STOKES LAYERS IN HORIZONTAL-WAVE OUTER FLOWS

Results are reported of a computational study investigating the respon ses of flat plate boundary layers and wakes to horizontal wave outer f lows. Solutions are obtained for temporal, spatial, and traveling wave s using Navier Stokes, boundary layer and perturbation expansion equat ions. A wide range of parameters are considered for all the three wave s. The results are presented in terms of Stokes-layer overshoots, phas e lends (lags), and streaming. The response to the temporal wave showe d all the previously reported features. The magnitude and nature of th e response ave small and simple such that it is essentially a small di sturbance on the steady solution. Results ave explainable in terms of one parameter xi (the frequency of oscillation). For the spatial wave, the magnitude and the nature of the response are significantly increa sed and complex such that it cannot be considered simply a small distu rbance on the without-wave solution. The results are explainable in te rms of the two parameters lambda(-1) and x/lambda (where lambda is the wavelength). A clear asymmetry is observed in the wake response for t he spatial wave. An examination of components of the perturbation expa nsion equations indicates that the asymmetry is a first-order effect d ue to nonlinear interaction between the steady and first-harmonic velo city components. For the traveling wave, the responses are more comple x and art additional parameter, c (the wave speed), is required to exp lain the results. In general, for small wave speeds the results are si milar to a spatial wave, whereas for higher wave speeds the response a pproaches the temporal wave response. The boundary layer and perturbat ion expansion solutions compares well with the Navier Stokes solution in their range of validity.