Numerical studies of slow viscous rotating flow past a sphere—1

The Navier-Stokes equations for a steady, viscous rotating fluid, rotating about the z-axis with angular velocity ω are linearized using the Stokes approximation. The linearized Navier-Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity and rotational velocity components. One parameter, R_eω = 2ωa²/v, enters the resulting equations. For R_eω « 1, the coupled equations are solved by the Peaceman-Rachford A.D.I. (Alternating Direction Implicit) method and the resulting algebraic equations are solved by the ‘method of sweeps’. Stream lines for ψ = 0·05, 0·2, 0·5 and magnitude of the vorticity vector z = 0·2 are plotted for R_eω = 0·1, 0·3, 0·5. Correction to the Stokes drag due to the rotation of fluid is calculated.