Frictional Convergence in a Decaying Weak Vortex

Abstract

ross-isobaric flow and Ekman pumping are investigated in the frictional spindown of an initially barotropic vortex in a stratified atmosphere. Consistent with early work by Holton and others, it is found that the stratification limits the vertical penetration of the secondary circulation driven by friction, resulting in more rapid spindown than in the unstratified case. As a result, the cross-isobaric flow and Ekman pumping are weaker and shallower than classical calculations ignoring the stratification would lead one to believe. The effect of stability becomes stronger as the vortex becomes smaller for fixed boundary layer depth. For weak geostrophic vortices with horizontal scales of several hundred kilometers or less, such as tropical easterly waves, the reduction is particularly pronounced, which raises questions about the efficacy of Ekman pumping in forcing convection in such vortices. These results suggest a revised conceptual model for the role of Ekman pumping in the atmosphere. The theory as it stands is limited to weak, linear vortices in which geostrophic balance holds approximately, corresponding to small Rossby number, though extensions of the analytical theory to stronger vortices may be possible.