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

Olson, Britton J.; Larsson, Johan; Lele, Sanjiva K.; Cook, Andrew W.

doi:10.1063/1.3660723

Cited by 55 publications

(34 citation statements)

References 10 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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“…The Miranda simulation code has been used extensively for simulating turbulent flows with high Reynolds numbers and multi-species mixing (Cabot & Cook 2006;Cook et al 2004;Olson & Cook 2007;Olson et al 2011;Weber et al 2013). Miranda employs a 10 thorder compact difference scheme (Lele 1992) for spatial differentiation and a five stage, 4 th -order Runge-Kutta scheme (Kennedy et al 2000) for temporal integration of the compressible multicomponent Navier-Stokes equations.…”

Section: The Miranda Simulation Codementioning

confidence: 99%

On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface

et al. 2014

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We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma = 1.5. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Wellresolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ∼t 7/12 before re-shock and ∼(t − t 0 ) 2/7 long after re-shock. The decay rate of turbulence kinetic energy is consistently ∼(t − t 0 ) −10/7 at late times, where the molecular mixing fraction approaches an asymptotic limit Θ ≈ 0.85. The anisotropy measure a xyz approaches an asymptotic limit of ≈0.04, implying that no full recovery of isotropy within the mixing zone is obtained, even after re-shock. Spectra of density, turbulence kinetic energy, scalar dissipation rate and enstrophy are presented and show excellent agreement for the resolved scales. The probability density function of the heavy-gas mass fraction and vorticity reveal that the light-heavy gas composition within the mixing zone is accurately predicted, whereas it is more difficult to capture the long-term behaviour of the vorticity.

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“…The Miranda code has been used extensively for simulating turbulent flows with high Reynolds numbers and multicomponent mixing 6,9,24,25 . Miranda uses a 10 th -order compact differencing scheme for spatial differentiation and a 5-stage, 4…”

Section: B the Miranda Codementioning

confidence: 99%

Large eddy simulation requirements for the Richtmyer-Meshkov instability

Olson

Greenough

2014

Physics of Fluids

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The shock induced mixing of two gases separated by a perturbed interface is investigated through Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). In a simulation, physical dissipation of the velocity field and species mass fraction often compete with numerical dissipation arising from the errors of the numerical method. In a DNS the computational mesh resolves all physical gradients of the flow and the relative effect of numerical dissipation is small. In LES, unresolved scales are present and numerical dissipation can have a large impact on the flow, depending on the computational mesh. A suite of simulations explores the space between these two extremes by studying the effects of grid resolution, Reynolds number and numerical method on the mixing process. Results from a DNS are shown using two different codes, which use a high-and low-order numerical method and show convergence in the temporal and spectral dependent quantities associated with mixing. Data from an unresolved, high Reynolds number LES are also presented and include a grid convergence study. A model for an effective viscosity is proposed which allows for an a posteriori analysis of the simulation database that is agnostic to the LES model, numerics, and the physical Reynolds number of the simulation. An analogous approximation for an effective species diffusivity is also presented. This framework is then used to estimate the effective Reynolds number and Schmidt number of future simulations, elucidate the impact of numerical dissipation on the mixing process for an arbitrary numerical method, and provide guidance for resolution requirements of future calculations.

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

Cited by 55 publications

References 10 publications

Linear stability of a horizontal phase boundary subjected to shear motion

Linear stability of a horizontal phase boundary subjected to shear motion

On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface

Large eddy simulation requirements for the Richtmyer-Meshkov instability

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