A linear analysis of rotating stratified flow past a circular cylinder on a β-plane

Abstract

A linear analysis of rotating stratified quasi-geostrophic flow past a circular cylinder on a β-plane is performed for moderate stratification, i.e. for σS = O(E^½), covering effectively the range $E^{\frac{2}{3}} \ll \sigma \ll 1$, and for strong stratification such that σS = O(1). E [Lt ] 1 is the Ekman number and σS is the product of the Prandtl number and the inverse rotational Froude number. The parameter β measures the importance of the production of relative vorticity by meridional motion. The analysis pivots about a range of β which constrains the interior motion to follow geostrophic contours. For moderate stratification β = O(E^1/4), covering effectively the range E^½ [Lt ] β [Lt ] E^⅛, while for strong stratification E [Lt ] β [Lt ] 1. The dominance of β in the interior is responsible for creating a narrow intense boundary layer along the eastern sector of the cylinder and an extensive blocked flow region surrounded by intense free shear layers west of the cylinder. These narrow regions which channel horizontally O(1) mass flux communicate through corner-like regions centred about the extreme meridional locations of the cylinder. The effect of stratification is to shear the flow vertically and to induce counter-flows laterally. When the stratification is strong the z-dependence is parametric. Nonlinear effects can be ignored when the Rossby number, ε, satisfies the constraints $\epsilon \ll E^{\frac{11}{12}}$ for moderate stratification and $\epsilon \ll \beta^{\frac{1}{7}} E^{\frac{6}{7}}$ for strong stratification. When expressed in terms of the Reynolds number, Re = ε/E, smallness of nonlinear effects can be assured also for high-Reynolds-number flows.