THERMAL CONVECTION IN A ROTATING ANNULUS OF LIQUID: NUMERICAL STUDIES OF THE AXISYMMETRIC REGIME OF FLOW by STEVE

Numerical studies have been made of the mean thermal structure and of heat transfer by the axisymmetric regime of thermal convection in an annulus of liquid that rotates at .. rad/sec about a vertical axis and is subject to a horizontal temperature contrast dT C*. The non-linear time-dependent equations for axisymmetric flow have been integrated numerically on an I.B.M. 7094 computer for values of Y, P, C, 4 and a where Ya P149/ 2 V2 0 , 9 cuATIL if v denotes kinematic viscosity, K thermal diffusivity, g acceleration of gravity, cc thermal coefficient of cubical expansion, b and a the radii of the cylindrical surfaces of the annulus and d the depth of the fluid. The integration was done for values of the mechanical and thermal boundary conditions suggested by previous laboratoTy experiments, namely G = (0.8 to 5) x 10-3,19 = 0.33 to 1,(9 = 0.1 to 5.0, horizontal bounding surfaces rigid or free. Details of the temperature and velocity fields in the transient and steady states have thus been obtained, from which values of certain gross parameters have been calculated. In all cases the final steady flow in most of the inviscid "interior" region was zonal and quasi-geostrophic. The meridional circulation, the streamlines of which were closely related to the isotherms, occurred mainly in comparatively thin layers near the bounding surfaces of the fluid, although in certain circumstances, notably when 49 aA 1 and at the lowest values of . studied, the meridional component of the flow in the "interior" region was not insignificant. Within the side-wall boundary layers the radial temperature variation was not always monotonic. Typical values of Crz, the vertical stability parameter, were 0.7 to 0.8; the corresponding range of N, the Nusselt number, was from 3.5 to 7.5. Typical values of the Rossby number of the interior flow were less than 0.15. Under conditions that are known from experiments to give rise to non-axisymmetric flow, the numerical time iteration failed to converge. Thesis Supervisor: Raymond Hide Title: Professor of Geophysics and Physics