03 0.4983e-01 0.2268e-03 0.3301e-01 0.4782e-03 0.1650e+00 0.2072e-02 0.1053e+00 0.1006e-02 0.3454e+00 0.8532e-02 0.2092e+00 0.1726e-02 0.5898e+00 0.2278e-01 0.3337e+00 0.2640e-02 0.8922e+00 0.4741e-01 0.4666e+00 0.3747e-02 0.1237e+01 0.8346e-01 0.5980e+00 0.5049e-02 0.1595e+01 0.1304e+00 0.7209e+00 0.6546e-02 0.1927e+01 0.1867e+00 0.8317e+00 0.8240e-02 0.2199e+01 0.2502e+00 0.9299e+00 0.1013e-01 0.2393e+01 0.3185e+00 0.1016e+01 0.1223e-01 0.2509e+01 0.3893e+00 0.1091e+01 0.1452e-01 0.2557e+01 0.4599e+00 0.1156e+01 0.1702e-01 0.2552e+01 0.5284e+00 0.1211e+01 0.1972e-01 0.2511e+01 0.5930e+00 0.1256e+01 0.2263e-01 0.2446e+01 0.6525e+00 0.1292e+01 0.2575e-01 0.2367e+01 0.7060e+00 0.1318e+01 0.2908e-01 0.2280e+01 0.7530e+00 0.1336e+01 0.3263e-01 0.2191e+01 0.7931e+00 0.1346e+01 0.3639e-01 0.2101e+01 0.8266e+00 0.1352e+01 0.4038e-01 0.2016e+01 0.8537e+00 0.1354e+01 0.4460e-01 0.1939e+01 0.8745e+00 0.1354e+01 0.4904e-01 0.1871e+01 0.8898e+00 0.1353e+01 0.5372e-01 0.1814e+01 0.8999e+00 0.1352e+01 0.5863e-01 0.1766e+01 0.9053e+00 0.1349e+01 0.6379e-01 0.1725e+01 0.9069e+00 0.1344e+01 0.6920e-01 0.1690e+01 0.9055e+00 0.1337e+01 0.7486e-01 0.1660e+01 0.9019e+00 0.1326e+01 0.8077e-01 0.1632e+01 0.8970e+00 0.1313e+01 0.8696e-01 0.1607e+01 0.8913e+00 0.1300e+01 0.9341e-01 0.1581e+01 0.8850e+00 0.1289e+01 0.1001e+00 0.1554e+01 0.8783e+00 0.1280e+01 0.1072e+00 0.1524e+01 0.8711e+00 0.1270e+01 0.1145e+00 0.1492e+01 0.8638e+00 0.1259e+01 0.1221e+00 0.1459e+01 0.8576e+00 0.1245e+01 0.1300e+00 0.1426e+01 0.8523e+00 0.1230e+01 0.1383e+00 0.1393e+01 0.8467e+00 0.1217e+01 0.1469e+00 0.1362e+01 0.8407e+00 0.1207e+01 0.1558e+00 0.1327e+01 0.8360e+00 0.1198e+01 0.1651e+00 0.1292e+01 0.8331e+00 0.1193e+01 0.1748e+00 0.1257e+01 0.8307e+00 0.1192e+01 0.1849e+00 0.1221e+01 0.8271e+00 0.1190e+01 0.1953e+00 0.1176e+01 0.8207e+00 0.1188e+01 0.2062e+00 0.1126e+01 0.8100e+00 0.1183e+01 0.2175e+00 0.1072e+01 0.7950e+00 0.1172e+01 0.2293e+00 0.1013e+01 0.7770e+00 0.1153e+01 0.2416e+00 0.9559e+00 0.7576e+00 0.1127e+01 0.2543e+00 0.9045e+00 0.7372e+00 0.1097e+01 0.2676e+00 0.8584e+00 0.7147e+00 0.1070e+01 0.2815e+00 0.8222e+00 0.6881e+00 0.1048e+01 0.2960e+00 0.7954e+00 0.6598e+00 0.1024e+01 0.3110e+00 0.7751e+00 0.6333e+00 0.9966e+00 0.3268e+00 0.7555e+00 0.6119e+00 0.9599e+00 0.3433e+00 0.7334e+00 0.5979e+00 0.9136e+00 0.3605e+00 0.7148e+00 0.5888e+00 0.8602e+00 0.3786e+00 0.7016e+00 0.5801e+00 0.8064e+00 0.3975e+00 0.6872e+00 0.5667e+00 0.7612e+00 0.4174e+00 0.6588e+00 0.5440e+00 0.7217e+00 0.4383e+00 0.6243e+00 0.5122e+00 0.6826e+00 0.4603e+00 0.5928e+00 0.4820e+00 0.6455e+00 0.4836e+00 0.5479e+00 0.4579e+00 0.6028e+00 0.5082e+00 0.4994e+00 0.4365e+00 0.5495e+00 0.5343e+00 0.4702e+00 0.4174e+00 0.5050e+00 0.5620e+00 0.4598e+00 0.3999e+00 0.4762e+00 0.5916e+00 0.4542e+00 0.3850e+00 0.4423e+00 0.6232e+00 0.4343e+00 0.3743e+00 0.4012e+00 0.6572e+00 0.4080e+00 0.3631e+00 0.3618e+00 0.6939e+00 0.3914e+00 0.3411e+00 0.3238e+00 0.7337e+00 0.3665e+00 0.3055e+00 0.2982e+00 0.7772e+00 0.3270e+00 0.2697e+00 0.2739e+00 0.8251e+00 0.2695e+00 0.2329e+00 0.2299e+00 0.8783e+00 0.1883e+00 0.1815e+00 0.1735e+00 0.9381e+00 0.1130e+00 0.1258e+00 0.1046e+00 0.1006e+01 0.6843e-01 0.8009e-01 0.6028e-01 0.1086e+01 0.4466e-01 0.5070e-01 0.3990e-01 0.1180e+01 0.2544e-01 0.3511e-01 0.2558e-01 0.1297e+01 0.1973e-01 0.2395e-01 0.2180e-01 0.1451e+01 0.1672e-01 0.2132e-01 0.1586e-01 0.1674e+01 0.1119e-01 0.1691e-01 0.1241e-01 0.2088e+01 0.6449e-02 0.9765e-02 0.6177e-02