Flow past a circular cylinder on a β-plane

Abstract

This paper gives analytical and numerical solutions for both westward and eastward flows past obstacles on a β-plane. The flows are considered in the quasi-geostrophic limit where nonlinearity and viscosity allow deviations from purely geostrophic flow. Asymptotic solutions for the layer structure in almost-inviscid flow are given for westward flow past both circular and more elongated cylindrical obstacles. Structures are given for all strengths of nonlinearity from purely linear flow through to strongly nonlinear flows where viscosity is negligible and potential vorticity conserved. These structures are supported by accurate numerical computations. Results on detraining nonlinear western boundary layers and corner regions in Page & Johnson (1991) are used to present the full structure for eastward flow past an obstacle with a Huff rear face, completing previous analysis in Page & Johnson (1990) of eastward flow past obstacles without rear stagnation points. Viscous separation is discussed and analytical structures proposed for separated flows. These lead to predictions for the size of separated regions that reproduce the behaviour observed in experiments and numerical computations on β-plane flows.