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

Yoshikawa, Harunori; Wesfreid, José Eduardo

doi:10.1017/s0022112011000140

Cited by 32 publications

(33 citation statements)

References 28 publications

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“…These are given to compare the maximal amplitude and to emphasize the slowness of the amplitude relaxation. A qualitatively similar trend was reported by Yoshikawa & Wesfreid (2011a) for immiscible fluids with a large viscosity contrast. They divided the growing part into a linear and a nonlinear regime and drew an analogy with sand ripples.…”

Section: Wave Propertiessupporting

confidence: 88%

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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: Wave Propertiessupporting

confidence: 88%

“…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.…”

mentioning

confidence: 99%

Dynamics of the interface between miscible liquids subjected to horizontal vibration

et al. 2015

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“…Extension of the analysis is dedicated to the viscous KH or RT instabilities. In this case the mode analysis shows [37][38][39], that the neutral curve for KH instability may have shorter regions of stability, depending on the values of viscosity and wavenumber. It is interesting to note that viscosity may play a destabilizing role [38], where air-water stratified system is considered.…”

Section: Problem Overviewmentioning

confidence: 87%

Numerical Analysis of Laminar‐Turbulent Bifurcation Scenarios in Kelvin‐Helmholtz and Rayleigh‐Taylor Instabilities for Compressible Flow

Evstigneev¹,

AlexandrovitchMagnitskii²

2017

Turbulence Modelling Approaches - Current State, Development Prospects, Applications

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In the chapter, we are focused on laminar-turbulent transition in compressible flows triggered by Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilities. Compressible flow equations in conservation form are considered. We bring forth the characteristic feature of supersonic flow from the dynamical system point of view. Namely, we show analytically and confirm numerically that the phase space is separated into independent subspaces by the systems of stationary shock waves. Floquet theory analysis is applied to the linearized problem using matrix-free implicitly restarted Arnoldi method. All numerical methods are designed for CPU and multiGPU architecture using MPI across GPUs. Some benchmark data and features of development are presented. We show that KH for symmetric 2D perturbations undergoes cycle bifurcation scenarios with many chaotic cycle threads, each thread being a Feigenbaum-Sharkovskiy-Magnitskii (FShM) cascade. With the break of the symmetry, a 3D instability develops rapidly, and the bifurcations includes Landau-Hopf scenario with computationally stable 4D torus. For each torus, there exist threads of cycles that can develop chaotic regimes, so the flow is more complicated and difficult to study. Thus, we present laminar-turbulent development of compressible RT and KH instabilities as the bifurcations scenarios.

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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 1. A viscous theory

Cited by 32 publications

References 28 publications

Dynamics of the interface between miscible liquids subjected to horizontal vibration

Dynamics of the interface between miscible liquids subjected to horizontal vibration

Numerical Analysis of Laminar‐Turbulent Bifurcation Scenarios in Kelvin‐Helmholtz and Rayleigh‐Taylor Instabilities for Compressible Flow

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

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