Transient Buoyant Convection of a Contained Fluid Driven by the Changes in the Boundary Temperatures

Finite-difference numerical solutions are obtained for transient buoyant convection at high Rayleigh numbers of a Boussinesq fluid in a closed cylinder. We consider the linear motions that occur due to a small change in the boundary temperature profiles linear in the vertical coordinate. Previous theoretical studies showed that the meridional circulation, driven by the sidewall boundary layer pumping, brings about the final state on a time scale t_h = R_a^1/4 N⁻¹, where N is the Brunt-Va¨isa¨la¨ frequency. By choosing t_h as the time scale of interest, the theory filters out the internal-gravity oscillations of time scale N⁻¹. New details on the radial and vertical structures of the flow and temperature fields are presented. The impact of the internal-gravity 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 internal-gravity 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.