BAROCLINIC-BAROTROPIC INSTABILITIES OF THE GULF-STREAM EXTENSION

In this paper, the baroclinic-barotropic instability of the Gulf Strea m is studied numerically. The quasigeostrophic potential vorticity equ ation is linearized around the mean flow, which is modeled using data from field measurements in the Gulf Stream off Cape Hatteras. The pert urbation around the mean flow is decomposed into waves along the strea mwise direction using a Fourier transformation in space and a Laplace transformation in time. For each wave, an eigenvalue problem is obtain ed, which is solved numerically to yield the frequency as a function o f the wavenumber. The instability is of the convective type, in the se nse that any localized perturbation will propagate out of any fixed re gion in space in finite time. External noise can, however, drive the i nstability creating spatially growing waves. The spatial growth rates of the waves are computed as a function of their frequency using an it erative procedure and are found to be in good agreement with growth ra tes from field measurements. Visualizations of the computed spatial in stability modes show strong resemblance with the meandering patterns o bserved in pictures of the Gulf Stream.