LINEAR INSTABILITY OF A ZONAL JET ON AN F-PLANE

The linear instability of a zonal geostrophic jet with a cosh(-2) meri dional profile on an f plane is investigated in a reduced-gravity, sha llow-water model. The stability theory developed here extends classic quasigeostrophic theory to cases where the change of active-layer dept h ac:ross the jet is not necessarily small. A shooting method is used to integrate the equations describing the cross-scream structure of th e alongstream wave perturbations. The phase speeds of these waves are determined by the boundary conditions of regularity at infinity. Regio ns exist in parameter space where the waves that propagate along the j et will grow exponentially with rime. The wavelength of the most unsta ble waves is 2 pi R, 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 re sembling that of the isopycnals across the Gulf Stream. The unstable w aves obtained in the present analysis have a wavelength that is in agr eement with some recent observations-based on infrared imaging of the sea surface temperature field-of the fastest-growing meanders' wavelen gth. Calculated growth rates fall toward the low end of the range of v alues obtained from these infrared observations on the temporal evolut ion of Gulf Stream meanders.