Spin-up of a double-diffusive fluid in a cylinder

Abstract

A numerical study is made of the linearized spin-up process of a double-diffusive fluid in a vertically mounted cylindrical vessel of aspect ratio O(1). Both the temperature and concentration conditions render gravitationally stable contributions to the overall density profile. Numerical solutions are acquired to the time-dependent axisymmetric Navier-Stokes equations, using the standard Boussinesq fluid approximations. The major nondimensional parameters are identified. Results are compiled for small Ekman number, the Prandtl number ∼ O(1), and broad ranges of the stratification number St, buoyancy ratio R ϱ , and Lewis number Le, are dealt with. The evolution of the azimuthal velocities is described, and the attendant meridional flows are depicted. The global spin-up process is retarded for a double-diffusive fluid, and this trend is more pronounced as R ϱp increases. The spatial nonuniformity of the rate of spin-up is enhanced as St and R ϱ increase. The effects of double-diffusion on the fields of perturbation density, temperature, and concentration are plotted. The impact of Le on spin-up is illustrated, and the plots of the perturbation physical variables of interest are presented.