Phys. Rev. E 72, 017302 (2005) [4 pages]Analytic solutions to the shallow water equationsReceived 25 March 2005; published 29 July 2005 Analytic, two-dimensional steady-state solutions to the rotating shallow water equations over variable topography are derived, by exploiting a drastic simplification of the equilibrium problem that occurs for nondivergent flows. For such flows, the equilibrium system decouples, and the cross-stream component of the momentum equation formally reduces to the barotropic vorticity equation. Thus, any solution to the barotropic vorticity equation can be used, in principle, to construct exact equilibrium solutions to the shallow water equations. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.72.017302
DOI:
10.1103/PhysRevE.72.017302
PACS:
47.10.+g, 47.32.−y
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