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 7 === W2 BUDGET FIG 13DR: y- Convection Viscous Pressure Time-dep Total 0.0000e+00 0.3321e-21 -0.6531e-10 0.8488e-11 -0.8352e-23 -0.5682e-10 0.1426e-03 -0.4627e-03 -0.9079e+01 0.3662e+01 0.3075e-03 -0.5417e+01 0.4782e-03 -0.1866e-01 -0.1275e+02 0.1087e+02 0.3420e-02 -0.1896e+01 0.1006e-02 -0.1626e+00 -0.2005e+02 0.1992e+02 0.1525e-01 -0.2712e+00 0.1726e-02 -0.6922e+00 -0.2967e+02 0.2875e+02 0.4554e-01 -0.1564e+01 0.2640e-02 -0.1842e+01 -0.3483e+02 0.3580e+02 0.1078e+00 -0.7669e+00 0.3747e-02 -0.3445e+01 -0.3857e+02 0.4160e+02 0.2170e+00 -0.1991e+00 0.5049e-02 -0.4972e+01 -0.4271e+02 0.4650e+02 0.3821e+00 -0.7944e+00 0.6546e-02 -0.5757e+01 -0.4545e+02 0.5019e+02 0.5978e+00 -0.4202e+00 0.8240e-02 -0.5338e+01 -0.4834e+02 0.5282e+02 0.8397e+00 -0.2007e-01 0.1013e-01 -0.4057e+01 -0.5106e+02 0.5376e+02 0.1074e+01 -0.2879e+00 0.1223e-01 -0.2231e+01 -0.5151e+02 0.5237e+02 0.1271e+01 -0.9772e-01 0.1452e-01 0.2399e+00 -0.5085e+02 0.4934e+02 0.1412e+01 0.1404e+00 0.1702e-01 0.2772e+01 -0.4963e+02 0.4527e+02 0.1494e+01 -0.9279e-01 0.1972e-01 0.4996e+01 -0.4700e+02 0.4051e+02 0.1520e+01 0.2119e-01 0.2263e-01 0.6893e+01 -0.4414e+02 0.3579e+02 0.1501e+01 0.3813e-01 0.2575e-01 0.8157e+01 -0.4154e+02 0.3158e+02 0.1454e+01 -0.3491e+00 0.2908e-01 0.8906e+01 -0.3814e+02 0.2776e+02 0.1390e+01 -0.9134e-01 0.3263e-01 0.9065e+01 -0.3528e+02 0.2454e+02 0.1323e+01 -0.3507e+00 0.3639e-01 0.9274e+01 -0.3291e+02 0.2189e+02 0.1261e+01 -0.4788e+00 0.4038e-01 0.9425e+01 -0.3002e+02 0.1937e+02 0.1205e+01 -0.2071e-01 0.4460e-01 0.9871e+01 -0.2762e+02 0.1692e+02 0.1158e+01 0.3343e+00 0.4904e-01 0.1016e+02 -0.2560e+02 0.1479e+02 0.1124e+01 0.4750e+00 0.5372e-01 0.9947e+01 -0.2340e+02 0.1302e+02 0.1097e+01 0.6629e+00 0.5863e-01 0.9782e+01 -0.2148e+02 0.1149e+02 0.1078e+01 0.8657e+00 0.6379e-01 0.9887e+01 -0.1988e+02 0.9997e+01 0.1066e+01 0.1070e+01 0.6920e-01 0.9613e+01 -0.1831e+02 0.8552e+01 0.1058e+01 0.9175e+00 0.7486e-01 0.9682e+01 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0.1953e+00 0.8348e+01 -0.4932e+01 -0.3612e+01 0.7735e+00 0.5773e+00 0.2062e+00 0.8035e+01 -0.4614e+01 -0.3742e+01 0.6796e+00 0.3588e+00 0.2175e+00 0.7568e+01 -0.4179e+01 -0.3823e+01 0.5721e+00 0.1382e+00 0.2293e+00 0.7269e+01 -0.3735e+01 -0.3804e+01 0.4823e+00 0.2127e+00 0.2416e+00 0.6817e+01 -0.3301e+01 -0.3610e+01 0.4188e+00 0.3248e+00 0.2543e+00 0.6133e+01 -0.2852e+01 -0.3443e+01 0.3535e+00 0.1910e+00 0.2676e+00 0.5543e+01 -0.2524e+01 -0.3149e+01 0.2827e+00 0.1535e+00 0.2815e+00 0.5135e+01 -0.2322e+01 -0.2761e+01 0.2182e+00 0.2707e+00 0.2960e+00 0.4621e+01 -0.2108e+01 -0.2425e+01 0.1608e+00 0.2492e+00 0.3110e+00 0.4120e+01 -0.1891e+01 -0.2219e+01 0.1102e+00 0.1208e+00 0.3268e+00 0.3846e+01 -0.1649e+01 -0.2044e+01 0.6139e-01 0.2147e+00 0.3433e+00 0.3534e+01 -0.1418e+01 -0.1965e+01 0.2292e-02 0.1542e+00 0.3605e+00 0.3247e+01 -0.1194e+01 -0.1875e+01 -0.5550e-01 0.1233e+00 0.3786e+00 0.3052e+01 -0.9971e+00 -0.1670e+01 -0.9296e-01 0.2922e+00 0.3975e+00 0.2663e+01 -0.9075e+00 -0.1348e+01 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