Gravity currents from a dam-break in a rotating channel

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Helfrich, Karl R.
Mullarney, Julia C.
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Gravity current
Dam-break problem
The generation of a gravity current by the release of a semi-infinite region of buoyant fluid of depth $H$ overlying a deeper, denser and quiescent lower layer in a rotating channel of width $w$ is considered. Previous studies have focused on the characteristics of the gravity current head region and produced relations for the gravity current speed $c_{b}$ and width $w_b$ as a functions of the local current depth along the wall $h_b$, reduced gravity $g^\prime$, and Coriolis frequency $f$. Here, the dam-break problem is solved analytically by the method of characteristics assuming reduced-gravity flow, uniform potential vorticity and a semigeostrophic balance. The solution makes use of a local gravity current speed relation $c_{b} \,{=}\, c_b(h_b,\ldots)$ and a continuity constraint at the head to close the problem. The initial value solution links the local gravity current properties to the initiating dam-break conditions. The flow downstream of the dam consists of a rarefaction joined to a uniform gravity current with width $w_b$ (${\le}\, w$) and depth on the right-hand wall of $h_b$, terminated at the head moving at speed $c_b$. The solution gives $h_b$, $c_b$, $w_b$ and the transport of the boundary current as functions of $w/L_R$, where $L_R \,{=}\, \sqrt{g^\prime H}/f$ is the deformation radius. The semigeostrophic solution compares favourably with numerical solutions of a single-layer shallow-water model that internally develops a leading bore. Existing laboratory experiments are re-analysed and some new experiments are undertaken. Comparisons are also made with a three-dimensional shallow-water model. These show that lateral boundary friction is the primary reason for differences between the experiments and the semigeostrophic theory. The wall no-slip condition is identified as the primary cause of the experimentally observed decrease in gravity current speed with time. A model for the viscous decay is developed and shown to agree with both experimental and numerical model data.
Author Posting. © Cambridge University Press, 2005. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 536 (2005): 253-283, doi:10.1017/S0022112005004544.
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Journal of Fluid Mechanics 536 (2005): 253-283
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