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Internal bores: an improved model via a detailed analysis of the energy budget

Published online by Cambridge University Press:  13 June 2012

Zachary Borden ,
Eckart Meiburg  and
George Constantinescu
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
George Constantinescu
Affiliation:
Department of Civil and Environmental Engineering, University of Iowa, Iowa City, IA 52242, USA
*
†Email address for correspondence: [email protected]
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Abstract

Internal bores, or internal hydraulic jumps, arise in many atmospheric and oceanographic phenomena. The classic single-layer hydraulic jump model accurately predicts the bore height and propagation velocity when the difference between the densities of the expanding and contracting layers is large (i.e. water and air), but fails in the Boussinesq limit. A two-layer model, which conserves mass separately in each layer and momentum globally is more accurate in the Boussinesq limit, but it requires for closure an assumption about the loss of energy across a bore. It is widely believed that bounds on the bore speed can be found by restricting the energy loss entirely to one of the two layers, but under some circumstances, both bounds overpredict the propagation speed. A front velocity slower than both bounds implies that, somehow, the expanding layer is gaining energy. We directly examine the flux of energy within internal bores using two- and three-dimensional direct numerical simulations and find that although there is a global loss of energy across a bore, a transfer of energy from the contracting to the expanding layer causes a net energy gain in the expanding layer. The energy transfer is largely the result of turbulent mixing at the interface. Within the parameter regime investigated, the effect of mixing is much larger than non-hydrostatic and viscous effects, both of which are neglected in the two-layer analytical models. Based on our results, we propose an improved two-layer model that provides an accurate propagation velocity as a function of the geometrical parameters, the Reynolds number, and the Schmidt number.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Gravity currents
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 279 - 314
Copyright
Copyright © Cambridge University Press 2012

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