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, Reω = 2ωa2/v, enters the resulting equations. For Reω « 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 Reω = 0·1, 0·3, 0·5. Correction to the Stokes drag due to the rotation of fluid is calculated. Copyright © 1987 John Wiley & Sons, Ltd