Equilibrium solutions of the shallow water equations

Details Equilibrium solutions of the shallow water equations Equilibrium solutions of the shallow water equations

2000-08-29

arxiv.org/abs/physics/0008236v1

Physics

Fluid Dynamics

4 pages, no figures. Submitted to Physical Review Letters

Scientific paper

10.1103/PhysRevLett.86.1761

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy cascade, and a 2-d turbulent {\it inverse} energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrain the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.

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