The effect of horizontal shear flow on geostrophic adjustment in a barotropic fluid

Abstract

The effect of a basic horizontal shear flow on the linear geostrophic adjustment process in an unbounded barotropic fluid is investigated. It is shown that the basic flow is absolutely stable to axially symmetric transverse disturbances and that energy is not abstracted from the basic flow through the action of Reynolds stresses. A potential vorticity equation is derived and solved numerically in order to determine the relative amount of initial energy which is partitioned to geostrophic kinetic and available potential energy, as a function of the initial current width. It is also shown that, in contradistinction to the adjustment process in an atmosphere with a basic state at rest, a significant portion of geostrophic energy resides in the low wave-number part of the energy spectrum. This latter feature is most noticeable when a large gradient of the basic flow exists.