Author(s): J. N. McElwaine; N. A. Konopliv; E. Meiburg

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Keywords: Gravity currents; Non-Boussinesq; Front condition; High Reynolds number

Abstract: Powder snow avalanches and turbidity currents are particle-laden gravity currents in which the particles are largely or wholly suspended by fluid turbulence. Despite years of study there is still controversy about the appropriate front condition at high Reynolds number. We describe a theory that reconciles the approaches of von Kármán (1940) and Benjamin (1968) settling the controversy. We compare the vorticity-based modelling approach of Borden and Meiburg (2013) for non-Boussinesq gravity currents to that of Benjamin (1968) and von Kármán (1940). We argue that in the limit of high Reynolds number the only significant dissipation occurs in a mixing layer at the rear of the current. If the von Kármán (1940) theory is modified to include this we show that it is equivalent to the Borden and Meiburg (2013) theory. The Benjamin (1968) theory becomes rather complicated, but is then brought into agreement, though there remain small differences. We give theoretical arguments to justify our assumptions and also show that they agree with direct numerical simulations.

DOI: https://doi.org/10.3850/978-981-11-2731-1_041-cd

Year: 2018