On the fundamental dynamics of barotropic circulation in shallow seas

It is suggested that the shallow sea circulation should be related to the Lagrangian residual circulation but not to the conventional Eulerjan mean circulation, and further, the first order Lagrangian residual circulation the mass-transport velocity field is used to define the steady circulation as the lowest order shallow sea circulation.
The set of equation governing the shallow sea circulation is reformulated, which shows that there are no the so-called "tidal surface source" and the "tidal stress".A vorticity equation for the stream function of horizontal transports is derived, which is easily solved by the conventional numerical methods.
An intertidal convection-diffusion equation governing the concentration of conservative and passive tracer is derived.Differing from the conventional equation, the equation derived in the present paper reveals the Lagrangian convection and has no need to introduce the artificial hypothesis for the so-called "tidal dispersion".
The theory presented here is base on a three-dimensional weakly nonlinear dynamic system.