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The Quarterly Journal of Mechanics and Applied Mathematics 1970 23(1):119-125; doi:10.1093/qjmam/23.1.119
© 1970 by Oxford University Press
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ON VISCOUS FLOW WITHIN A ROTATING SPHEROIDAL CONTAINER

DAVID LOPER

( Geophysical Fluid Dynamics Institute, Florida State University Tallahassee )

The response of the rigid body mode of a slightly viscous, incompressible rotating fluid to small perturbations of the axis of rotation of its spheroidal container is found by considering the torque interaction between the fluid and its container. It is shown that, of the infinity of Greenspan's inviscid inertial oscillation modes, only the mode corresponding to rigid rotation about an arbitrary axis possesses angular momentum; all other modes are neglected. This simplification allows consideration of a larger class of container angular velocity vector motions than previously studied. The fluid angular velocity vector has transient oscillations whose frequency is a function of the container shape and the Taylor number. These oscillations die out in time R1/2/{omega} leaving a steady solution having the same period as the prescribed motion of the container angular velocity vector.


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