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A limitation on Long's model in stratified fluid flows

Segur, Harvey (1971) A limitation on Long's model in stratified fluid flows. Journal of Fluid Mechanics, 48 (1). pp. 161-179. ISSN 0022-1120. doi:10.1017/S0022112071001526.

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The flow of a continuously stratified fluid into a contraction is examined, under the assumptions that the dynamic pressure and the density gradient are constant upstream (Long's model). It is shown that a solution to the equations exists if and only if the strength of the contraction does not exceed a certain critical value which depends on the internal Froude number. For the flow of a stratified fluid over a finite barrier in a channel, it is further shown that, if the barrier height exceeds this same critical value, lee-wave amplitudes increase without bound as the length of the barrier increases. The breakdown of the model, as implied by these arbitrarily large amplitudes, is discussed. The criterion is compared with available experimental results for both geometries.

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Additional Information:© 1971 Cambridge University Press. Received 15 July 1970 and in revised form 21 December 1970. Published online: 29 March 2006. The author gratefully acknowledges the help he received from Drs Jorg Imberger, J. V. Wehausen, G. M. Corcos, F. S. Sherman, all of the University of California, Berkeley. The work on contractions was carried out while the author was a graduate student at Berkeley. He also thanks Drs H. B. Keller and G. B. Whitham of the California Institute of Technology for their helpful comments on the presentation of the material. Various parts of this work were supported by the National Aeronautics and Space Administration, the National Science Foundation and the Office of Naval Research, U.S. Navy.
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Office of Naval Research (ONR)UNSPECIFIED
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ID Code:32948
Deposited By: Tony Diaz
Deposited On:06 Aug 2012 21:01
Last Modified:09 Nov 2021 21:31

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