Maximum Entropy Mixing in Estuaries

by Dominic M. Di Toro,

Serial Information: Journal of the Hydraulics Division, 1969, Vol. 95, Issue 4, Pg. 1247-1272

Document Type: Journal Paper


A review of the theories of estuarine mixing which have been proposed indicates 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 proposed by Preddy forms the basis for the theory of maximum entropy mixing which is developed in terms of the theory of Markov chains. Three conservation laws which any physically reasonable mixing process must satisfy are related to the properties of a Markov chain. The estimate of the appropriate mixing matrix is then based on the maximum entropy principle of statistical mechanics and information theory. A numerical technique is employed for the solution of the resulting simultaneous transcendental equations. A comparison of the equilibrium salinity intrusion data from the Delaware River Model and the theoretical predictions based on the maximum entropy estimate of the mixing process indicate that the theory of maximum entropy mixing is a sound theoretical and practical solution to the problem of characterizing the mxing process in an estuary.

Subject Headings: Markov process | Entropy methods | Estuaries | Diffusion | Tides | Matrix (mathematics) | Statistics | Numerical methods | Delaware | United States

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