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- W2100022071 abstract "We consider the propagation of a non-Boussinesq gravity current in an axisymmetric configuration (full cylinder or wedge). The current of density ρ c is released from rest from a lock of radius r 0 and height h 0 into an ambient fluid of density ρ a in a container of height H . When the Reynolds number is large, the resulting flow is governed by the parameters ρ c /ρ 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 ρ c /ρ a ≪ 1, Boussinesq ρ c /ρ a ≈ 1, and heavy ρ c /ρ 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." @default.
- W2100022071 created "2016-06-24" @default.
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- W2100022071 date "2009-12-24" @default.
- W2100022071 modified "2023-10-16" @default.
- W2100022071 title "The propagation of high-Reynolds-number non-Boussinesq gravity currents in axisymmetric geometry" @default.
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- W2100022071 doi "https://doi.org/10.1017/s0022112009992527" @default.
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