Improved Numerical Computing Method for the 3D Tidally Induced Lagrangian Residual Current and Its Application in a Model Bay with a Longitudinal Topography

An improved method for computing the three-dimensional (3D) first-order Lagrangian residual velocity (u(L)) is established. The method computes tidal body force using the harmonic constants of the zeroth-order tidal current. Compared with using the tidal-averaging method to compute the tidal body force, the proposed method filters out the clutter other than the single-frequency tidal input from the open boundary and obtains u(L) that is more consistent with the analytic solution. Based on the new method, u(L) is calculated for a wide bay with a longitudinal topography. The strength and pattern of u(L) are mostly determined by the parts of the tidal body force related to the vertical mixing of the Stokes' drift and the Coriolis effect, with a minor contribution from the advection effect. The geometrical shape of the bay can influence u(L) through the topographic gradient. The magnitude of u(L) increases with the increases in tidal energy input and vertical eddy viscosity and decreases in terms of the bottom friction coefficient.