Geostrophic adjustment

Abstract

The conservation of potential vorticity of a rotating homogeneous or stratified fluid may, in principle, be used to determine steady‐state field distributions from a given initial state. If the governing equations are linear, if the basic‐state is one of rest, and if the initial field of motion is geostrophically balanced, then no change in this equilibrium state occurs. However, nongeostrophic initial conditions excite transient gravity‐inertia waves that redistribute mass and momentum to ultimately establish a geostrophic steady state, whose potential vorticity is equal to the potential vorticity of the initial state. A steady state may not become established if, for example, hydrodynamic instabilities occur or if wave energy becomes trapped because of inherent refractive properties of the medium. Some examples, which illustrate the properties of geostrophic adjustment and nonadjustment, are presented and discussed. A simple model, which incorporates gross features of atmospheric and ocean flows, is also presented in order to summarize the relationships between the spatial scales associated with the initial conditions and the partition of energy between the allowable modes of oscillation, both transient and steady. The oceanic response to imposed stresses from atmospheric circulation systems and the atmospheric response to sources of wave energy, which includes the introduction of incorrect initial data into numerical simulations, provide practical applications of the theory.