A Simple Model for Stratified Shelf Flow Fields with Bottom Friction

Abstract

The effect of bottom friction on the subinertial frequency motion of stratified shelf flow fields is studied in a two-layer f-plane model with idealized shelf and slope bottom topography. Coastal-trapped fire waves and motion forced by the alongshore component of the wind stress at the coast are considered. Vertical turbulent-diffusion effects are assumed to be present in thin surface and bottom-boundary layers, but not at the density interface. Simplifications are achieved by assuming that typical alongshore scales are larger than the offshore scales given by the internal Rossby radius of deformation δ?R and the shelf-slope width, that the upper-layer depth is small compared with the lower-layer depth, and that the topography of the continental margin may be represented by a linear bottom slope of small magnitude. Some results are not dependent on the presence of variable bottom topography; these are obtained first with a flat-bottom ocean adjacent to a vertical coast. A characteristic feature of free and forced motion with alongshore gradients is a decrease of lower-layer velocity and a resultant concentration of flow in the upper layer as the frequency approaches zero. For internal Kelvin waves of frequency ?, this change in velocity structure occurs for ?/α ? 1, where α?1 is barotropic spin-down time, and is accompanied by a decrease in frictional decay as ?/α ? 0. As a result, coastal internal Kelvin waves may be able to participate with relatively small damping by bottom friction in low-frequency phenomena such as El Niño. For motion forced at frequency σ and alongshore wavenumber l, this change in structure occurs for σ/α ? l and σ(lδR)?1 ? 1. Concurrently, the magnitude of the barotropic, forced-shelf-wave component of the flow goes to zero as σ ? 0. Thus, the ?arrested topographic wave? is absent and plays no role in the steady solutions. Qualitatively similar behavior is found on the Oregon shelf in the summer where monthly mean alongshore current at midshelf have substantial vertical shear, but corresponding fluctuations on the several-day time scale are nearly depth-independent. Generalized first-order wave equations are derived to describe the alongshore (y) and time (t) dependence of the lowest-order baroclinic and barotropic components. The response to a wind strees with Heaviside-unit-function behavior in both y and t clearly illustrates how the effects of stratification liberate the ?arrested topographic wave? and how a steady state is achieved where the current to the upper layer and to a region near the coast with offshore scale of O(δR).