It is suggested that the shallow sea circulation should be related to the Lagrang residual circulation but not to the conventional Eulerian mean circulation, and further, the first orden Lagrang residual circulation the mass-transport velocity field is used to define the steady cireulation as the lowest order shallow sea circulation. The set of equation governing the shallow sca circulation is reformulated, which shows that there are no the socalled "tidal surface source" and the "tidal stress". A vorticity equation for the stream function of horizontal transports is derived, which is easity 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 s called "tidal dispersion". The theory presented here is hased on a three dimensional weakly nonlinear dynamic system.

Nondimensional equations for dissipative trapped-waves over a continental shelf on an f-plane and solutions xith out consideration of forced functions, namely solutions of free uaves are obtained; nondispersivc shelf waves and edgewaves are investigated, particularly the poroperty of dissipative nondisper. sive shelf waves of broad width and the effect of bottom streses on edgewaves.