Thermal Convection in a Large Rotating Fluid Annulus: Some Effects of Varying the Aspect Ratio

Abstract

Previous experiments on thermal convection in a rotating fluid annulus (of depth d, inner radius a and outer radius b subject to an impressed horizontal temperature contrast ΔT have been extended to very small values of the aspect ratio &lambda=D(b-a by using in apparatus of large gap width b−a = 15.34 cm [and mean radius ½( b&plusa = 30.77 cm] and values of d as low as 1 cm. Particular attention was given to 1) the stable vertical temperature contrast (average value σ2ΔT established by the fluid motions; and the dependence on λ and other parameters of (Θc the value of the dimensionless parameter Θ=gdΔp at the transition, due to baroclinic instability, from axismmetric to non-axisymmetric flow. (Here g denotes acceleration due to gravity, Δp/p is the fractional density contrast corresponding to ΔT, and &Omega is the angular speed of basic rotation.) At very low values of λ the area of the side walls, 2π(b+a is so very much less than that of the two rigid end walls,π(b2a2 that the experimental results can usefully he compared with the only available theoretical models in which frictional forces arise only in Ekman boundary layers on the end walls. In agreement with theory, within the axisymmettic régimeσ2 is approximately equal to ½Π(Π=gδν½λ2/(8κρ¯ω2) where ν denotes kinematic viscosity, and k thermal diffusivity] when II≪1 and approaches a value ≲1 when Π≫1; determinations of σ2 in the non-axisymmetric regime show that its value is comparatively unaffected by the presence of baroclinic waves. Experimental values of Θc for values of λ<1 when the effects of viscosity are important, are compatible both quantitatively and qualitatively with theories of the effect of Ekman layer friction on Eady's theory of baroclinic instability. Furthermore, the values of the wavenumber close to the transition from axisymmetric to non-axisymmetric flow, for all values of λ considered, are in reasonable agreement with the linear theories.