Experiments on the late-time development of single-mode Richtmyer–Meshkov instability

Jacobs, J. W.; Krivets, V. V.

doi:10.1063/1.1852574

Cited by 150 publications

(121 citation statements)

References 19 publications

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“…The roll-up in the WENO5M, WENO5F and WENO9 simulations contains a vortex bilayer with strong negative vorticity surrounded by a small layer of positive vorticity and vice versa: this bilayer becomes sharper as the order and resolution increase, and additional complex structures form within the roll-up in the WENO9F simulation. Such structures have also been seen in piecewise-parabolic method simulations [31,32], and is apparently a manifestation of a physical process observed in experi- ments [3,[33][34][35]. A qualitative correspondence in both ρ and ω can be seen between simulations along a diagonal, so that doubling the resolution approximately corresponds to doubling the order (as also found in Rayleigh-Taylor instability and double Mach reflection simulations [11]).…”

Section: Simulations Of Reshocked Single-mode Richtmyer-meshkov Instamentioning

confidence: 49%

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability

Latini

Schilling

Don

2007

Journal of Computational Physics

121

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Weighted essentially non-oscillatory (WENO) simulations of the reshocked twodimensional single-mode Richtmyer-Meshkov instability using third-, fifth-and ninthorder spatial flux reconstruction and uniform grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, production and mixing fractions, energy spectra, statistics, probability distribution functions, numerical turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and numerical viscosity on the order and resolution is investigated to long evolution times. The results are interpreted using the implicit numerical dissipation in the characteristic projection-based, finite-difference WENO method. It is shown that higher order higher resolution simulations have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition by the second shock-interface interaction induces the formation of small-scale structures. Lower-order lower-resolution simulations preserve large-scale structures and flow symmetry to late times, while higher-order higher-resolution simulations exhibit fragmentation of the structures, symmetry breaking and increased mixing. Similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling shows that increasing the order is more advantageous than increasing the resolution for the flow considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.

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Section: Simulations Of Reshocked Single-mode Richtmyer-meshkov Instamentioning

confidence: 49%

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability

Latini

Schilling

Don

2007

Journal of Computational Physics

121

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“…Among the main relevant studies of single-shock-induced mixing at a single contact surface, Jacobs & Krivets (2005) presented experiments on a planar, membraneless air-SF 6 interface impacted by relatively weak Mach numbers, M I = 1.1, 1.2 and 1.3 in a light-to-heavy configuration. PLIF provided detailed images of the disintegration of initial, large vortical structures into smaller, disordered scales at which molecular mixing occurs.…”

Section: Introductionmentioning

confidence: 99%

Transition to turbulence in shock-driven mixing: a Mach number study

Lombardini¹,

Pullin²,

Meiron³

2011

J. Fluid Mech.

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Large-eddy simulations of single-shock-driven mixing suggest that, for sufficiently high incident Mach numbers, a two-gas mixing layer ultimately evolves to a late-time, fully developed turbulent flow, with Kolmogorov-like inertial subrange following a −5/3 power law. After estimating the kinetic energy injected into the diffuse density layer during the initial shock-interface interaction, we propose a semi-empirical characterization of fully developed turbulence in such flows, based on scale separation, as a function of the initial parameter space, as, which corresponds to late-time Taylor-scale Reynolds numbers 250. In this expression, η 0 + represents the post-shock perturbation amplitude, u the change in interface velocity induced by the shock refraction, ν the characteristic kinematic viscosity of the mixture, L ρ the inner diffuse thickness of the initial density profile, A + the post-shock Atwood ratio, and C (A + , η 0 + /λ 0 ) ≈ 0.3 for the gas combination and post-shock perturbation amplitude considered. The initially perturbed interface separating air and SF 6 (pre-shock Atwood ratio A ≈ 0.67) was impacted in a heavy-light configuration by a shock wave of Mach number M I = 1.05, 1.25, 1.56, 3.0 or 5.0, for which η 0 + is fixed at about 25 % of the dominant wavelength λ 0 of an initial, Gaussian perturbation spectrum. Only partial isotropization of the flow (in the sense of turbulent kinetic energy and dissipation) is observed during the late-time evolution of the mixing zone. For all Mach numbers considered, the late-time flow resembles homogeneous decaying turbulence of Batchelor type, with a turbulent kinetic energy decay exponent n ≈ 1.4 and large-scale (k → 0) energy spectrum ∼ k 4 , and a molecular mixing fraction parameter, Θ ≈ 0.85. An appropriate time scale characterizing the Taylor-scale Reynolds number decay, as well as the evolution of mixing parameters such as Θ and the effective Atwood ratio A e , seem to indicate the existence of low-and high-Mach-number regimes.

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“…Zhang & Sohn 1997;Herrmann et al 2008), and experimental evidence points to the growth becoming nonlinear at late times (Collins & Jacobs 2002;Jacobs & Krivets 2005). At this point, the interface has transitioned from sinusoidal through the appearance of 'bubbles and spikes' to the onset of turbulence.…”

Section: Models Of the Instabilitymentioning

confidence: 99%

Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

et al. 2009

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The single-mode Richtmyer-Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier-Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models.

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Experiments on the late-time development of single-mode Richtmyer–Meshkov instability

Cited by 150 publications

References 19 publications

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability

Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer–Meshkov instability

Transition to turbulence in shock-driven mixing: a Mach number study

Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

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