Equilibrium solutions of the shallow water equations
arXiv:physics/0008236 · doi:10.1103/PhysRevLett.86.1761
Abstract
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.
4 pages, no figures. Submitted to Physical Review Letters
Cited by in corpus (7)
- Planetary Atmospheres as Non-Equilibrium Condensed Matter
- A statistical mechanics approach to mixing in stratified fluids
- Equilibrium statistical mechanics and energy partition for the shallow water model
- Long-range correlations and coherent structures in magnetohydrodynamic equilibria
- Rotating Shallow Water Dynamics: Extra Invariant and the Formation of Zonal Jets
- Strong vorticity fluctuations and antiferromagnetic correlations in axisymmetric fluid equilibria
- Statistical equilibrium principles in 2D fluid flow: from geophysical fluids to the solar tachocline