The Steady Flow Around A Rotating Sphere With Variable Viscosity

A new model of the steady flow around a rotating sphere at large Reynolds numbers is obtained and analysed which has been further augmented with a temperature dependent viscosity. As the sphere rotates, Boundary Layers are formed at the poles and are convected along the sphere surface towards the equator where a collision takes place resulting in a toroidal vortex around the equator. Using Boundary Layer approximations, the full Navier-Stokes problem is reduced to solving simpler, albeit still non-linear, PDE systems in distinct regions around the sphere including the equatorial flow. This area of the flow possesses interesting physical behaviours such as Boundary Layer Separation and Reattachment that forms a Radial Jet causing the toroidal vortex. The current models of the equatorial flow are compared to numerical simulations of the full Navier-Stokes problem, but by incorporating additional azimuthal terms due to the similarity of the equatorial geometry of the sphere with the cylinder, results are greatly improved. The full flow is then compiled and is integrated with a temperature dependent viscosity where results qualitatively agree with similar studies.