Rapid formation of taylor columns: Obstacles against sidewalls

Abstract

Abstract The problem of topographic forcing by an obstacle against the boundary of a rotating flow is considered in various parameter regimes. The timescale for the motion is the topographic vortex-stretching time, which is inversely proportional to the background rotation rate and the fractional height of the obstacle. For slow flows this time is short compared with the advection time and the governing equation of conservation of potential vorticity is linear. The final state satisfies the non-linear equation for the advection of potential vorticity, however, and so time dependence has given a specific solution to a non-linear problem. The presence of the sidewall causes a stagnant Taylor column to be set up far more rapidly than cases with no sidewall. It is shown that viscosity and mixing arrests the inviscid evolution at some stage, thus some fluid still crosses the obstacle in the steady state. These solutions suggest that experimental results on separation obtained by Griffiths and Linden (1983) can tentatively be ascribed to entrainment and expulsion of fluid through vertical shear layers at the edge of the topography.