Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

Abstract

The quasi-geostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Where possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.

Extended version, 24 pages, 1 figure

References in corpus (6)

• New results on group classification of nonlinear diffusion-convection equations
• Symmetry preserving parameterization schemes
• Lie symmetries and exact solutions of the barotropic vorticity equation
• Point symmetry group of the barotropic vorticity equation
• Symmetry Analysis of Barotropic Potential Vorticity Equation
• Symmetry justification of Lorenz' maximum simplification

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• Complete point symmetry group of the barotropic vorticity equation on a rotating sphere
• Solutions of quasi-geostrophic turbulence in multi-layered configurations
• Lie symmetry analysis and one-dimensional optimal system for the generalized 2+1 Kadomtsev-Petviashvili equation
• Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations
• Lie group analysis of a generalized Krichever-Novikov differential-difference equation
• Invariant parameterization of geostrophic eddies in the ocean
• Group foliations, invariant solutions, and conservation laws of the geopotential forecast equation
• Similarity transformations and linearization for a family of dispersionless integrable PDEs
• Exact Anti-Self-Dual four-manifolds with a Killing symmetry by similarity transformations