Conservation equations for a mixture of fluids with two components are reviewed. Equations of continuity for sea (salt) water and for river (fresh) water in a turbulent mixing process in an estuary are developed. One source of error in certain similar equations in the literature is the omission of the turbulent diffusion flux.
Arthur, Robert S.. 1964. "The equations of continuity for seawater and river water in estuaries." Journal of Marine Research 22, (2). https://elischolar.library.yale.edu/journal_of_marine_research/1029