Line singularities in unbounded stratified flow

Abstract

We obtain the solutions, under the Oseen and Boussinesq approximations, for the flow field disturbance due to a line singularity in an otherwise uniform, horizontal, inviscid, incompressible flow of a vertically stratified fluid. The results obtained show no upstream influence for those singularities across which [xdtri ]2ψ + (N/U)2ψ is continuous. Doublet and vortex singularities are examples of these. Uniform flows past doublets and vortices are considered for a range of internal Froude numbers, including the calculation of the pressure distributions and drag for the doublet. An application of the vortex solution to flows in the β-plane is discussed.