The Motion of a Disc at Angle of Attack in a Rapidly Rotating Fluid

Citation

Wilcox, David Clinton (1970) The Motion of a Disc at Angle of Attack in a Rapidly Rotating Fluid. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EJBR-X182. https://resolver.caltech.edu/CaltechETD:etd-04032009-113521

Abstract

The motion of a thin disc in a slightly viscous incompressible rotating fluid is studied. The axis of rotation is termed the vertical axis and the fluid and disc are in a container which is bounded by horizontal planes. Nonlinear inertia terms and unsteady effects are assumed small relative to the Coriolis acceleration and hence neglected. Of most importance is the fact that the disc is inclined to the container walls at an angle, α, which is not necessarily small. The angle is assumed to be large enough so that there are no closed geostrophic contours between the disc and the walls. Since the equations of motion are linear, the motions in the six degrees of freedom are considered independently. In all cases, a Taylor column is present although, in all but one case, there is fluid flowing across the boundary of the column. The detailed structure of the shear column is examined for infinitesimal angle of incidence. It is shown that it is possible to solve for the geostrophic flow without actually doing the detailed solution for the shear column structure. A static stability study is done and the disc is found to be unstable to small disturbances. The motion of an elliptical plate at finite angle of attack for which the Taylor column is circular is studied. Using the techniques developed for infinitesimal α, an equation relating the geostrophic flow inside and outside the Taylor column is proposed. This equation is general enough to be used for arbitrary motion of any thin plate. However, only the solution for horizontal translation in a specific direction of the elliptical plate is done.

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