Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast

Yoshikawa, Harunori; Wesfreid, José Eduardo

doi:10.1017/s0022112011000152

Cited by 28 publications

(37 citation statements)

References 16 publications

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“…It is worth highlighting that it is the first experimental evidence of spatially modulated waves on an interface caused by horizontal vibrations. Previous experimental studies of wave patterns under horizontal vibrations with immiscible fluids (Jalikop & Juel 2009;Yoshikawa & Wesfreid 2011b;Gandikota et al 2014b) did not report wave modulation, although it was theoretically predicted by Varas & Vega (2007) in a nearly inviscid fluid subjected to horizontal vibration. We will return to this pattern in § 4.3.…”

Section: Dynamics Of An Interface Near the Onset Of Instabilitymentioning

confidence: 92%

“…The effect of horizontal vibrations on two superposed immiscible liquids has been examined both experimentally (Wolf 1969(Wolf , 1970Ivanova, Kozlov & Evesque 2001;Talib, Jalikop & Juel 2007;Mialdun et al 2008;Jalikop & Juel 2009;Yoshikawa & Wesfreid 2011b) and theoretically (Lyubimov & Cherepanov 1987;Khenner et al 1999), where it was shown that if the state of the flat contact line is unstable, nonpropagating periodic waves may occur on the interface. Following Wunenburger et al (1999), these waves, which are stationary in the reference frame of the vibrated cell, are referred to as 'frozen waves'.…”

mentioning

confidence: 99%

“…The stability of two superposed immiscible liquids in a axisymmetric geometry was studied numerically (Yoshikawa & Wesfreid 2011a) and experimentally (Yoshikawa & Wesfreid 2011b). The vibrational motion was imposed by alternating the rotation of a container around its axis.…”

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confidence: 99%

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Dynamics of the interface between miscible liquids subjected to horizontal vibration

et al. 2015

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We present experimental evidence of the existence of an interfacial instability between two miscible liquids of similar (but non-identical) viscosities and densities under horizontal vibration. A stably stratified two-layer system is composed of the same binary mixture with different concentrations placed in a confined cell (with length twice as large as the height). Unlike the case of immiscible fluids, here, the interface is a transient layer of small but non-zero thickness. In the experiments, the frequency and amplitude were varied within the ranges 2-24 Hz and 1.5-16 mm, respectively. When the value of the oscillatory forcing increases, the amplitudes of the interface perturbations grow continuously, forming a saw-tooth frozen structure. This evolution is also examined numerically. In addition to the solutions of full 3-D Navier-Stokes equations, an averaging approach with separation of time scales is used for situations in which the forcing period is very small compared to the natural time scales of the problem. The simulation of averaged equations provides the explanation of the instability development, the calculations of the full nonlinear equations shed light on the decay of a wavy pattern. The results of numerical modelling perfectly support the experimental observations.

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Section: Dynamics Of An Interface Near the Onset Of Instabilitymentioning

confidence: 92%

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confidence: 99%

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Dynamics of the interface between miscible liquids subjected to horizontal vibration

et al. 2015

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“…They found formation of waves perpendicular to the motion. In our experimental paper which is coupled with the present one (Yoshikawa & Wesfreid 2010), our setup utilized the same principle. Wolf (1969), Beysens et al (1998), Ivanova et al (2001a) and used the horizontal vibration of a fluid container to drive flows with a horizontal pressure gradient.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory Kelvin–Helmholtz instability. Part 1. A viscous theory

Yoshikawa

Wesfreid

2011

J. Fluid Mech.

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The stability of oscillatory two-layer flows is investigated with a linear perturbation analysis. An asymptotic case is considered where the oscillation amplitude is small compared to the perturbation wavelength. The focus of the analysis is on the influence of viscosity and its contrast at the interface. The flows are unstable when the relative velocity of the layers is larger than a critical value. Depending on the oscillation frequency, the flows are in different dynamical regimes, which are characterized by the relative importance between capillary wavelength and the thicknesses of the Stokes boundary layers developed on the interface. A particular regime is found in which instability occurs at a substantially lower critical velocity. The mechanism behind the instability is studied by identifying the velocity-and shear-induced components in the disturbance growth rate. They interchange dominance depending on the frequency and the viscosity contrast. Results of the analysis are compared with experiments in the literature. Good agreement is found with the experiments that have a small oscillation amplitude. The validity condition of the asymptotic theory is estimated.

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“…The mechanism is a parametric viscous instability in which the term 2 irkU in (14) resonates weakly damped modes described by (11). The mechanism is similar to the instability that causes surface waves in channel flow over a flat plat oscillating in its own plane [ Yih , ; Or , ; Gao and Lu , ], and is related to other parametric instabilities in viscous oscillatory flows [e.g., Yoshikawa and Wesfreid , ]. Instability in (14) requires that the squared Froude number

{true(ρ_{\infty} / ρ true)}^{2} \overset{U_{\infty}^{2}}{true} / (g' h)

exceed a threshold dependent on

r / ω

and the dimensionless wave number

k \sqrt{g' h} / ω

, with favored growth near

k \sqrt{g' h} / ω = 1

, qualitatively consistent with the observations [ Traykovski et al ., ], for

r / ω = O (1)

.…”

Section: Model Solutionsmentioning

confidence: 99%

Coupled dynamics of interfacial waves and bed forms in fluid muds over erodible seabeds in oscillatory flows

Trowbridge

Traykovski

2015

JGR Oceans

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Recent field investigations of the damping of ocean surface waves over fluid muds have revealed waves on the interface between the thin layer of fluid mud and the overlying much thicker column of clear water, accompanied by bed forms on the erodible seabed beneath the fluid mud. The frequencies and wavelengths of the observed interfacial waves are qualitatively consistent with the linear dispersion relationship for long interfacial waves, but the forcing mechanism is not known. To understand the forcing, a linear model is proposed, based on the layer‐averaged hydrostatic equations for the fluid mud, together with the Meyer‐Peter‐Mueller equation for the sediment transport within the underlying seabed, both subject to oscillatory forcing by the surface waves. If the underlying seabed is nonerodible and flat, the model indicates parametric instability to interfacial waves, but the threshold for instability is not met by the observations. If the underlying seabed is erodible, the model indicates that perturbations to the seabed elevation in the presence of the oscillatory forcing create interfacial waves, which in turn produce stresses within the fluid mud that force a net transport of sediment within the seabed toward the bed form crests, thus causing growth of both bed forms and interfacial waves. The frequencies, wavelengths, and growth rates are in qualitative agreement with the observations. A competition between mixing created by the interfacial waves and gravitational settling might control the thickness, density, and viscosity of the fluid muds during periods of strong forcing.

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Oscillatory Kelvin–Helmholtz instability. Part 2. An experiment in fluids with a large viscosity contrast

Cited by 28 publications

References 16 publications

Dynamics of the interface between miscible liquids subjected to horizontal vibration

Dynamics of the interface between miscible liquids subjected to horizontal vibration

Oscillatory Kelvin–Helmholtz instability. Part 1. A viscous theory

Coupled dynamics of interfacial waves and bed forms in fluid muds over erodible seabeds in oscillatory flows

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