A Method for Estimating Wind-Driven Frictional, Time-Dependent, Stratified Shelf and Slope Water Flow

Abstract

Friction, the alongshore pressure gradient and time-dependent effects are all of lowest-order importance in the dynamics of wind-driven fluctuating currents and sea levels on continental shelves. Previous work has shown that when all these effects are included, the ocean response can be described by an infinite sum of coastal- trapped waves whose amplitudes satisfy a fully coupled infinite set of forced, first-order wave equations. We present a practical method for solving this coupled set of equations for general low-frequency, large-scale wind stress forcing as input. Convergence properties of the solution are examined analytically. For the same accuracy, more modes are required to describe alongshore currents than sea level and fewer modes are required to describe barotropic than depth-dependent motion. As an example, numerical calculations were carried out for a model of the West Florida Shelf. The sea level field was effectively described by one mode but the alongshore velocity field was not Seven modes were necessary to represent the solution accurately. Decoupling the equations by setting off diagonal elements of the friction coupling coefficients equal to zero significantly changed the alongshore velocity amplitude. For realistic parameter values the Gill and Schumann functionless alongshore velocity field and the Arrested-Topographic Wave alongshore velocity field differed significantly from that of the more general case.