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A numerical investigation of constant-volume non-Boussinesq density currents

Bonometti, Thomas and Ungarish, Marius and Balachandar, Sivaramakrishnan A numerical investigation of constant-volume non-Boussinesq density currents. (2010) In: 7th International Conference on Multiphase Flow - ICFM 2010, 30 May 2010 - 4 June 2010 (Tampa, United States).

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The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents of density ρc, released from a lock of height h₀ and length x₀ into a ambient of height H and density ρₐ, is considered. We use two dimensional Navier-Stokes simulations to cover a wide range of density ratio ρc/ρₐ (for both "heavy"-bottom and "light"-top currents) and geometric ratios (H*=H/h₀, λ=x₀/h₀). To our knowledge, the ranges of parameters and times of propagation considered here were not covered in previous experimental or numerical studies. In the first part, we set the lock aspect ratio to λ=18.75, and vary the density ratio 10-⁴<ρc/ρₐ<10⁴ and initial depth ratio 1≤H*≤50. The Navier-Stokes results are compared with predictions of a shallow-water model, in the regime of constant-speed (slumping) phase. Good agreement is observed in a large region of the parameter space (ρc/ρₐ; H*). The larger discrepancy is observed in the range of high-H* and low-ρc/ρₐ for which the shallow-water model overpredicts the velocity of the current. Two possible reasons are suspected, namely the fluid motion in the ambient fluid which is not accounted for in the model, and the choice of the model for the front condition. In the second part, we set the initial depth ratio to H*=10, and vary the density ratio 10-²<ρc/ρₐ<10² and lock aspect ratio 0.5≤λ≤18.75. In particular, we derive novel insights on the influence of the lock aspect ratio λ=x₀/h₀ on the shape and motion of the current in the slumping stage. It is shown that a critical value exists, λcrit; the dynamics of the current is significantly influenced by λ if below λcrit. We present a simple analytical model which support the observation that for a light current the speed of propagation is proportional to λ¼ when λ<λcrit.

Item Type:Conference or Workshop Item (Paper)
HAL Id:hal-04026603
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Technion – Israel Institute of Technology (ISRAEL)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > University of Florida (USA)
Laboratory name:
Deposited On:12 Dec 2013 12:55

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