Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability

Mikaelian, Karnig O.

doi:10.1103/physrevfluids.1.033601

Cited by 10 publications

(1 citation statement)

References 54 publications

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“…This initial imprint leaves the initial conditions for the Rayleigh-Taylor instability that develops later in the acceleration phase of the early implosion [15]. The whole problem is a very complicated phenomenon, and it is therefore clear that Richtmyer-Meshkov (RM) like flows have become the object of continuous analytical [15,[18][19][20][21][22][23][24][25][26][27], numerical [14,15,16,[28][29][30] and experimental research [17,[31][32][33][34][35][36] during the last 20 years. Due to the limited space allowed, we will only focus on the dynamics of corrugated shock fronts and its influence on the properties of the perturbation field that develops downstream the corrugated wavefront and we concentrate our analytical efforts in obtaining the size of the strongest vortices generated by a rippled wavefront.…”

Section: Introductionmentioning

confidence: 99%

Linear theory of Richtmyer–Meshkov like flows

Wouchuk¹,

Campos²

2016

Plasma Phys. Control. Fusion

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The hydrodynamic flow generated by rippled shocks and rarefactions (Richtmyer-Meshkov like flows) is presented. When a corrugated shock travels inside an homogeneous fluid, it leaves pressure, density and velocity perturbations in the compressed fluid. The velocity perturbations generated in the composed fluid are inherently rotational. Vorticity is an important quantity in order to determine the asymptotic rate of growth in the linear stage. The size of the strongest vortices generated by the rippled shocks is analyzed as a function of the shock Mach number for different boundary conditions downstream. Comparison to experiments and simulations is provided for the RMI in the shock and rarefaction reflected cases and the validity of the growth law ψ δ + ∞ ∞ v t i is emphasized.

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Section: Introductionmentioning

confidence: 99%

Linear theory of Richtmyer–Meshkov like flows

Wouchuk¹,

Campos²

2016

Plasma Phys. Control. Fusion

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Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I

2017

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Evaluation of turbulent mixing transition in a shock-driven variable-density flow

et al. 2017

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The effect of initial conditions on transition to turbulence is studied in a variable-density shock-driven flow. Richtmyer–Meshkov instability (RMI) evolution of fluid interfaces with two different imposed initial perturbations is observed before and after interaction with a second shock reflected from the end wall of a shock tube (reshock). The first perturbation is a predominantly single-mode long-wavelength interface which is formed by inclining the entire tube to 80$^{\circ }$ relative to the horizontal, yielding an amplitude-to-wavelength ratio, $\unicode[STIX]{x1D702}/\unicode[STIX]{x1D706}=0.088$, and thus can be considered as half the wavelength of a triangular wave. The second interface is multi-mode, and contains additional shorter-wavelength perturbations due to the imposition of shear and buoyancy on the inclined perturbation of the first case. In both cases, the interface consists of a nitrogen-acetone mixture as the light gas over carbon dioxide as the heavy gas (Atwood number, $A\sim 0.22$) and the shock Mach number is $M\approx 1.55$. The initial condition was characterized through Proper Orthogonal Decomposition and density energy spectra from a large set of initial condition images. The evolving density and velocity fields are measured simultaneously using planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques. Density, velocity, and density–velocity cross-statistics are calculated using ensemble averaging to investigate the effects of additional modes on the mixing and turbulence quantities. The density and velocity data show that a distinct memory of the initial conditions is maintained in the flow before interaction with reshock. After reshock, the influence of the long-wavelength inclined perturbation present in both initial conditions is still apparent, but the distinction between the two cases becomes less evident as smaller scales are present even in the single-mode case. Several methods are used to calculate the Reynolds number and turbulence length scales, which indicate a transition to a more turbulent state after reshock. Further evidence of transition to turbulence after reshock is observed in the velocity and density fluctuation spectra, where a scaling close to $k^{-5/3}$ is observed for almost one decade, and in the enstrophy fluctuation spectra, where a scaling close to $k^{1/3}$ is observed for a similar range. Also, based on normalized cross correlation spectra, local isotropy is reached at lower wave numbers in the multi-mode case compared with the single-mode case before reshock. By breakdown of large scales to small scales after reshock, rapid decay can be observed in cross-correlation spectra in both cases.

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Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability

Cited by 10 publications

References 54 publications

Linear theory of Richtmyer–Meshkov like flows

Linear theory of Richtmyer–Meshkov like flows

Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I

Evaluation of turbulent mixing transition in a shock-driven variable-density flow

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