Flow of a double-diffusive stratified fluid in a differentially-rotating cylinder

Abstract

A study is made of steady axisymmetric flows of a doublediffusive stratified fluid in a differentially-rotating cylinder. The previous studies on the flow of a single-diffusive fluid are extended to the case of double-diffusive fluid flows. The rotational Reynolds number is large and the overall stratification number is 0(1). The fluid system is thermally stable and solutally unstable; the overall density profile is gravitationally stable. The study is centered on the usual cases of the aspect ratio, A(= height/radius)-0(1), but extreme cases, i.e., A 1 and A 1, are also dealt with. Finite-difference techniques are employed to integrate the full Navier-Stokes equations. Results on the structures of flow, temperature and solute fields are presented. Specific comparisons are made with the flows of a single-diffusive fluid. For aspect ratios 0(1), the main body of the flow field is characterized by the thermal-wind relation. As the effect of double-diffusion increases, the meridional fluid transport intensifies; the effective stratification decreases. These can be interpreted by the fountain effect. The solute boundary layers become very thin at large Lewis numbers. The effective stratification increases with the Prandtl number. For small aspect ratios, the flow field is principally occupied by strong shear flows and effect of stratification is minor. The influence of double-diffusion on the flow is insubstantial. For large aspect ratios, the bulk of the flow field is in state of rigid body rotation. The fountain effect becomes appreciable only when the meridional flows are significant; the impact of doublediffusion is unimportant in the bulk of the flow field.