On axisymmetric intrusive gravity currents in a stratified ambient – shallow-water theory and numerical results

Ungarish, Marius; Zemach, T.

doi:10.1016/j.euromechflu.2006.06.003

Cited by 14 publications

(18 citation statements)

References 22 publications

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“…In two-dimensional intrusions, the conserved quantity is has dimensions [L 2 T −1 ], leading to a current that grows as t 1/2 (Ungarish 2005). In axisymmetric intrusions, this conserved quantity is r f 0 rb dr , with dimensions [L 3 T −1 ], leading to a current that grows as t 1/3 (Ungarish & Zemach 2007).…”

Section: Unsteady Drag-free Flowmentioning

confidence: 98%

“…In contrast to the intrusions supplied by a source of constant flux, intrusions that result from an instantaneous release of a fixed volume of mixed fluid are governed by similarity solutions both in 'two-dimensional' and axisymmetric geometries (Ungarish 2005;Ungarish & Zemach 2007). In such constant-volume releases, neither the dimensional governing equations (when written in terms of u r and b = N h ) nor the boundary conditions involve a dimensional parameter: the only dimensional parameters occur in the specification of the initial conditions.…”

Section: Unsteady Drag-free Flowmentioning

confidence: 99%

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Modelling intrusions through quiescent and moving ambients

et al. 2015

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Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these plumes cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, and in this paper we develop a shallow-layer model that governs their motion. We couple this dynamical model to a model for particle transport and sedimentation, to predict both the time-dependent distribution of ash within volcanic intrusions and the flux of ash that falls towards the ground. In an otherwise quiescent atmosphere, the intrusions spread axisymmetrically. We find that the buoyancy-inertial scalings previously identified for continuously supplied axisymmetric intrusions are not realised by solutions of the governing equations. By calculating asymptotic solutions to our model we show that the flow is not self-similar, but is instead time-dependent only in a narrow region at the front of the intrusion. This non-self-similar behaviour results in the radius of the intrusion growing with time t as t 3/4 , rather than t 2/3 as suggested previously. We also identify a transition to drag-dominated flow, which is described by a similarity solution with radial growth now proportional to t 5/9 . In the presence of an ambient wind, intrusions are not axisymmetric. Instead, they are predominantly advected downstream, while at the same time spreading laterally and thinning vertically due to persistent buoyancy forces. We show that close to the source, this lateral spreading is in a buoyancy-inertial regime, whereas far downwind, the horizontal buoyancy forces that drive the spreading are balanced by drag. Our results emphasise the important role of buoyancy-driven spreading, even at large distances from the source, in the formation of the flowing thin horizontally extensive layers of ash that form in the atmosphere as a result of volcanic eruptions.

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Section: Unsteady Drag-free Flowmentioning

confidence: 98%

Section: Unsteady Drag-free Flowmentioning

confidence: 99%

Modelling intrusions through quiescent and moving ambients

et al. 2015

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“…In the absence of drag, a buoyancy-inertial spreading regime becomes 818 established Ungarish and Zemach (2007), with a radial growth rate of t 1/3 . However, our 819 numerical results (Fig.…”

Section: Radius (M)mentioning

confidence: 99%

Interpretation of umbrella cloud growth and morphology: implications for flow regimes of short-lived and long-lived eruptions

et al. 2015

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“…al. [2] , Ungarish & Zemach [13] and Ungarish [10] to perform numerical solution using a finite-difference, two-step Lax-Wendroff method. To facilitate the implementation of the boundary conditions, the r -coordinate was mapped into the coordinate y = r r N (t) .…”

Section: Numerical Resultsmentioning

confidence: 99%

The flow of high-Reynolds axisymmetric gravity currents of a stratified fluid into a stratified ambient: shallow-water and box model solutions

Zemach

Ungarish

2012

Environ Fluid Mech

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We consider the axisymmetric flow (in a full cylinder or a wedge) of high-Reynolds-number Boussinesq gravity currents and intrusions systems in which both the ambient and the propagating "current" are linearly stratified. The main focus is on a current of fixed volume released from a cylinder lock; the height ratio of the fluids H , and the stratification parameter of the ambient S, are quite general. We develop a one-layer shallow-water model. The internal stratification enters as a new dimensionless parameter, σ ∈ [0, 1]. In general, the time-dependent motion is obtained by standard finite-difference solutions; a self-similar analytical solution exists for S = 0. We show that, in general, the speed of propagation decreases when the internal stratification becomes more pronounced (σ increases). We also developed a box-model approximation, and show that the resulting radius of propagation is in good agreement with the more rigorous shallow-water prediction.

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On axisymmetric intrusive gravity currents in a stratified ambient – shallow-water theory and numerical results

Cited by 14 publications

References 22 publications

Modelling intrusions through quiescent and moving ambients

Modelling intrusions through quiescent and moving ambients

Interpretation of umbrella cloud growth and morphology: implications for flow regimes of short-lived and long-lived eruptions

The flow of high-Reynolds axisymmetric gravity currents of a stratified fluid into a stratified ambient: shallow-water and box model solutions

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