Stability of a coastal upwelling front: 2. Model results and comparison with observations

Abstract

A two‐layer shallow water equation model is used to investigate the linear stability of a coastal upwelling front. The model features a surface front parallel to a coastal boundary and bottom topography which is an arbitrary function of the cross‐shelf coordinate. The existence of unstable waves on the model coastal upwelling front, as suggested by the general stability theorem developed in a companion paper, is confirmed by solving directly the linearized equations of motion. The unstable wave motions are frontally trapped and dominant in the upper layer. The wave propagates phase in the direction of the basic state flow, and the primary energy conversion is via baroclinic instability. The effect of varying the model parameters is presented. Moving the front closer than ∼2 Rossby radii to the coastal boundary results in a decrease in the growth rate of the fastest growing wave. Increasing the overall vertical shear of the basic state flow, by either decreasing the lower layer depth or increasing the steepness of the interface, results in an increase in the growth of the fastest growing wave. A bottom sloping in the same sense as the interface results in a decrease of the growth rates and alongfront wave numbers of the unstable waves in the system. Linearized bottom friction is included in the stability model and results in a decrease in the growth rates of the unstable waves by extracting energy from the system. Since the unstable mode is strongest in the upper layer, bottom…