Treatment of the Discontinuity in the Spin-up Problem with Impulsive Start

摘要

The spin-up equation derived from the Wedemeyer model is considered. For an impulsive start, the boundary conditions prescribe a discontinuity in the velocity on the boundary. The finite difference solution of the spin-up equation is significantly in error unless the discontinuity is treated properly. A solution in the neighborhood of the discontinuity is derived by a direct coordinate expansion, after a stretching transformation is applied. This solution is used as an approximate initial condition; the approximation is evaluated and tests show that the error is negligible. The details are given for laminar Ekman layers; just the results are given for the turbulent case.