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The Quarterly Journal of Mechanics and Applied Mathematics 1972 25(3):303-318; doi:10.1093/qjmam/25.3.303
© 1972 by Oxford University Press
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TRANSIENT AND STEADY STATE VORTICITY GENERATED BY HORIZONTAL TEMPERATURE GRADIENTS

CLAIRE JACOBS

( Department of Mathematics, University of Reading )

The vertical vorticity generated in a viscous fluid bounded by two infinite horizontal disks is examined when, initially, the fluid and the disks are at some constant temperature and are in rigid rotation with constant angular velocity, and then, from t = 0, a steady spatially varying temperature distribution is applied on the lower disk. The solution of the linearized initial-value problem is obtained for small Ekman number. The time required for the transient effects to decay is discussed and the final steady state is shown to be composed of Ekman layers on the disks and an interior flow which is a particular solution of the thermal wind equations.


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