The initial and gravity-spreading phases of heavy gas dispersion: Comparison of models with phase I data

Rottman, James W.; Hunt, J. C. R.; Mercer, A. McD.

doi:10.1016/0304-3894(85)85041-x

Cited by 25 publications

(14 citation statements)

References 11 publications

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“…It has been noted that the detailed flow structure of the head of a gravity current is extremely sensitive to anomalies in the flow relative to it. For currents generated by a fixed-flux release, both Jirka & Arita (1987) and Rottman, Hunt & Mercer (1985) have formulated simple models of the flow in the region near the stagnation point at the foremost point of the head. Jirka & Arita (1987) conclude that the interface is flattened when the ambient flow is less than the velocity of the current and is steepened when the ambient exceeds the current.…”

Section: Discussionmentioning

confidence: 99%

Effects of external flow on compositional and particle gravity currents

1998

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The propagation at high Reynolds number of a heavy, two-dimensional gravity current of given initial volume at the base of a uniform flow is considered. An experimental setup is described for which a known volume of fluid is rapidly introduced halfway down a 9 m channel in which there is a uniform flow of water. The density excess of the released fluid is produced by either dissolving salt or suspending particles in water. The upstream and downstream propagation of the current was measured for different initial salt concentrations, particle sizes and concentrations. A simple box model for the motion of and deposit from the gravity current is constructed. The analytical results obtained compare well with our numerical solutions of one-layer and two-layer models incorporating the appropriate shallow-water equations. Both sets of results are in very good agreement with the experimental data.

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Section: Discussionmentioning

confidence: 99%

Effects of external flow on compositional and particle gravity currents

1998

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“…We denote these terms byŨ (E,1) ,Ũ (E,2) . Then we consider whether it is necessary to relax this constraint, to calculate the complete terms at these orders (as in the calculation of the shear effect by Rottman et al 1985).…”

Section: Leading-order Effects Of Weak Rotationmentioning

confidence: 99%

“…This paper is organized as follows. In § 2, we consider perturbations for small f t from the von Kármán (1940) solution for a gravity current head in a weakly rotating flow, and then generalize these results to gravity currents on sloping surfaces, using the approach of Rottman et al (1985). Two fluid systems are considered here.…”

Section: Introductionmentioning

confidence: 99%

Effects of rotation and sloping terrain on the fronts of density currents

et al. 2005

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The initial stage of the adjustment of a gravity current to the effects of rotation with angular velocity f/2 is analysed using a short time analysis where Coriolis forces are initiated in an inviscid von Kármán-Benjamin gravity current front at t F = 0. It is shown how, on a time-scale of order 1/f , as a result of ageostrophic dynamics, the slope and front speed U F are much reduced from their initial values, while the transverse anticyclonic velocity parallel to the front increases from zero to O(NH 0 ), where N = √ g /H 0 is the buoyancy frequency, and g = g ρ/ρ 0 is the reduced acceleration due to gravity. Here ρ 0 is the density and ρ and H 0 are the density difference and initial height of the current. Extending the steady-state theory to account for the effect of the slope σ on the bottom boundary shows that, without rotation, U F has a maximum value for σ = π/6, while with rotation, U F tends to zero on any slope. For the asymptotic stage when f t F 1, the theory of unsteady waves on the current is reviewed using nonlinear shallow-water equations and the van der Pol averaging method. Their motions naturally split into a 'balanced' component satisfying the Margules geostrophic relation and an equally large 'unbalanced' component, in which there is horizontal divergence and ageostrophic vorticity. The latter is responsible for nonlinear oscillations in the current on a time scale f −1 , which have been observed in the atmosphere and field experiments. Their magnitude is mainly determined by the initial potential energy in relation to that of the current and is proportional to the ratio √ Bu = L R /R 0 , where L R = NH 0 /f is the Rossby deformation radius and R 0 is the initial radius. The effect of slope friction also prevents the formation of a steady front. From the analysis it is concluded that a weak mean radial flow must be driven by the ageostrophic oscillations, preventing the mean front speed U F from halting sharply at f t F ∼ 1. Depending on the initial value of L R /R 0 , physical arguments show that U F decreases slowly in proportion to (f t F ) −1/2 , i.e. U F /U F 0 = F (f t F , Bu). Thus the front only tends to the geostrophic asymptotic state of zero radial velocity very slowly (i.e. as f t F → ∞) for finite values of L R /R 0 . However, as L R /R 0 → 0, it reaches this state when f t F ∼ 1. This analysis of the overall nonlinear behaviour of the gravity current is consistent with two two-dimensional non-hydrostatic (Navier-Stokes) and axisymmetric hydrostatic (shallow-water) Eulerian numerical simulations of the varying form of the rotating gravity current. When the effect of surface friction is considered, it is found that the mean movement of the front is significantly slowed. Furthermore, the oscillations with angular frequency f and the slow growth of the radius, when f t F > 1, are consistent with recent experiments.

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“…Prior to RKW only two studies of the effects of environmental shear existed in the gravity current literature (Rottman et al 1985;Jirka and Arita 1987). Both studies found through theoretical analysis that vertical shear in the direction of gravity current motion should produce a more vertical flow at the leading edge of the gravity current; these results were experimentally confirmed in the laboratory.…”

Section: Introductionmentioning

confidence: 99%

The Optimal State for Gravity Currents in Shear

Bryan

Rotunno

2013

Journal of the Atmospheric Sciences

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This study examines the lifting of sheared environmental air by gravity currents, focusing primarily on the theoretical ''optimal state'' in which near-surface flow is turned into a vertically oriented jet. Theoretical models are presented from multiple perspectives, including the vorticity perspective that was first presented by Rotunno, Klemp, and Weisman and a flow-force balance perspective based on conservation of mass and momentum. The latter approach reveals a constraint on the depth of the environmental shear layer relative to the depth of the cold pool. Based on these control-volume constraints, a numerical solution for steady, inviscid, isentropic flow is obtained that shows how the cold-pool interface has a slightly concave shape and is nearly (although not strictly) vertical. Then, by initializing a time-dependent numerical model with a stagnant cold pool in an environment with low-level shear, it is shown that a statistically steady flow can be maintained with all the important elements of the analytic solution. Most notably, the front-relative flow is negligible behind the surface gust front at all levels, the interface of the cold pool maintains a predominantly vertical structure, and the net generation of vorticity by buoyancy within a control volume closely matches the horizontal flux of environmental vorticity on the side of the control volume. Sensitivity simulations confirm that the constraints identified by the analytic study must be met for the optimal state to be realized and that lifting of near-surface environmental air is optimized when a vertically oriented jet is created and maintained.

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The initial and gravity-spreading phases of heavy gas dispersion: Comparison of models with phase I data

Cited by 25 publications

References 11 publications

Effects of external flow on compositional and particle gravity currents

Effects of external flow on compositional and particle gravity currents

Effects of rotation and sloping terrain on the fronts of density currents

The Optimal State for Gravity Currents in Shear

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