Journal of Fluid Mechanics

A limitation on Long's model in stratified fluid flows

Harvey  Segur a1
a1 California Institute of Technology, Pasadena, California 91109

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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.

(Published Online March 29 2006)
(Received July 15 1970)
(Revised December 21 1970)