Effect of shear flow and magnetic field on the Rayleigh–Taylor instability

Zhang, Wenlu; Wu, Zhengwei; Ding, Li

doi:10.1063/1.1872892

Cited by 24 publications

(18 citation statements)

References 9 publications

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“…2a, where the increase in the intensity of the imposed flow leads to a stronger growth of the modes with the longer wavelengths, and to a weaker growth of the modes with the shorter wavelengths. Thus, the instabilities do not sum up, as some modes develop slower, but this result agrees well with the simple analytic formula (25) for sharp interfaces and also with the earlier studies [8][9][10], in which the stability of smeared interfaces was previously examined. [1]).…”

Section: Gr < 0: the Lighter Liquid Is Superposed By The Heavier Onesupporting

confidence: 78%

“…In the case of gravitationally unstable configuration (the heavier liquid superposes the lighter liquid) the RayleighTaylor and Kelvin-Helmholtz instabilities co-develop. These two instabilities primarily affect the modes of different wavelengths, so they do not amplify each other, and, on opposite, the imposed flow may even reduce the growth of the modes with shorter wavelengths [8][9][10]. The codevelopment of these instabilities was already studied for smeared interfaces [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Linear stability of a horizontal phase boundary subjected to shear motion

Kheniene

Vorobev

2015

Eur. Phys. J. E

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Abstract. We investigate the stability of slowly smearing phase boundary that appears at the contact of two miscible liquids. A hydrodynamic flow is imposed along the boundary. The aim is to find out whether the slow diffusive smearing of a boundary can be overrun by faster mixing. The phase-field approach is used to model the evolution of the binary mixture. The linear stability in respect to 2D perturbations is studied. If the heavier liquid lies above the lighter liquid, the interface is unconditionally unstable due to the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The imposed flow accelerates the growth of the long-wave modes and suppresses the growth of the short-wave perturbations. Viscosity, diffusivity and capillarity reduce the growth of perturbations. If the heavier liquid underlies the lighter one, the interface can be stable. The stability boundaries are defined by the strength of gravity (density contrast) and the intensity of the imposed flow. Thinner interfaces are usually characterised by larger zones of instability. The thermodynamic instability, identified for the thicker interfaces with the thicknesses greater than the thickness of a thermodynamically equilibrium phase boundary, makes such interfaces unconditionally unstable. The zones of instability are enlarged by diffusive and capillary terms. Viscosity plays its stabilising role. PACS

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Section: Gr < 0: the Lighter Liquid Is Superposed By The Heavier Onesupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Linear stability of a horizontal phase boundary subjected to shear motion

Kheniene

Vorobev

2015

Eur. Phys. J. E

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“…2 shows differences in the mixing layer evolution as shear is incrementally added to the RT unstable configuration. This setup is identical, omitting the magnetic field, to the case studied by Zhang et al 2 It also models the experiment performed by Snider and Andrews, 3 where hot and cold streams of water at different speeds mix past the edge of a splitter plate.…”

Section: Introductionmentioning

confidence: 93%

Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability

et al. 2011

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The combined Rayleigh-Taylor/Kelvin-Helmholtz (RT/KH) instability is studied in the early nonlinear regime. Specifically, the effect of adding shear to a gravitationally unstable configuration is investigated. While linear stability theory predicts that any amount of shear would increase the growth rate beyond the Rayleigh-Taylor value, numerical (large eddy) simulations show a more complex and non-monotonic behavior where small amounts of shear in fact decrease the growth rate. A velocity scale for the combined instability is proposed from linear stability arguments and is shown to effectively collapse the growth rates for different configurations. The specific amount of shear that minimizes the peak growth rate is identified and the physical origins of this non-monotonic behavior are investigated.

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“…15 However, such arguments for stability ignore the fact that available free energy stored in the kinetic energy of the relative motion of different layers may be a potential source driving some other classes of instabilities. 16 As an example, Kelvin-Helmholtz instability is a well-known instability that results from the free energy of shear flow. The shear-induced instabilities have been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Effects of shear flow and transverse magnetic field on Richtmyer–Meshkov instability

Cao

Ren

et al. 2008

Physics of Plasmas

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A weakly nonlinear theory of the spatial evolution of disturbances in a shear flow with a parallel magnetic fieldThe effects of shear flow and transverse magnetic field on Richtmyer-Meshkov instability are examined and the expression of the interface perturbation is obtained by analytically solving the linear ideal magnetohydrodynamics equations. It shows that the perturbation evolves exponentially rather than linearly in the presence of shear flow and magnetic field when v a Ͻ ͱ 1−A T 2 ␦ u / 2, where v a is the modified Alfvén velocity, A T is the Atwood number, and ␦ u is the relative shear velocity, respectively. The shear flow acts as a destabilizing source, while the magnetic field is a stabilizing mechanism of the shocked corrugated interface problem. The whole analysis is based on the assumption that the fluid is incompressible.

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Effect of shear flow and magnetic field on the Rayleigh–Taylor instability

Cited by 24 publications

References 9 publications

Linear stability of a horizontal phase boundary subjected to shear motion

Linear stability of a horizontal phase boundary subjected to shear motion

Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability

Effects of shear flow and transverse magnetic field on Richtmyer–Meshkov instability

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