Abstract
A multilayer model consisting of n homogeneous layers is used to describe the three-dimensional steady flow of a continuously stratified, incompressible fluid under the assumption of hydrostatic balance. For n = 1, one has the classical shallow water theory and the governing equations correspond to those for the steady two-dimensional flow of a compressible gas with y, the ratio of specific heats, equal to 2. For n > 1, the equations form a nonlinear system of partial differential equations of order 2 n. For most practical stratified flow problems this system is neither totally hyperbolic or totally elliptic; i.e., it possesses both real and imaginary characteristics over the entire domain of interest. A numerical algorithm for this “mixed” case is proposed and calculations for a two-layer model are presented. Continuous solutions are shown to exist for sufficiently flat and smooth obstacles.
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