Stationary waves on oceanic density fronts

Abstract

Persistent density fronts are a well recognized feature of the upper ocean, with the Gulf Stream front representing the best known example. Their mean flows are strong, along-front baroclinic jets that have order one Rossby numbers and are thus not inherently geostrophic. Usually the fronts are shallow features with pycnocline depths only a few percent of the total water depth, the Gulf Stream being an exception. Large-scale, large-amplitude waves or meanders frequently disturb the fronts with phase speeds that are slow compared to the mean current. A simple model of such waves is developed where a shallow, upper layer is treated, uncoupled from the heavier, lower layer (barotropic model). The flow basic state is essentially that suggested by Stommel as a simple model for the Gulf Stream. The potential vorticity of the upper-layer water in the frontal zone is taken to be uniform and equal to that in the adjacent reservoir of light water from which it originated. Thus, the basic state has zero cross-stream potential vorticity gradient in both layers. Small-amplitude, free wave perturbation solutions are found with zero phase speed relative to the heavier water. Thus the frontal meanders are stationary for all permitted along-front wave numbers. The waves are frontal trapped and occur as a sequence of normal modes. The lowest mode has a wavelength maximum of about 1.5 internal Rossby radii. The wave dynamics is ageostrophic. Perturbations in layer depth and downstream velocity are nearly out of phase while cross-stream velocity is in quadrature phase, thus producing zero mean wave-induced Reynolds stress. There is then no mechanism for energy exchange between the waves and the basic state, consistent with the steady-state wave solutions found. The condition may be altered, however, by small but finite, cross-stream flow in the basic state, neglected in the present model.