On the stratified Taylor column

Abstract

We analyse the effects of small, circularly symmetric topography on the slow flow of an inviscid, incompressible, diffusionless, horizontally uniform, baroclinic current and show that the vertical influence depends primarily on three parameters: a stratification measure S (the square of the ratio of buoyancy frequency times height scale to Coriolis parameter times length scale), a topographic parameter β (ratio of scaled topographic height multiplied by scaled bottom current to Rossby number ε) and the scaled upstream shear u′0(z) (the dimensional upstream shear divided by the ratio of the r.m.s. upstream flow speed to height scale). Investigating a linear stratification model we find that the topographic effect is depth independent if S ≲ ε and a Taylor column, as indicated by the appearance of closed streamlines above the bump, exists when β > 2. Moderate stratification (S ∼ 1) causes the flow to be fully three-dimensional and the Taylor column to be a conical vortex whose height depends on β S and u′0). The results are compared with Davies's (1971, 1972) experiments. Our results tend to support the Taylor column theory of Jupiter's Great Red Spot but effects due to variations in the Coriolis parameter with latitude have been (unjustifiably) ne glected. Using typical values for the earths oceans we find that Taylor columns of significant height could be found there. Some pertinent observations from the ocean are discussed. © 1973, Cambridge University Press. All rights reserved.