On the Lagrangian Residual Velocity and the Mass-Transport in a Multi-Frequency Oscillatory System

Abstract

Using a three-dimensional weakly nonlinear baroclinic shallow water model, the Lagrangian residual velocity associated with a multi-frequency tidal system has been analyzed. The first-order Lagrangian residual velocity, the mass-transport velocity, has been shown to be the sum of the mass-transport velocities derived from the respective constituents of astronomical tides, and both the wind-driven (barotropic) and the density-driven (baroclinic) components. The second-order perturbation Lagrangian residual velocity, i.e., the Lagrangian drift velocity, has been shown to involve a series of nonlinear interactions between the products of the respective constitutuents of tides, and reflects the periodicities of all the constituents of astronomical tides contained in the multi-frequency tidal system through the initial phases. As an example, the Lagrangian drift velocity induced by an M2-S2 tidal system is analyzed in detail for a more thorough understanding of the mechanism of nonlinear interactions of the second-order dynamics. A coupled set of nonlinear field equations for the mass-transport velocity and the zeroth-order apparent concentration has been derived and used to describe and understand the shallow water residual circulation along with the intertidal transport processes coupled by the wind stress over the sea surface, the heat flux across the water surface, the horizontal gradient of water density, and the tidal body force resulting from the nonlinear interaction among the multi-frequency astronomical tidal variables. An application of the model to the summer circulation in the Bohai Sea, China gives some heuristic results. The tide-induced component of the residual circulation in the Bohai Sea is more appropriately associated with an M2-K1 tidal system than an M2-tidal system alone.