The motion of a plate in a rotating fluid at an arbitrary angle of attack
Slow motion of a thin plate at a finite angle of attack in a rotating container filled with a viscous incompressible fluid is analysed. The Rossby and Ekman numbers are assumed to be small. The solution method is developed by studying horizontal translation of an elliptical plate. The plate is shown to carry a stagnant Taylor column with it as it moves. Detailed analysis of the structure of the vertical shear column bounding the Taylor column is circumvented by integrating the equations of motion across the shear column. A jump condition based upon mass conservation in the shear column which relates the geostrophic regions inside and outside the Taylor column results. This jump condition and its method of derivation can be used to analyse arbitrary (slow) motion of any thin plate at any angle of attack.
The fluid motion resulting when a disk moves using all six degrees of freedom at an infinitesimal angle of attack is discussed. The forces and moments on the disk are calculated and the streamlines of the geostrophic flow are displayed.(Published Online March 29 2006)
(Received September 23 1971)
(Revised April 3 1972)
1 Present address: Applied Theory, Inc., 1010 Westwood Blvd., Los Angeles, California