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The propagation of high-Reynolds-number non-Boussinesq gravity currents in axisymmetric geometry
Published online by Cambridge University Press: 24 December 2009
Abstract
We consider the propagation of a non-Boussinesq gravity current in an axisymmetric configuration (full cylinder or wedge). The current of density ρc is released from rest from a lock of radius r0 and height h0 into an ambient fluid of density ρa in a container of height H. When the Reynolds number is large, the resulting flow is governed by the parameters ρc/ρa and H* = H/h0. We show that the one-layer shallow-water model, carefully combined with a Benjamin-type front condition, provides a versatile formulation for the thickness and speed of the current, without any adjustable constants. The results cover in a continuous manner the range of light ρc/ρa ≪ 1, Boussinesq ρc/ρa ≈ 1, and heavy ρc/ρa ≫ 1 currents in a fairly wide range of depth ratio, H*. We obtain finite-difference solutions for the propagation and show that a self-similar behaviour develops for large times. This reveals the main features, in particular: (a) The heavy current propagates faster and its front is thinner than that for the light counterpart; (b) For large time, t, both the heavy and light currents spread like t1/2, but the thickness profiles display significant differences; (c) The energy-constrained propagation with the thickness of half-ambient-depth (when H* is close to 1) is a very limited occurrence, in contrast to the rectangular geometry counterpart in which this effect plays a major role. The predictions of the simple model are supported by some axisymmetric Navier–Stokes finite-difference simulations.
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- Copyright © Cambridge University Press 2009
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