Rotating barotropic flow over finite isolated topography

Abstract

The flow of a rotating, incompressible fluid over isolated topography whose non-dimensional height (i.e. topographic height divided by the mean fluid depth) is large compared with the Rossby number is studied. Attention is restricted to flow which is sufficiently shallow that the free-surface equations provide an adequate description. The flow is forced laterally by a specified upstream inflow (obtained from solutions of the zonally symmetric model equations) and by a prescribed surface stress. Dissipation is incorporated using a Rayleigh friction acting anti-parallel to the flow.Steady-state solutions for uniform inflow on an f-plane are found for (a) linear viscous flow, (b) quasi-geostrophic flow with and without friction and (c) inviscid flow with and without a rigid lid. The presence of friction produces an upstream–downstream flow asymmetry over the obstacle and an associated topographic drag while inertial terms produce left-right (relative to an observer looking downstream) asymmetry. The blocking efficiency B (the percentage of the incident mass flux going around the obstacle rather than over it) of a Gaussian obstacle is largest (∼ 100%) for case (a) when viscous effects are small. In contrast quasi-geostrophic theory calculates no flow blocking (B ≡ O). For inviscid inertial theory, B ∼ 10% and is independent of the Rossby number. The presence of a free surface decreases the blocking for small-Rossby-number flow.Numerical solutions of the appropriate initial, boundary-value problem for the complete model equations confirm these results and extend them to include the effects of (i) horizontal shear in the upstream inflow, (ii) the magnitude and shape of the topography, and (iii) variations in the Coriolis parameter (β-effect).