Journal article
Internal bores: an improved model via a detailed analysis of the energy budget
Journal of fluid mechanics, Vol.703, pp.279-314
07/25/2012
DOI: 10.1017/jfm.2012.213
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.
Details
- Title: Subtitle
- Internal bores: an improved model via a detailed analysis of the energy budget
- Creators
- Zachary Borden - 1Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USAEckart Meiburg - 1Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USAGeorge Constantinescu - 2Department of Civil and Environmental Engineering, University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- Journal of fluid mechanics, Vol.703, pp.279-314
- Publisher
- Cambridge University Press; Cambridge, UK
- DOI
- 10.1017/jfm.2012.213
- ISSN
- 0022-1120
- eISSN
- 1469-7645
- Number of pages
- 36
- Language
- English
- Date published
- 07/25/2012
- Academic Unit
- Civil and Environmental Engineering
- Record Identifier
- 9983991974002771
Metrics
8 Record Views