Linear Instability of a Zonal Jet on an f Plane

Abstract

The linear instability of a zonal geostrophic jet with a cosh?2 meridional profile on an f plane is investigated in a reduced-gravity, shallow-water model. The stability theory developed here extends classic quasigeostrophic theory to cases where the change of active-layer depth across the jet is not necessarily small. A shooting method is used to integrate the equations describing the cross-stream structure of the alongstream wave perturbations. The phase speeds of these waves are determined by the boundary conditions of regularity at infinity. Regions exist in parameter space where the waves that propagate along the jet will grow exponentially with time. The wavelength of the most unstable waves is 2πR, where R is the internal deformation radius on the deep side, and their e-folding time is about 25 days. The upper-layer thickness of the basic state in the system has a spatial structure resembling that of the isopycnals across the Gulf Stream. The unstable waves obtained in the present analysis have a wavelength that is in agreement with some recent observations?based on infrared imaging of the sea surface temperature field?of the fastest- growing meanders? wavelength. Calculated growth rates fall toward the low end of the range of values obtained from these infrared observations on the temporal evolution of Gulf Stream meanders.