Some Aspects of the Forced Wave Response of Stratified Coastal Regions

Abstract

A two-layer model with an idealized continental shelf and slope bottom topography is utilized to study some properties of the response of stratified coastal regions to meteorological forcing with variations in the alongshore direction. The model is such that the coastline is straight, there are no alongshore variations in the bottom topography, and the parameter ?=δ?R/δ?B is small, i.e., ?Lt;1, where δ?R is the internal Rossby radius of deformation and δ?B is a scale length of the bottom topography. In that case, the inviscid response to forcing by an alongshore wind stress is composed of uncoupled baroclinic and barotropic components. The baroclinic component consists of forced internal Kelvin waves, with an offshore scale of the order of δ?R (?15 km) and the barotropic component consists of forced continental shelf waves, with an offshore scale the order of the width L of the continental shelf and slope (L≈100 km). The alongshore scale of the forcing is assumed to be greater than L and the method of solution of Gill and Schumann and of Gill and Clarke is used. As a result, the alongshore and time-dependent behavior of the baroclinic and barotropic components is governed by forced, first-order wave equations. The response to an impulsively applied, upwelling-favorable wind stress with a specialized alongshore structure, i.e., a constant value for a distance of limited extent, is studied to give insight into the qualitative nature of the behavior of the forced time-dependent, baroclinic and barotropic components. The solutions show clearly how the region of forced upward motion of density surfaces may propagate alongshore to locations distant from that of the wind stress which causes the up-welling. They also illustrate how the barotropic onshore flow to the coast is influenced by the propagation of forced continental shelf waves such that the region of onshore flow from the interior to the slope and shelf may also propagate alongshore.