Front conditions of high-Re gravity currents produced by constant and time-dependent influx: An analytical and numerical study

Shringarpure, Mrugesh; Lee, Hyungoo; Ungarish, Marius; Balachandar, S.

doi:10.1016/j.euromechflu.2013.04.004

Cited by 12 publications

(6 citation statements)

References 18 publications

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“…The essential point is that the jump of the front is relative to the embedding ambient fluid, as demonstrated by Shringarpure et al. (2013), Chowdhury & Testik (2014) and Hogg et al. (2016).…”

Section: Formulationmentioning

confidence: 95%

On simple models for gravity currents from moving sources

Ungarish

2022

J. Fluid Mech.

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The propagation of the gravity current generated from a moving source of buoyancy is of interest in deep-sea mining and related technologies. The study by Ouillon et al. (J. Fluid Mech., vol. 924, 2021, A43) elucidated some salient patterns of the flow concerning a source close to the bottom on the basis of direct numerical simulation on a supercomputer. Here, we present a simple box model that provides further insights and useful analytical approximations for this gravity-current flow system. We show that this flow is very different from that produced by a moving source at the top, studied by Hogg et al. (J. Fluid Mech., vol. 539, 2005, pp. 349–385). The model confirms that the main governing parameter is the ratio $a$ of speed of source to that of buoyancy propagation. The model points out dependency also on the front-jump Froude number (which implies dependency on the height of the ambient fluid). For a sufficiently large $a >a_{crit}$ , a supercritical regime appears in which the gravity current forms a wedge behind the moving source; in the subcritical regime, the upstream propagation attains a maximum $x_m$ at time $t_m$ . The model predicts the value $a_{crit}$ , the distance and time $x_m$ and $t_m$ in the subcritical case, and the shape of the wedge in the supercritical case, without any adjustable constant. Comparisons with the numerical data show fair agreement.

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Section: Formulationmentioning

confidence: 95%

On simple models for gravity currents from moving sources

Ungarish

2022

J. Fluid Mech.

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“…Gravity currents due to the sustained emission of relatively dense fluid within a channel have recently been studied by Shringapure et al (2013). These authors conducted Here we quantitatively investigate their results in terms of the shallow layer formulation developed above ( §3).…”

Section: Simulationsmentioning

confidence: 99%

“…The creation and dynamics of this third, intermediate density layer plays a crucial role for modelling aspects of density-driven motion in the presence of adverse ambient flow; the dense currents in these scenarios can be arrested and the layer of intermediate density provides a model for the recirculation of relatively dense fluid. Recently Shringapure et al (2013) have performed computational simulations of the motion and interpreted the results using integral models of the steady dynamics. The latter study was among the first to extend direct numerical simulations of the Navier-Stokes equations of gravity currents to 'open' flows in which there is a sustained in-and outflow.…”

Section: Introductionmentioning

confidence: 99%

Sustained gravity currents in a channel

et al. 2016

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Gravitationally-driven motion arising from a sustained constant source of dense fluid in a horizontal channel is investigated theoretically using shallow layer models and direct numerical simulations of the Navier-Stokes equations, coupled to an advectiondiffusion model of the density field. The influxed dense fluid forms a flowing layer underneath the less dense fluid, which initially filled the channel, and in this study its speed of propagation is calculated; the outflux is at the end of the channel. The motion, under the assumption of hydrostatic balance, is modelled using a two-layer shallowwater model to account for the flow of both the dense and the overlying less dense fluids. When the relative density difference between the fluids is small (the Boussinesq regime), the governing shallow layer equations are solved using analytical techniques. It is demonstrated that a variety of flow-field patterns is feasible, including those with constant height along the length of the current and contrasted with those where the height varies continuously and discontinuously. The type of solution realised in any scenario is determined by the magnitude of the dimensionless flux issued from the source and the source Froude number. Two important phenomena may occur: the flow may be choked, whereby the excess velocity due to the density difference is bounded and the height of the current may not exceed a determined maximum value, and it is also possible for the dense fluid to completely displace all of the less dense fluid originally in the channel in an expanding region close to the source. The onset and subsequent evolution of these types of motions are also calculated using analytical techniques. The same range of phenomena occurs for non-Boussinesq flows; in this scenario the solutions of the model are calculated numerically. The results of direct numerical simulations of the Navier-Stokes equations are also reported for unsteady two-dimensional flows in which there is inflow of dense fluid at one end of the channel and outflow at the other end. These simulations reveal the detailed mechanics of the motion and the bulk properties are compared with the predictions of the shallow-layer model to demonstrate good agreement between the two modelling strategies.

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“…We note, however, that in the non-Boussinesq case the pressure no longer fully decouples from the equations for the velocity field. Other recent extensions of conceptual gravity current models address such issues as two-layer and linearly stratified ambients, nonrectangular cross sections, in-and outflow, as well as fluctuations about the average [29][30][31][32][33].…”

Section: Conceptual Models: the Froude Number As A Function Of The Cumentioning

confidence: 99%

Modeling Gravity and Turbidity Currents: Computational Approaches and Challenges

Meiburg

Radhakrishnan

Nasr-Azadani

2015

Applied Mechanics Reviews

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In this review article, we discuss recent progress with regard to modeling gravity-driven, high Reynolds number currents, with the emphasis on depth-resolving, high-resolution simulations. The initial sections describe new developments in the conceptual modeling of such currents for the purpose of identifying the Froude number–current height rela-tionship, in the spirit of the pioneering work by von Karman and Benjamin. A brief intro-duction to depth-averaged approaches follows, including box models and shallow water equations. Subsequently, we provide a detailed review of depth-resolving modeling strat-egies, including direct numerical simulations (DNS), large-eddy simulations (LES), and Reynolds-averaged Navier–Stokes (RANS) simulations. The strengths and challenges associated with these respective approaches are discussed by highlighting representative computational results obtained in recent years. [DOI: 10.1115/1.4031040]

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Front conditions of high-Re gravity currents produced by constant and time-dependent influx: An analytical and numerical study

Cited by 12 publications

References 18 publications

On simple models for gravity currents from moving sources

On simple models for gravity currents from moving sources

Sustained gravity currents in a channel

Modeling Gravity and Turbidity Currents: Computational Approaches and Challenges

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