Abstract
The energy‐Casimir method is employed to examine the stability of both non‐parallel and parallel basic flows in the semi‐geostrophic (SG) model in isentropic coordinates (ICs) based on the wave‐activity invariants. It is found that the stability criteria for non‐parallel basic flow under small‐amplitude disturbances are more complicated than those for parallel basic flow, and the spatial structure of basic flow at a horizontal boundary has a great impact on the stability of both parallel and non‐parallel basic flow. Results obtained in this work extend the stability results of Eliassen which are valid for parallel basic flow with non‐normal geostrophic flow as lateral boundary conditions. It is shown that, although there is a strong similarity between the SG model in ICs and the shallow‐water SG (SWSG) model, the finite‐amplitude stability theorems for the latter model cannot be extended to the SG model in ICs and the reasons for the failure are discussed.
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