Baroclinic–Barotropic Instabilities of the Gulf Stream Extension

Abstract

In this paper, the baroclinic-barotropic instability of the Gulf Stream is studied numerically. The quasigeo-strophic potential vorticity equation is linearized around the mean flow, which is modeled using data from field measurements in the Gulf Stream off Cape Hatteras. The perturbation around the mean flow is decomposed into waves along the streamwise direction using a Fourier transformation in space and a Laplace transformation in time. For each wave, an eigenvalue problem is obtained, which is solved numerically to yield the frequency as a function of the wavenumber. The instability is of the convective type, in the sense that any localized perturbation will propagate out of any fixed region in space in finite time. External noise can, however, drive the instability creating spatially growing waves. The spatial growth rates of the waves are computed as a function of their frequency using an iterative procedure and are found to be in good agreement with growth rates from field measurements. Visualizations of the computed spatial instability modes show strong resemblance with the meandering patterns observed in pictures of the Gulf Stream.