Journal of Fluid Mechanics

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A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient

THOMAS BONOMETTIa1a2, MARIUS UNGARISHa3 and S. BALACHANDARa4 c1

a1 Université de Toulouse, INPT, UPS, Institut de Mécanique des Fluides de Toulouse, Allée Camille Soula, F-31400 Toulouse, France

a2 CNRS, Institut de Mécanique des Fluides de Toulouse (IMFT), F-31400 Toulouse, France

a3 Department of Computer Science, Technion, Haifa 32000, Israel

a4 Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA

Abstract

The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents, released from a lock of height h0 and length x0 into a deep ambient and spreading over horizontal flat boundaries, is considered. We use two-dimensional Navier–Stokes simulations to cover: (i) a wide range of current-to-ambient density ratios, (ii) a range of length-to-height aspect ratios of the initial release within the lock (termed the lock aspect ratio λ = x0/h0) and (iii) the different phases of spreading, from the initial acceleration phase to the self-similar regimes. The Navier–Stokes results are compared with predictions of a one-layer shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio (λ) on the shape and motion of the current. It is shown that for lock aspect ratios below a critical value (λcrit), the dynamics of the current is significantly influenced by λ. We conjecture that λcrit depends on two characteristic time scales, namely the time it takes for the receding perturbation created at the lock upon release to reflect back to the front, and the time of formation of the current head. A comparison of the two with space–time diagrams obtained from the Navier–Stokes simulations supports this conjecture. The non-Boussinesq effect is observed to be significant. While the critical lock aspect ratio (λcrit) is of order 1 for Boussinesq currents, its value decreases for heavy currents and increases significantly (up to about 20) for light currents. We present a simple analytical model which captures this trend, as well as the observation that for a light current the speed of propagation is proportional to λ1/4 when λ < λcrit.

(Received June 07 2010)

(Revised September 16 2010)

(Accepted December 17 2010)

(Online publication March 15 2011)

Key words:

  • gravity currents

Correspondence:

c1 Email address for correspondence: bala1s@ufl.edu

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