Scale Evolution of Finite-Amplitude Instabilities on a Coastal Upwelling Front

Abstract

Nonlinear model simulations of a coastal upwelling system show frontal instabilities that initiate at short alongshore scales but rapidly evolve to longer wavelengths. Several factors associated with the nonstationarity of this basic state contribute to the progression in scale. A portion of the system evolution is associated with the external forcing. Another portion is associated with the alteration of the alongshore mean flow resulting from wave growth. Direct interactions between the finite-amplitude disturbances also promote emergence of new scales. The relative role of each of these mechanisms is isolated through tangent linear simulations about basic states that approximate the nonlinear system to differing degrees. The basic states include an alongshore uniform time-evolving upwelling solution, the alongshore average of a three-dimensionally evolving upwelling solution, and the full three-dimensional nonlinear solution. Disturbance growth about a frozen-field upwelling state is also examined. Perturbation experiments are performed for persistent and relaxed wind forcing. Although the frontal disturbances in the nonlinear model exhibit a progression to larger scale over the full range of forcing scenarios considered, the mechanisms most responsible for the process differ between wind-forced and unforced cases. Under relaxed wind conditions, the perturbation growth experiments indicate that the scale evolution over the first four days is reflected in the way linear disturbances respond to the adjustment of an alongshore uniform upwelling front to wind cessation. The continued increase in scale between days 4 and 7 is related to the linear disturbance evolution on the alongshore average of a flow state that has been altered by wave?mean flow interaction. Past day 7, the observed scale change is not captured in the linear growth experiments and evidently results largely from nonlinear wave?wave interaction processes. Under sustained upwelling winds, the linear growth experiments fail to describe even the earliest scale change in the nonlinear solutions, indicating that nonlinear wave?wave effects are significant from very near the start of the simulations.