Two-Layer Quasigeostrophic Flow over Finite Isolated Topography

Abstract

A quasigeostrophic two-layer model of flow over finite topography is developed. The topography is a right circular cylinder that extends through the lower layer and an order Rossby number amount into the upper layer (finite topography model). Thus, each layer depth remains constant to first order, and the quasigeostrophic approximation can be applied consistently. The model solutions axe compared to those found when the total topographic height is order Rossby number (small topography model). The steady solution for the finite topography model consists of two parts: one similar to the small topography solution and forced by the anticyclonic potential vorticity anomaly over the topography and the other similar to the solution of potential flow around a cylinder and forced by the matching conditions on the edge of the topography. The finite topography model breaks down when the interface goes above the topography. This occurs most easily when the stratification is weak. Closed streamlines occur more readily over the topography when the stratification is weak, opposite to the tendency of the small topography model. The initial value problem is studied in both two-layer geometries. A modified contour dynamics method is developed to apply the boundary and matching conditions on the edge of the topography in the finite topography model. In the small topography model, an eddy is shed that is cyclonic, warm core, and bottom trapped; while the shed eddy is cyclonic, cold core, and surface intensified in the finite topography model.