The propagation of high-Reynolds-number non-Boussinesq gravity currents in axisymmetric geometry

作者：Ungarish Marius^*

来源：Journal of Fluid Mechanics, 2010, 643: 267-277.

DOI：10.1017/S0022112009992527

• axisymmetric
• bare spot
• gravity current
• Navier Stokes
• non-Boussinesq
• self-similar
• shallow water

We consider the propagation of a non-Boussinesq gravity current in an axisymmetric configuration (Full cylinder or wedge). The current of density rho(c) is released from rest from a lock of radius r(0) and height h(0) into an ambient fluid of density rho(a) in a container of height H. When the Reynolds number is large, the resulting flow is governed by the parameters rho(c)/rho(a) and H* = H/h(0). 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 rho(c)/rho(a) << 1, Boussinesq rho(c)/rho(a) approximate to 1, and heavy rho(c)/rho(a) >> 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 t(1/2), 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.

• 出版日期2010-1-25