Gravity Currents from a dam-break in a rotating channel

Abstract

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 cb and width wb as a functions of the local current depth along the wall hb, reduced gravity g′, 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 cb = cb(hb,...) 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 wb (≤ w) and depth on the right-hand wall of hb, terminated at the head moving at speed cb. The solution gives hb, cb, wb and the transport of the boundary current as functions of w/LR, where LR = √g′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.