A coupled set of partial differential equations and associated boundary conditions is written to describe circulation and salt-flux processes for estuaries in which turbulent mixing results primarily from tidal currents. Similarity solutions, motivated by characteristic salinity distributions observed in estuaries, are obtained for this set of equations and are compared with observational data. The circulation is separated into modes analogous to the barotropic, baroclinic, and Ekman modes of oceanic circulation. The salinity distribution, although coupled to the velocity distribution, is found to vary independently of it as well. The theoretical results are discussed in regard to: (i) correlation between the vertical variations of mean velocity and salinity, (ii) the role of this correlation in maintaining the steady-state salinity distribution in estuaries, and (iii) some implications for computations of flushing and dispersion of contaminants.
Hansen, Donald V., and Maurice Rattray. 2021. "Classic Article: Gravitational circulation in straits and estuaries." Journal of Marine Research 79, (2). https://elischolar.library.yale.edu/journal_of_marine_research/503