Thermally-forced stratification build-up in an initially isothermal, contained fluid

Abstract

A study is made of transient motions of an initially isothermal, contained fluid in response to an impulsively imposed vertical temperature gradient at the boundaries. Finite-difference numerical solutions have been obtained for a Boussinesq fluid in a circular cylinder with the final state temperature profile linear in the vertical coordinate, with large Rayleigh numbers. New details of the transient flow and the development of temperature field are presented. Descriptions are given for the fundamental mechanism of meridional circulation driven by buoyant boundary layer pumping. A propagating front divides the temperature field into two regions; ahead of the front, the fluid remains to be non-stratified, and behind the front the fluid is being stratified. The flow evolution in the core behaves in a decaying oscillatory manner. The oscillatory nature is due to the presence of internal waves. The temperature evolution in the core is less oscillatory. The temperature adjustment process is governed primarily by the diffusive effects at very early times, by advection at intermediate times, and by the diffusion effects at very large times. Specific comparisons of the terms in the vorticity equation are presented to assess the effect of the Rayleigh number.