Lateral controls on grounding-line dynamics

Pegler, Samuel S.; Kowal, Katarzyna; Hasenclever, Leonard Q.; Worster, M. Grae

doi:10.1017/jfm.2013.140

Cited by 28 publications

(50 citation statements)

References 18 publications

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“…A further aspect of confinement relates to the contact between the injected current and the underlying boundary, which partitions the flow at a moving contact line between a region spanning the depth of the medium and a region containing the interface between the fluids. This moving contact line is analogous to that which arises in studies of shear-dominated viscous flows that are separated between a floating and a grounded component (Pegler et al 2013b).…”

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confidence: 64%

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Fluid injection into a confined porous layer

2014

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We present a theoretical and experimental study of viscous flows injected into a porous medium that is confined vertically by horizontal impermeable boundaries and filled with an ambient fluid of different density and viscosity. General three-dimensional equations describing such flows are developed, showing that the dynamics can be affected by two separate contributions: spreading due to gradients in hydrostatic pressure, and that due to the pressure drop introduced by the injection. In the illustrative case of a two-dimensional injection of fluid at a constant volumetric rate, the injected fluid initially forms a viscous gravity current insensitive both to the depth of the medium and to the viscosity of the ambient fluid. Beyond a characteristic time scale, the dynamics transition to being dominated by the injection pressure, and the injected fluid eventually intersects the second boundary to form a second moving contact line. Three different late-time asymptotic regimes can emerge, depending on whether the viscosity of the injected fluid is less than, equal to or greater than that of the ambient fluid. With a less viscous injection, the flow undergoes a slow decay towards a similarity solution in which the two contact lines extend linearly in time with differing prefactors. Perturbations from this long-term state are shown to decay algebraically with time. Equal viscosities result in both contact lines approaching the same leading-order asymptotic position but with a first-order correction to the distance between them that expands as t 1/2 due to gravitational spreading. For a more viscous injection, the distance between the contact lines approaches a constant value, with perturbations decaying exponentially. Data from a new series of laboratory experiments confirm these theoretical predictions.

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confidence: 64%

“…Instead, the closure of the integration of (2.14) for h is maintained by the imposition of (2.8a,b), which govern the evolution of the newly formed contact line (cf. Pegler et al 2013b). Condition (3.1) presupposes that the flow is introduced horizontally at the source.…”

Section: Injection At a Line Sourcementioning

confidence: 99%

Fluid injection into a confined porous layer

2014

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“…By making the minor alteration of replacing the reduced gravity ∆ρg/ρ 0 with the reduced gravity relevant to a floating fluid layer ∆ρg/ρ a (e.g. Pegler et al 2013b), the relevant value of U is found to be Figure 15. Comparison between the experimental thickness profile H(x, t) (solid curves) and the theoretical prediction (dashed curve), plotted in terms of the similarity variables defined by (3.3) and (3.4).…”

Section: Experimental Studymentioning

confidence: 99%

Stratified gravity currents in porous media

2016

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We consider theoretically and experimentally the propagation in porous media of variable-density gravity currents containing a stably stratified density field, with most previous studies of gravity currents having focused on cases of uniform density. New thinlayer equations are developed to describe stratified fluid flows in which the density field is materially advected with the flow. Similarity solutions describing both the fixed-volume release of a distributed density stratification and the continuous input of fluid containing a distribution of densities are obtained. The results indicate that the density distribution of the stratification significantly influences the vertical structure of the gravity current. When more mass is distributed into lighter densities, it is found that the shape of the current changes from the convex shape familiar from the uniform-density case to a concave shape in which lighter fluid accumulates primarily vertically above the origin of the current. For a constant-volume release, the similarity solutions show that the density contours stratify horizontally, a simplification which is used to develop analytical solutions. For currents introduced continuously, the horizontal velocity varies with vertical position, a feature which does not apply to uniform-density gravity currents in porous media. Despite significant effects on vertical structure, the density distribution has almost no effect on overall horizontal propagation, for a given total mass. Good agreement with data from a laboratory study confirms the predictions of the model.

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“…However, at this juncture the argument used in appendix A cannot be continued to develop an equation forẋ U because the flux towards the upper contact line q(x U , t) does not vanish in accord with (2.18). The same difficulty arises in modelling the contact line that separates a floating and grounded component of a gravity current in a Hele-Shaw cell (Pegler et al 2013).…”

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confidence: 99%

“…To evaluate the right-hand side of (2.20) numerically, we utilize the same method of Pegler et al (2013), whereby ∂h/∂t is calculated using the result of a trial integration step under an artificial imposition ofẋ U = 0. The predicted penetration of the current through the top boundary δh = h − H arising from this trial is then used to evaluate the rate of propagation (2.20) asẋ…”

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Fluid invasion of an unsaturated leaky porous layer

Pegler

Bain²,

Huppert

et al. 2015

J. Fluid Mech.

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We study the flow and leakage of gravity currents injected into an unsaturated (dry), vertically confined porous layer containing a localized outlet or leakage point in its lower boundary. The leakage is driven by the combination of the gravitational hydrostatic pressure head of the current above the outlet and the pressure build-up from driving fluid downstream of the leakage point. Model solutions illustrate transitions towards one of three long-term regimes of flow, depending on the value of a dimensionless parameter D, which, when positive, represents the ratio of the hydrostatic head above the outlet for which gravity-driven leakage balances the input flux, to the depth of the medium. If D 0, the input flux is insufficient to accumulate any fluid above the outlet and fluid migrates directly through the leakage pathway. If 0 < D 1, some fluid propagates downstream of the outlet but retains a free surface above it. The leakage rate subsequently approaches the input flux asymptotically but much more gradually than if D 0. If D > 1, the current fills the entire depth of the medium above the outlet. Confinement then fixes gravity-driven leakage at a constant rate but introduces a new force driving leakage in the form of the pressure build-up associated with mobilizing fluid downstream of the outlet. This causes the leakage rate to approach the injection rate faster than would occur in the absence of the confining boundary. This conclusion is in complete contrast to fluid-saturated media, where confinement can potentially reduce long-term leakage by orders of magnitude. Data from a new series of laboratory experiments confirm these predictions.

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Lateral controls on grounding-line dynamics

Cited by 28 publications

References 18 publications

Fluid injection into a confined porous layer

Fluid injection into a confined porous layer

Stratified gravity currents in porous media

Fluid invasion of an unsaturated leaky porous layer

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