Boundary Currents, Free Currents and Dissipation in the Low-Frequency Scattering of Shelf Waves

Abstract

The low-frequency scattering of barotropic shelf waves is considered in the limit of small but nonzero dissipation. For a rectilinear shelf it is shown that an intense oscillatory boundary layer forms on the incident side of any obstacle. This layer destroys incident shelf wave energy and turns volume flux to pass smoothly round the obstacle. By confining attention to low frequencies the results of Wilkin and Chapman for scattering at a discontinuity in shelf width are extended to more general changes in width and more general shelf profiles. A spreading along-shelf free shear layer is present downstream of a widening shelf. For a narrowing shelf this layer carries fluid from the dissipation layer and for a headland the layer represents an intense free midshelf current. It is also shown that a change in shelf width can scatter energy from an oscillatory geostrophic current into shelf waves. This corresponds in a flow with a free surface to scattering of Kelvin wave energy into shelf waves.