Transient buoyant convection of a contained fluid driven by the changes in the boundary temperatures
Abstract
Finitedifference numerical solutions are obtained for transients buoyant convection at high Rayleigh numbers of a Boussinesq fluid in a closed cylinder. The linear motions that occur due to a small change in the boundary temperature profiles linear in the vertical coordinate are considered. Previous theoretical studies showed that the meridional circulation, driven by the sidewall boundary layer pumping, brings about the final state on a time scale th = R sub a exp 1/4 N exp 1, where N is the BruntVaisala frequency. By choosing th as the time scale of interest, the theory filters out the internalgravity oscillations of time scale N exp 1. New details on the radial and vertical structures of the flow and temperature fields are presented. The impact of the internalgravity oscillations on the temperature field is shown to be minor. However, the evolution of the velocities is highly oscillatory in time due to the dominant presence of the internalgravity oscillations. Numerically calculated contour maps of the temperature and stream function are constructed, which illustrate the effect of Ra on the flow patterns and on the temperature adjustment process.
 Publication:

ASME Journal of Applied Mechanics
 Pub Date:
 March 1985
 Bibcode:
 1985ATJAM..52..190H
 Keywords:

 Asymptotic Methods;
 Circular Cylinders;
 Incompressible Flow;
 Steady Flow;
 Stream Functions (Fluids);
 Viscous Flow;
 Iterative Solution;
 Poisson Equation;
 Time Dependence;
 Fluid Mechanics and Heat Transfer