Mechanisms and Parameterizations of Geostrophic Adjustment and a Variational Approach to Balanced Flow

Abstract

Abstract Geostrophic balance is shown to be the minimum energy state, for a given linear potential vorticity field, for small deviations of the height field around a resting state, in the shallow-water equations. This includes (but is not limited to) the linearized shallow-water equations. Quasigeostrophic motion is evolution on the slow manifold defined by advection of linear potential vorticity by the velocity field that minimizes that energy. Other linear and nonlinear arguments suggest that geostrophic adjustment is a process whereby the energy of a flow is minimized consistent with the maintenance of the potential vorticity field. A variational calculation that minimizes energy for a given potential vorticity field leads to a balance relationship that for the unapproximated shallow-water equations is similar but not identical to geostrophic balance. Preliminary numerical evidence, involving the inversion of potential vorticity for a simple model, indicates that this balance is a somewhat better appro...