© 1981 by Oxford University Press
THE STEADY FLOW OF A VISCOUS FLUID DUE TO A ROTATING SPHERE
(
1Department of Applied Mathematics, University of Western Ontario London, Canada
2Department of Applied Mathematical Studies, University of Leeds Leeds, England
3Department of Mechanical Engineering, University of Kentucky Lexington, Kentucky, U.S.A.
)
The viscous, incompressible, rotationally symmetric flow due to a sphere rotating with a constant angular velocity about a diameter is investigated. The equations of motion can be written in the form of three coupled, nonlinear, elliptic partial differential equations. These equations are expressed in finite-difference form using a specialized technique which is everywhere second-order accurate. Solutions of the finite-difference equations are presented for Reynolds numbers in the range 1 to 5000. No difficulties were encountered in obtaining numerical solutions at values of the Reynolds number higher than 5000, but in these cases the mesh size used was too crude to deal adequately with the boundary layers which form on the sphere.
The numerical results show how the theories which exist at both low and high Reynolds numbers are being approached. There is excellent agreement with previous numerical solutions up to a Reynolds number of 100 and with experimental results over the whole range of Reynolds numbers considered. The equatorial jet which develops with increasing Reynolds number agrees well with that predicted theoretically using the boundary-layer approximations. In the range considered there is no separation of the flow near the equator and the results give no indication that it is likely to occur at higher values of the Reynolds number.