Instability waves in the Gulf Stream front and its thermocline layer

We carried out linear instability calculations on a three layer Gulf Stream front model in an attempt to elucidate the interaction of the thermocline layer with surface slopewater shoreward of the front. The basic state is geostrophic balance and constant potential vorticity in the two active layers, but the perturbations are ageostrophic. We found the flow to be unstable to long wave perturbations, the wavelength of the most unstable wave to be of the order of 10 radii of deformation. The instability is mainly baroclinic, 75–85% of the energy supply to the growing perturbation coming from basic flow potential energy. Calculated wavelengths, phase speeds and growth rates, using parameters typical of the Gulf Stream, are similar to those observed. The eigenfunctions of the perturbations show peak cross-front thermocline motions near the inflection points of a frontal wave, and a cyclonic eddy with closed streamlines under a trough, an anticyclonic eddy under a crest. The combined flow (basic state plus perturbation) in the thermocline layer follows the surface streamlines closely, except for small cross-stream anomalies, shoreward just upstream of a wave crest, seaward upstream of a trough. Calculated trajectories have characteristics similar to those observed by RAFOS floats, except that they suggest exchange of thermocline waters exclusively with slopewater