Rotating gravity currents. Part 1. Energy loss theory
Martin, J.R. and LaneSerff, G.F. (2005) Rotating gravity currents. Part 1. Energy loss theory Journal of Fluid Mechanics, 522, pp. 3562. (doi:10.1017/S0022112004001983).
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Description/Abstract
A comprehensive energy loss theory for gravity currents in rotating rectangular channels is presented. The model is an extension of the nonrotating energy loss theory of Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) and the steadystate dissipationless theory of rotating gravity currents of Hacker (PhD thesis, 1996). The theory assumes the fluid is inviscid, there is no shear within the current, and the Boussinesq approximation is made. Dissipation is introduced using a simple method. A head loss term is introduced into the Bernoulli equation and it is assumed that the energy loss is uniform across the stream. Conservation of momentum, volume flux and potential vorticity between upstream and downstream locations is then considered. By allowing for energy dissipation, results are obtained for channels of arbitrary depth and width (relative to the current). The results match those from earlier workers in the two limits of (i) zero rotation (but including dissipation) and (ii) zero dissipation (but including rotation). Three types of flow are identified as the effect of rotation increases, characterized in terms of the location of the outcropping interface between the gravity current and the ambient fluid on the channel boundaries. The parameters for transitions between these cases are quantified, as is the detailed behaviour of the flow in all cases. In particular, the speed of the current can be predicted for any given channel depth and width. As the channel depth increases, the predicted Froude number tends to $\surd 2$, as for nonrotating flows.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1017/S0022112004001983  
ISSNs:  00221120 (print) 

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ePrint ID:  15053  
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Date Deposited:  17 Mar 2005  
Last Modified:  16 Apr 2017 23:34  
Further Information:  Google Scholar  
URI:  http://eprints.soton.ac.uk/id/eprint/15053 
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