On axisymmetric rotating gravity currents: two-layer shallow-water and numerical solutions

Ungarish, Marius; Zemach, T.

doi:10.1017/s0022112002003658

Cited by 15 publications

(10 citation statements)

References 18 publications

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“…[4] This model of a spreading intrusion into a stratified environment differs in detail from the dynamics of radially spreading gravity currents in rotating systems into an homogeneous environment [Griffiths, 1986;Sparks et al, 1997;Ungarish and Huppert, 1998;Hallworth et al, 2001;Ungarish and Zemach, 2003]. The homogeneous case gives d = d 0 (1 À (r/r m ) 2 ), whereas the stratified case has d 2 = d 0 2 (1 À (r/r m ) 2 ).…”

Section: Models For Large Ash Cloud Formationmentioning

confidence: 99%

Dynamics of giant volcanic ash clouds from supervolcanic eruptions

Baines

Sparks

2005

Geophysical Research Letters

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The largest explosive volcanic eruptions that have occurred on Earth generated giant ash clouds from rising plumes that spread in the stratosphere around a height of neutral buoyancy, with estimated supply rates that are in the range 1011 to 1013 m3/s. These giant ash clouds are controlled by a balance between gravity and Coriolis forces, forming spinning bodies of nearly fixed proportions after a few hours and are initially insensitive to stratospheric winds. In contrast, volcanic plumes from eruptions with small to intermediate magnitude spread as inertial intrusions under the influence of stratospheric winds, with the Earth's rotation being unimportant. In the largest eruptions the giant spinning ash clouds typically develop diameters greater than 600 km and up to 6000 km in the most powerful super‐eruptions, thus explaining why areas of continental size can be covered with volcanic ash. The radial expansion and spinning velocities are calculated at tens of metres per second and increase with eruption intensity. Higher spreading velocities carry larger ash grain sizes to a given radius, so that grain size at a given distance from the source increases with eruption intensity, consistent with geological observations.

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Section: Models For Large Ash Cloud Formationmentioning

confidence: 99%

Dynamics of giant volcanic ash clouds from supervolcanic eruptions

Baines

Sparks

2005

Geophysical Research Letters

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“…Similarly, a cylindrical current is statistically axisymmetric and homogeneous along the circumferential direction. The two-dimensionality of the planar current and the axisymmetry of the cylindrical current have been exploited both in theoretical formulations and in computations (Daly & Pracht 1968;Droegemeier & Wilhelmson 1986Terez & Knio 1998a, b;Hallworth, Huppert & Ungarish 2001;Özgökmen & Chassignet 2002;Ungarish & Zemach 2003;Birman, Martin & Meiburg 2005;Patterson et al 2006). At high Re, gravity currents are strongly threedimensional and fully turbulent.…”

Section: Introductionmentioning

confidence: 99%

On the front velocity of gravity currents

et al. 2007

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Highly resolved three-dimensional and two-dimensional simulations of gravity currents in planar and cylindrical configurations are presented. The volume of release of the heavy fluid is varied and the different phases of spreading, namely acceleration, slumping, inertial and viscous phases, are studied. The incompressible Navier–Stokes equations are solved assuming that the Boussinesq approximation is valid for small density difference. The simulations are performed for three different Reynolds numbers (Re): 895, 3450 and 8950 (this particular choice corresponds to values of Grashof number: 105, 1.5 × 106 and 107, respectively). Following their sudden release, the gravity currents are observed to go through an acceleration phase in which the maximum front velocity is reached. As the interface of the current rolls up, the front velocity slightly decreases from the maximum and levels off to a nearly constant value. At higher Re, three-dimensional disturbances grow rapidly and the currents become strongly turbulent. In contrast, in two-dimensional simulations, the rolled-up vortices remain coherent and very strong. Depending on the initial Re of the flow and on the size of the release, the current may transition from the slumping to the inertial phase, or directly to the viscous phase without an inertial phase. New criteria for the critical Re are introduced for the development of the inertial phase. Once the flow transitions to the inertial or viscous phase, it becomes fully three-dimensional. During these phases of spreading, two-dimensional approximations underpredict the front location and velocity. The enhanced vortex coherence of the two-dimensional simulations leads to strong vortex interaction and results in spurious strong time variations of the front velocity. The structure and dynamics of the three-dimensional currents are in good agreement with previously reported numerical and experimental observations.

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“…A number of numerical simulations have reported on gravity currents. Many of these computation have focused on two‐dimensional models of planar current [ Daly and Pracht , 1968; Droegemeier and Wilhelmson , 1986, 1987; Terez and Knio , 1998b, 1998a; Hallworth et al , 2001; Choi and García , 2002; Özgökmen and Chassignet , 2002; Ungarish and Zemach , 2003; Birman et al , 2005]. At sufficiently large Reynolds numbers, gravity currents are strongly three‐dimensional and fully turbulent, and in such situations two‐dimensionality of the current is only in a statistical sense.…”

Section: Introductionmentioning

confidence: 99%

Turbulent structures in planar gravity currents and their influence on the flow dynamics

Cantero¹,

Balachandar²,

García³

et al. 2008

J. Geophys. Res.

107

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[1] Direct numerical simulations (DNS) of planar gravity current in the Boussinesq limit have been conducted with the objective of identifying, visualizing, and describing turbulent structures and their influence on the flow dynamics. The simulations are performed for Reynolds numbers of Re = 8950 and Re = 15,000 with 31-and 131-million grid point resolutions, respectively. This range of Reynolds numbers ensures fully developed turbulent gravity currents, which have never been simulated before using DNS. The flow develops zones with different turbulence characteristics, which eventually interact with each other. The near-wall bottom flow resembles boundary layer flow with several hairpin-like vortices oriented in the direction of the flow and preferential patterns of low-and high-speed streaks. The separation between low-speed streaks at the front scales with the lobe size, which is about 200 wall units for Re = 15,000. Upstream of the front, the separation between low-speed streaks scales with the well-accepted value of 100 wall units for turbulent boundary layers. These patterns have associated regions of low and high bottom shear stresses with implications for sediment erosion and bed load transport. Most of the erosive power of the flow is found in the gravity current front. The interface between heavy and light fluids rolls up by baroclinic generation of KelvinHelmholtz vortices, which undergo sudden breakup and decay to small-scale turbulence. The effect of turbulence and three-dimensionality on the flow dynamics is addressed by comparing two-and three-dimensional simulations. Three-dimensional simulations present active mechanisms that undermine the strong flow coherence, comparing well with experimental observations.

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On axisymmetric rotating gravity currents: two-layer shallow-water and numerical solutions

Cited by 15 publications

References 18 publications

Dynamics of giant volcanic ash clouds from supervolcanic eruptions

Dynamics of giant volcanic ash clouds from supervolcanic eruptions

On the front velocity of gravity currents

Turbulent structures in planar gravity currents and their influence on the flow dynamics

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