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Internal waves in a contained rotating stratified fluid

Published online by Cambridge University Press:  20 April 2006

Susan Friedlander  and
William L. Siegmann
Susan Friedlander
Affiliation:
Department of Mathematics, University of Illinois, Chicago Circle, Chicago, Illinois 60680
William L. Siegmann
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12181
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Abstract

Small-amplitude time-dependent motions of a uniformly rotating, density-stratified, Boussinesq non-dissipative fluid in a rigid container are examined for the case of the rotation axis parallel to gravity. We consider a variety of container shapes, along with arbitrary values for the (constant) Brunt-Väisälä and rotation frequencies. We demonstrate a number of properties of the eigenvalues and eigenfunctions of square-integrable oscillatory motions. Some of these properties hold generally, while others are shown for specific classes of containers (such as with symmetry about the container axis). A full solution is presented for the response of fluid in a cylindrical container to an arbitrary initial disturbance. Features of this solution which are different from the cases of no stratification or no rotation are emphasized. For the situation when Brunt-Väisälä and rotation frequencies are equal, characteristics of the oscillation frequencies and modal structures are found for containers of quite general shape. This situation illustrates, in particular, effects which are possible when rotation and stratification act together and which have been overlooked in previous investigations that assume that the vertical length scale is much smaller than the horizontal scales.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 123 - 156
Copyright
© 1972 Cambridge University Press

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