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The hydraulics of a stratified fluid flowing through a contraction

Published online by Cambridge University Press:  26 April 2006

Laurence Armi  and
Richard Williams
Laurence Armi
Affiliation:
Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093–0230, USA
Richard Williams
Affiliation:
Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093–0230, USA
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Abstract

The steady hydraulics of a continuously stratified fluid flowing from a stagnant reservoir through a horizontal contraction was studied experimentally and theoretically. As the channel narrows, the flow accelerates through a succession of virtual controls, at each of which the flow passes from sub-critical to supercritical with respect to a particular wave mode. When the narrowest section acts as a control, the flow is asymmetric about the narrowest section, supercritical in the divergent section and self- similar throughout the channel. With increased flow rate a new enclosed self-similar solution was found with level isopycnals and velocity uniform with depth. This flow is only symmetric in the immediate neighbourhood of the narrowest section, and in the divergent section remains supercritical with respect to higher internal modes, has separation isopycnals and splits into one or more jets separated by regions of stagnant, constant-density fluid. Flows which are subcritical with respect to lowest modes can also be asymmetric about the narrowest section for higher internal modes. The experiments are interpreted using steady, inviscid hydraulic theory. Solutions require separation isopycnals and regions of stationary, constant-density fluid in the divergent section.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 251 , June 1993 , pp. 355 - 375
Copyright
© 1993 Cambridge University Press

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