Viscous free-surface flows past cylinders

Hinton, Edward M.; Hogg, Andrew J.; Huppert, Herbert E.

doi:10.1103/physrevfluids.5.084101

Cited by 11 publications

(28 citation statements)

References 57 publications

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“…In future studies, it would be interesting to analyse further controls on the interactions with topography that emerge if the flowing material exhibit some of the non-Newtonian rheology associated with lava flows. Additionally, it would be interesting to analyse the motion around tall, surface-piercing obstacles and to carry out analogue laboratory experiments to complement our theoretical work; this work is currently underway (Hinton, Hogg & Huppert 2019). The application of our results to field data from real lava flows is another area of our concern.…”

Section: Resultsmentioning

confidence: 99%

Interaction of viscous free-surface flows with topography

2019

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The interaction of gravitationally driven, free-surface flows of viscous fluid with topographic features is investigated theoretically. The motion is studied in the regime where the depth of the flow is much smaller than the streamwise extent of the topography. A lubrication model of the motion is developed, integrated numerically and analysed asymptotically. For small mounds, it is shown that the flow surmounts the obstacles, but for larger mounds the flow is deflected around it and can form dry zones in its wake into which fluid does not flow, as well as forming deeper ponded regions upstream. Which of these phenomena prevails is shown to depend upon the amplitude of the mound height and the thickness of the oncoming flow relative to the streamwise length scale over which the topography varies. By using numerical and asymptotic results, we demonstrate that relatively wide mounds lead to the development of deep ponds of material upstream, which may lead to flow overtopping if the mound is not sufficiently high. These insights can be used to inform the design of barriers that defend built infrastructures from lava flows, and it is shown how this model can also provide an upper bound on the force exerted by the flow on them.

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Section: Resultsmentioning

confidence: 99%

Interaction of viscous free-surface flows with topography

2019

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“…The steady state is found iteratively; we take an initial guess to be h = 1 everywhere and iterate until a converged solution is found. A similar approach has previously been used for flow over a mound and flow past a cylinder [9,12]. We solve the system with the following boundary conditions.…”

Section: Methodsmentioning

confidence: 99%

“…In this expression we have assumed that the effects of surface tension are negligible; for the experiments described below the capillary length is approximately 2 mm [12], which is much smaller than the streamwise length scale. On adopting dimensionless variables h = H/H ∞ and (x, y) = [X/(H ∞ cot β), Y/(H ∞ cot β)], we find that the steady governing dimensionless equation is…”

Section: Formulationmentioning

confidence: 99%

“…The interaction between gravity-driven flows and topographic mounds has been well studied and controls on when the mound is surmounted by the flow have been determined [4][5][6][7][8][9]. There have also been theoretical, numerical and experimental analyses of the flow behaviour upstream of surface piercing cylinders of various cross-sections [2,[10][11][12]. These works have shown that there may be a dry zone (in which there is no fluid) downstream of the obstruction and there have been investigations into the location and extent of the dry zone in the regime that capillary forces play a dominant role [11].…”

Section: Introductionmentioning

confidence: 99%

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Shallow free-surface Stokes flow around a corner

Hinton

Hogg

Huppert

2020

Phil. Trans. R. Soc. A.

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The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle α to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of α using analytical and numerical methods. Far downslope after detachment, it is shown that the motion is accurately modelled in terms of a similarity solution. Moreover, the detachment point is well approximated by a simple expression for a broad range of opening angles. The results are corroborated through a series of laboratory experiments and the implication for the design of barriers to divert lava flows are discussed. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

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“…To determine the next term in the expansion ( 13), h 2 , the solution in the region r > 1 requires matched asymptotic expansions to handle far-field divergences. The details are provided in the supplementary material, which adapts the method of Hinton et al (2020). The inner solution, which is valid in r < 1, is given by…”

Section: Relatively Narrow Cylinders (  1)mentioning

confidence: 99%

Modeling the Influence of a Variable Permeability Inclusion on Free‐Surface Flow in an Inclined Aquifer

Hinton

Hogg²

2021

Water Resources Research

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Gravity-driven flows in porous media occur in a wide range of industrial and environmental contexts including hydrology, carbon dioxide storage, geothermal power generation, and contaminant leaks (Bear, 1971;Guo et al., 2016;MacFarlane et al., 1983). These sub-surface flows are difficult to monitor directly and therefore it is common to drill wells to sample the flow, for example in CO 2 storage projects to monitor breakthrough times (Hannis et al., 2015;Mathieson et al., 2011). Wells are also used for extracting fresh water from aquifers and for monitoring salt water intrusion (Barlow & Reichard, 2010;Dagan & Zeitoun, 1998;Masterson et al., 1998). Accurately determining the flow velocity from a single borehole presents difficulties, however, because its presence may significantly alter the flow field even in the case that no fluid is extracted because it alters the structure and permeability of the constituent porous media (Sekhar & Sano, 2001). It is vital to understand this effect in order to interpret the data acquired correctly.It is well-established that pressure-driven flows are focused by inclusions that are of higher permeability than the surroundings whilst lower permeability inclusions divert the flow, and the volume flux of fluid that passes through the inclusion has been calculated in each case (Hinch & Bhatt, 1990;Phillips, 1991). However, in many contexts, the flow forms a free-surface and is primarily driven by buoyancy. We develop a physical model to explore the interaction of free-surface flows driven by gravity (rather than by imposed pressure gradients) on an inclined plane with a cylindrical inclusion of different permeability (Figure 1). We investigate how the flow thickness and velocity field depend on the permeability ratio and the width of the cylinder relative to the oncoming flow thickness and slope inclination. In the case of a relatively narrow cylinder, we show that the behavior is analogous to the interaction of two-dimensional pressure-driven flows with inclusions. The interaction with relatively wide cylinders is substantially different, however. For example, we will show that upstream of a relatively wide impermeable inclusion, deep ponds of fluid will form. Similar behavior occurs on the downstream side of the interior of a high permeability inclusion. We are particularly interested in the flux of fluid into the cylinder from upstream and determining controls on whether the particle paths are predominantly diverted around, focused into or not significantly influenced

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Viscous free-surface flows past cylinders

Cited by 11 publications

References 57 publications

Interaction of viscous free-surface flows with topography

Interaction of viscous free-surface flows with topography

Shallow free-surface Stokes flow around a corner

Modeling the Influence of a Variable Permeability Inclusion on Free‐Surface Flow in an Inclined Aquifer

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