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Circulation-based models for Boussinesq internal bores

Published online by Cambridge University Press:  30 May 2013

Zachary Borden  and
Eckart Meiburg
Zachary Borden
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
Eckart Meiburg*
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: meiburg@engineering.ucsb.edu
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Abstract

Existing control-volume models for predicting the front velocity of internal bores enforce the conservation of mass and streamwise momentum, but not vertical momentum. Instead, they usually invoke an empirical assumption relating the up- and downstream energy fluxes to obtain an additional equation required for determining the pressure jump across a bore. The present investigation develops a control-volume model for internal bores on the basis of mass and momentum conservation alone, without the need for considering energy. This is accomplished by combining the streamwise and vertical momentum equations to obtain a vorticity relation that no longer involves pressure. Hence, this vorticity equation, in combination with the conservation of mass, is sufficient for evaluating the bore velocity. The energy loss across the bore can then be predicted by the streamwise energy equation and compared to the assumptions underlying earlier models. The flux of vorticity across the internal bore predicted by the new model is seen to be in close agreement with direct numerical simulation results. Any discrepancies with experimentally measured bore velocities are shown to be due to the effects of downstream mixing.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Stratified flows Vortex Flows: Vortex dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , R1
Copyright
©2013 Cambridge University Press 

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