Lee waves in a stratified flow. Part 2. Semi-circular obstacle

Abstract

A two-dimensional, semi-infinite, stratified shear flow in which the upstream dynamic pressure and density gradient are constant (Long's model) is considered. A complete set of lee-wavefunctions, each of which satisfies the condition of no upstream reflexion, is determined in polar co-ordinates. These functions are used to determine the lee-wave field produced by, and the consequent drag on, a semicircular obstacle as functions of the Froude number within the range of stable flow. The Green's function (point-source solution) for the half-space also is determined in polar co-ordinates.