Spin-up of a thermally stratified fluid in a cylinder with a conducting sidewall

Abstract

Abstract Numerical solutions for the impulsively started spin-up of a thermally stratified fluid in a cylinder with a perfectly conducting sidewall are presented. The meridional streamfunction plots show that, since the stratification constraint is less severe, the fluid penetrates to a higher level in the sidewall layer and that the corner jet is considerably weaker than for insulated sidewalls. For moderate stratification, the azimuthal flow in the bulk of the interior decays faster for a conducting sidewall. For strong stratification, in the region away from mid-depth the azimuthal flow decays faster for a conducting sidewall. However, for strong stratification and at locations close to mid-depth, since the viscous diffusion effects outweigh the effect of the meridional circulation, the azimuthal flow decays faster for an insulated sidewall.