Two-layer fluid flows on inclined surfaces

Shah, Kasturi; Pegler, Samuel S.; Minchew, Brent

doi:10.1017/jfm.2021.273

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…By contrast, when the lower layer is more mobile (e.g. figure 4 b ), the flux in the upper layer varies non-monotonically with hu=1−hl due to the strong effect of lubrication; at low values of hl, small increases in hl actually increase the upper layer flux even though the upper layer is thinner (for an in-depth investigation of two-layer Newtonian flow on an inclined plane, see Shah et al [10]). Similar features can be observed in figure 4 d .…”

Section: Case Studiesmentioning

confidence: 99%

“…Both these two-layer studies found that in the limit of equal density fluids, a frontal shock forms and this is associated with the hydrostatic pressure gradients that drive the flow becoming independent of the shape of the interface between the fluids. Flow on an inclined plane has also been investigated for one layer [9] and two layers [10] of Newtonian fluid with various steady flows and similarity solutions obtained. Two-layer flows in porous media lead to simpler governing equations than the viscous case but there is still a multiplicity of possible flow regimes that can occur depending on the viscosity, volume and density ratios [11].…”

Section: Introductionmentioning

confidence: 99%

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Two-layer gravity currents of generalized Newtonian fluids

Christy,

Hinton

2023

Proc. R. Soc. A.

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We examine gravity-driven two-layer flow of generalized Newtonian fluids. The two layers have different densities and constitutive laws, and the flow is assumed to be shallow and inertia-less. A depth-integrated model for flow over one-dimensional topography is derived with the volume fluxes written in terms of functions that depend only on the fluids’ rheology. The model enables two-layer flows of any combination of generalized Newtonian fluids to be computed without explicit knowledge of the velocity profile. For viscoplastic layers, the formulation provides a convenient way to determine the layer evolution without having to analyse the multiple yield surfaces that may occur. Motivated by the lubricated flow of ice sheets, we analyse the case in which the lower layer is relatively thin. The model reduces to a one-layer flow with an effective slip law that encapsulates the thickness and generalized Newtonian rheology of the lower layer. For flow over two-dimensional topography, a depth-integrated two-layer model cannot generally be derived because the direction of the shear stress varies across the lower layer. Progress is possible in the special cases that the lower layer is Newtonian or is relatively thin.

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Section: Case Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-layer gravity currents of generalized Newtonian fluids

Christy,

Hinton

2023

Proc. R. Soc. A.

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“…For instance, they can merge instead of passing through each other without significant change, with the latter being the case of two solitary waves governed by the well-known KdV equation [3,32]. The analysis of solitary-like surface waves in flowing liquid films is also important because liquid films, as well as similar physical systems [33][34][35], are often encountered in the fields of earth and planetary sciences [36,37] and in technological processes [38], where the liquids of interest can also experience temperature gradients [14,28] and vibrations [39][40][41]. Given this, the effect of vibrations on the wave dynamics of film flows has become an independent subject of fundamental and applied research [42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Experimental and Theoretical Study of Solitary-like Wave Dynamics of Liquid Film Flows over a Vibrated Inclined Plane

Maksymov¹,

Pototsky²

2023

Preprint

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Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in the physical system of other nature. Here we investigate, experimentally and theoretically, the dynamics of solitary-like surface waves in a liquid layer on an inclined plane that is subjected to a harmonic low-frequency vibration in the range from 30 to 50 Hz. We demonstrate that the vibration results in a decrease in the average and peak amplitude of the long solitary-like surface waves. However, the speed of these waves remains largely unaffected by the vibration, implying that they may propagate over large distances almost without changing their amplitude, thus rendering them suitable for a number of practical applications, where the immunity of pulses that carry information to external vibrations is required.

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