Formation of a counter current region near a gravitating sphere in a steady Stokes flow of a viscous ideal gas

The steady axisymmetric Stokes flow of a viscous ideal gas past a gravitating sphere is studied. A simple form for the viscosity and thermal conductivity of the gas is assumed and the flow is taken as a small perturbation on the equilibrium state at rest. The method of separation of variables is used to reduce the basic equations to an ordinary fourth order differential equation. Drag coefficients, flow configuations and velocity distributions are given. In particular, the formation of a counter current region near the sphere is clarified for cases with strong gravity.