On the Lagrangian Residual Velocity and the Mass-Transport in a Multi-Frequency Oscillatory System
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 mess-transport velocities derived from the respective constituencs of astronomical tides, and boch the wind-driven (barotropic) and the density-driven (baroclinic) componencs. The second-order perturbacion 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 conscitutuents of tides, and reflects the periodicities of all the constituents of astronomical tides contained in the multi-frequency tidai system through the initial phases. AS an example, the Lagranglan 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 velocicy and the zeroth-order apparent comcentration 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 resuleing from the nonlinear interaction among the multi-frequency astromomical tidal variables. An application of the model to the summer. The tide-induced component of the residual circulation in the Bohai Sea is more appropriately associated with and M2-K1 tidal system than an M2-tidal system alone.