A TRANSPORT APPROACH TO THE CONVOLUTION METHOD FOR NUMERICAL MODELINGOF LINEARIZED 3D CIRCULATION IN SHALLOW SEAS

A new method for solving the linearized equations of motion is present ed in this paper, which is the implementation of an outstanding idea s uggested by Welander: a transport approach to the convolution method. The present work focuses on the case of constant eddy viscosity and co nstant density but can be easily extended to the case of arbitrary but time-invariant eddy viscosity or density structure. As two of the thr ee equations of motion are solved analytically and the main numerical 'do-loop' only updates the sea level and the transport, the method fea tures succinctness and fast convergence. The method is tested in Heaps ' basin and the results are compared with Heaps' results for the trans ient state and with analytical solutions for the steady state. The com parison yields satisfactory agreement. The computational advantage of the method compared with Heaps' spectral method and Jelesnianski's bot tom stress method is analysed and illustrated with examples. Attention is also paid to the recent efforts made in the spectral method to acc elerate the convergence of the velocity profile. This study suggests t hat an efficient way to accelerate the convergence is to extract both the wind-induced surface Ekman spiral and the pressure-induced bottom Ekman spiral as a prespecified part of the profile. The present work a lso provides a direct way to find the eigenfunctions for arbitrary edd y viscosity profile. In addition, mode-truncated errors are analysed a nd tabulated as functions of mode number and the ratio of the Ekman de pth to the water depth, which allows a determination of a proper mode number given an error tolerance.