A Theory Of Maximum Entropy Mixing In Estuaries

A review and a critique of the theories of estuarine mixing which have been proposed is presented and it is concluded that the simplifications usually employed in the mixing theories based on the convective diffusion equation are not applicable to the mixing process in, an estuary. The theory of tidal mixing which has been proposed by Preddy is discussed and his approach forms the basis for the theory of maximum entropy mixing which is developed. The analysis of the mixing process in an estuary is formulated in terms of the theory of Markov chains. Three conservation laws which any physically reasonable mixing process must satisfy are formulated and related to the properties of a Markov chain. The estimate of the appropriate mixing matrix is based on the maximum entropy principle of statistical mechanics and information theory. A numerical technique is presented for the solution of the resulting simultaneous transcendental equations. The equilibrium salinity intrusion data from the Delaware River Model is analyzed and compared with the theoretical predictions based on the maximum entropy estimate of the mixing process. The resulting agreement is noted and it is concluded that the theory of maximum entropy mixing is a sound theoretical and practical solution to the problem of characterizing the mixing process in an estuary.Grant NSF-GP 57