On Nonlinear Geostrophic Adjustment

Abstract

Nonlinear features of the geostrophic adjustment process in a one-dimensional barotropic atmosphere are investigated by means of a perturbation expansion in the Froude number. The initial unbalanced velocity field is a continuous (nonconstant) even function of the spatial coordinate. The steady-state solution shows the southward shift of the axes of maximum geostrophic velocity and zero pressure, first found by Rossby. In addition, the geostrophic fields are asymmetric about their respective axes. The nonlinear oscillation of the whole current system approaches the inertial period and decays like t?½ as time t?∞. However, this oscillation continues for a significantly longer time, before approximate geostrophic balance is reached, than the ?adjustment time? determined from a linear analysis. A possible shortcoming in the quasi-geostrophic approximation, used in some large-scale dynamical models, is indicated by this result.