The Ekman Matching Condition in a Partially Filled, Rapidly Rotating Cylinder
Abstract
The use of an analytical matching condition in lieu of grid refinement and direct application of the noslip boundary condition in a finitedifference calculation is considered for the case of a partially filled, rapidly rotating cylinder. The right circular cylinder is rotating fast enough that the liquidair interface is nearly vertical. A nonwheelflow velocity is induced by the differential rotation of the top lid. For the flow conditions of interest, the Ekman boundary layers on the horizontal surfaces are quite thin and their resolution using a very fine mesh makes the overall calculation very timeconsuming and costly. We discuss the appropriate form of the Ekman matching condition, which has been widely used in rotating flow theory, to the case of a cylinder which is only partially full, and the fully implicit implementation of that condition into a MACderived, timemarching finitedifference calculation. The resulting algorithm is stable and efficient and the results compare quite well with calculations made using grid refinement and direct application of the noslip condition and with recently published LDV measurements.
 Publication:

Journal of Computational Physics
 Pub Date:
 February 1984
 DOI:
 10.1016/00219991(84)90041X
 Bibcode:
 1984JCoPh..53..266R
 Keywords:

 Computational Fluid Dynamics;
 Ekman Layer;
 Fluid Filled Shells;
 Rotating Cylinders;
 Computational Grids;
 Finite Difference Theory;
 Incompressible Fluids;
 Laser Doppler Velocimeters;
 Rotating Fluids;
 Time Marching;
 Fluid Mechanics and Heat Transfer