Nonlinear Displacement of the Geostrophic Velocity Jet Created by Mass Imbalance

Abstract

Nonlinear geostrophic adjustment to a mass imbalance is investigated analytically, focusing on horizontal displacement of the equilibrium velocity jet. For no initially imposed horizontal length scale, the jet displacement is the difference between the deformation radii of the two initial states; as the mass imbalance increases, the displacement approaches the deformation radius of the dominant state. For a disturbance of finite width, the jet displacement decreases as the initial width decreases, but disturbances of relatively small width can still produce appreciable displacements. For an axisymmetric disturbance, geometric dispersion reduces the jet displacement. A two-layer model creates two jets, the displacements of the lower and upper jets being, respectively, slightly larger and considerably smaller than that predicted by the one-layer model. For stratified fluids, these mass differences represent horizontal changes in stratification. An example of jet displacement resulting from horizontal stratification differences occurs at a surface temperature discontinuity, where reduced stratification produced by vertical mixing over a warmer surface creates jets in the boundary layer and in the free atmosphere: when the boundary layer becomes well mixed, the jet displacements approach a mesoscale deformation radius that depends upon the free atmosphere stratification and the boundary-layer depth.