Short‐wave length instabilities on coastal jets and fronts

Abstract

The stability of a coastal jet and front is investigated using the primitive equations applied to a continuously stratified flow in geostrophic balance. A linear stability analysis successfully explains the growth of two modes of instability with distinctly different horizontal scales. A long‐wavelength mode (fastest‐growing wavelength of 0(100 km)) is found which is a modified version of a traditional baroclinic instability. A second, rapidly growing frontal instability also exists. For a realistic basic state density and flow structure, this mode has its fastest growth at short wavelengths (0(20 km)), e‐folds in less than 1.5 days and propagates rapidly in the direction of the mean flow. The frontal instability grows primarily by extracting the available potential energy of the mean flow via a baroclinic instability mechanism. A small contribution from vertical Reynolds stress is also found, but the transfer via horizontal Reynolds stress is from the eddy to the mean kinetic energy. Further evidence shows that the frontal instability is not a result of horizontal shear instability nor is it an inertial instability. The frontal mode is trapped to the surface front and its influence is confined to the upper water column (z ≲ 70 m). A significant subsurface vertical velocity maximum (20 m d−1 at 30 m) is associated with a frontal instability with a reasonable, as judged by satellite sea surface temperature observations, surface temperature perturbation of 0.35°C. The linear stability predictions are verified by and compared with results from a time‐dependent, three‐dimensional, nonlinear ocean circulation model. Finally, the frontal instability is discussed in the context of other recent stability analyses that yield high‐wavenumber modes.