The authors build one-and-a-half order invariant parameterization schemes for the beta-plane barotropic vorticity equation, preserving scale symmetries as equivalence transformations, and report moderately better Fofonoff vortex formation than a standard non-invariant closure.
Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem
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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.
fields
physics.ao-ph 1years
2019 1verdicts
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Invariant parameterization of geostrophic eddies in the ocean
The authors build one-and-a-half order invariant parameterization schemes for the beta-plane barotropic vorticity equation, preserving scale symmetries as equivalence transformations, and report moderately better Fofonoff vortex formation than a standard non-invariant closure.