Stability of a coastal upwelling front over topography

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 near a coastal boundary and bottom topography which is an arbitrary function of the cross-shelf coordinate. By combining the various conservation statements for the global properties of the system, a general stability theorem is established which allows the a priori determination of the stability of a coastal upwelling front. Unstable waves are found for the modelled coastal upwelling front. 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 wavenumbers 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 friction will not stabilize the upwelling front. A comparison between the predictions from the simple two-layer model and observed alongfront variability for three areas of active upwelling is presented. Reasonable agreement is found, suggesting that observed alongfront variability can be interpreted in terms of the instability of a coastal upwelling front.