The Coastal Bottom Boundary Layer: A Note on the Model of Chapman and Lentz

Abstract

Abstract The bottom boundary layer of a stratified flow on a coastal continental shelf is examined using the model of Chapman and Lentz. The flow is driven by a surface stress, uniform in the alongshore coordinate, in a downwelling-favorable direction. The stress diminishes in the offshore direction and produces an Ekman pumping, as well as an onshore Ekman flux. The model yields an interior flow, sandwiched between an upper Ekman layer and a bottom boundary layer. The interior has a horizontal density gradient produced by a balance between horizontal diffusion of density and vertical advection of a background vertical density gradient. The interior flow is vertically sheared and in thermal wind balance. Whereas the original model of Chapman and Lentz considered an alongshore flow that is freely evolving, the present note focuses on the equilibrium structure of a flow driven by stress and discusses the vertical and lateral structure of the flow and, in particular, the boundary layer thickness. The vertical diffusivity of density in the bottom boundary layer is considered so strong, locally, as to render the bottom boundary layer’s density a function of only offshore position. Boundary layer budgets of mass, momentum, and buoyancy determine the barotropic component of the interior flow as well as the boundary layer thickness, which is a function of the offshore coordinate. The alongshore flow has enhanced vertical shear in the boundary layer that reduces the alongshore flow in the boundary layer; however, the velocity at the bottom is generally not zero but produces a stress that locally balances the applied surface stress. The offshore transport in the bottom boundary layer therefore balances the onshore surface Ekman flux. The model predicts the thickness of the bottom boundary layer, which is a complicated function of several parameters, including the strength of the forcing stress, the vertical and horizontal diffusion coefficients in the interior, and the horizontal diffusion in the boundary layer. The model yields a boundary layer over only a finite portion of the bottom slope if the interior diffusion coefficients are too large; otherwise, the layer extends over the full lateral extent of the domain.