Upwelling of a stratified fluid in a rotating annulus: steady state. Part 1. Linear theory

The linear theory of rotating stratified fluids is applied to describe the steady axisymmetric motion of a stratified fluid in a rotating annulus for values of the stratification parameter S̄ = σ N²/(2Ω)² that are order one or larger: S̄ O(1) . The motion is mechanically driven by either an applied velocity or by an applied stress at the top surface. The side walls are thermally insulated. Primary attention is given to a study of the meridional, or upwelling circulation. Simple analytical solutions are obtained with the aid of the narrow-gap approximation and a justifiable assumption of an infinite depth. In that case the meridional circulation is confined to a surface Ekman layer and to a Lineykin layer of thick-ness of O(S̄-1/2) . It is shown how the solutions for the stress-driven upwelling flow in the annulus apply to a two-dimensional linear model of coastal upwelling in a stratified ocean.