基于一个非均匀的不可压缩湍流方程组，首先给出了Ekman漂流的密度机制；其次，导出了一个“风旋度——热盐梯度方程式”，并对基进行了一般分析。利用该方程式建立了一个大洋风生——热盐歪流的丙层模型，并与观测和某些经典的大洋环流模型作了分析比较。

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.

Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When K is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on al hodograph plane. Several examples are given to further demonstate the unique properties of the Lagrangian residual current.