Taylor-Proudman columns in non-hydrostatic divergent baroclinic and barotropic flows

The Taylor-Proudman theorem states that the velocity of slow, steady flow in a rotating incompressible fluid does not change along the direction of the rotation axis. This fundamental result has been invoked to explain blocking phenomena observed over topographic features in oceanic and atmospheric flows on Earth and atmospheric patterns observed in giant gas planets even in cases where the assumption of incompressibility fails. The possible existence of Taylor-Proudman columns is analyzed here for a less restrictive family of non-hydrostatic divergent density-stratified flows, including situations where the stratification gradient and rotation axis are not parallel. The results show that Taylor-Proudman-like constraints are possible in baroclinic inviscid and viscous nonlinear flows of constant vorticity, Beltrami flows and low-Rossby-number flows. It is found that (1) the baroclinic term is moderated by a factor of the order of the Rossby number, (2) a conservation law can be found for baroclinic flows and (3) Taylor-Proudman columns will be eroded in viscous flows. One particular result stressed in this note is its interpretation in equatorial regions, where the rotation axis is perpendicular to the main stratification gradient, and it is argued that Taylor-Proudman columns could be difficult to discern with observational parameters from convective cells with only zonal and vertical transport. Copyright (C) 2009 Royal Meteorological Society