Analytical solution to the 3D tide-induced Lagrangian residual current in a narrow bay with vertically varying eddy viscosity coefficient

Abstract

The 3D Lagrangian residual velocity (LRV) is solved analytically in a narrow bay employing a vertically varying eddy viscosity coefficient. The nondimensional vertical profile of the eddy viscosity is described by a parabola that is characterized by its minimum value and the location of its symmetry axis. The results show that the LRV has similar structures as that under constant eddy viscosity coefficient when the magnitude is the same. The tidal body force that drives the residual velocity contains two terms, the advection and Stokes’ drift. The total LRV, as well as the LRV induced by each term, are very sensitive to the magnitude of the eddy viscosity coefficient, while the specific profile matters less. With a given magnitude, the specific profile of the varying eddy viscosity coefficient affects the total LRV by changing the LRV induced by the advection term. Moreover, the contribution mechanism of each component of the tidal body force to the total LRV is analyzed. The 3D LRV is mainly determined by the Stokes’ drift stress term regardless of the steepness of the across-bay topography. The depth-integrated and breadth-averaged LRV are mainly determined by the Stokes’ drift stress term with steep topography, but the Stokes’ drift contribution is no longer obvious with gentle topography.