On the Effects of Vorticity Entrainment in Zonal Jet Flows

Abstract

There is a tendency for certain flows in the atmosphere and oceans to concentrate into narrow streams or currents, which preserve their identity over very large distances. The ability of such flows to overcome the diffusive effects normally encountered in laboratory jet flows is usually explained in terms of the entrainment into the jet of relative vorticity, with a sign which helps to maintain the shear. A simple model which one would expect to exhibit this properly was described by Long who examined the flow of a two-dimensional, viscous jet on a beta-plane, and obtained the first term of an asymptotic series solution for the flow in a region far upstream from some origin. This term is essentially the solution of the linearized jet equations, which represent a balance between Coriolis and viscous forces with the pressure gradient. Unfortunately, Long did not calculate further terms in his expansion and his solution did not therefore contain the effects of advection (or entrainment) of fluid. In the present paper, the second term is calculated. This describes the largest effect of the nonlinear terms on the asymptotic flow and confirms that the entrainment of fluid into a westerly jet enhances the shear, in contrast to jet flows which have no background rotation. Further terms in Long's asymptotic series are also investigated and it is shown, in general, that these are indeterminate.