A VARIATIONAL FORMULATION FOR BAROTROPIC QUASI-GEOSTROPHIC FLOWS

We derive simplified balanced equations by introducing perturbation ex pansions in the variational principle of a low-order fluid model and i n that of the rapidly rotating shallow-water equations. In the case of the shallow-water equations, this provides a constrained variational principle for the barotropic quasi-geostrophic equations which is base d on the Lagrangian description of the fluid. Our results thus show th at the quasigeostrophic equations can be derived systematically in the context of Lagrangian variational principles.