A Lagrangian mean theory on coastal sea circulation with inter-tidal transports I. Fundamentals

A brief review is made on the theory of the Lagrangian residual circulation and inter-tidal transports in a convectively weakly nonlinear system. In the review the emphasis is put on the systematical development of the theory and its weakness of convectively weakly nonlinear approximation. The fundamentals of a Lagrangian tidally-averaged theory on circulation with inter-tidal transport processes have been proposed for a general nonlinear coastal/estuarine system. The Lagrangian residual velocity is strictly defined, and it has been verified to be able to embody the velocity field of circulation. A new concept of the concentration for intertidal transport processes is presented. The concentration describing the inter-tidal transport processes should be a "Lagrangian inter-tidal concentration" defined and named, but not the Eulerian tidally-averaged concentration used traditionally. The circulation described here contains a set of infinite temporal-spatial fields of velocity/concentration, each of which corresponds to a specific value of tidal phases varying continuously over one tidal cycle. When the convectively weakly nonlinear condition(with a smaller order of eddy diffusion and sources) is approximately satisfied, a set of infinite temporal-spatial fields of velocity/concentration can be reduced to a single one:the mass transport velocity/the Eulerian tidally averaged concentration as exhibited traditionally.