Scalar Power Spectra and Scalar Structure Function Evolution in the Richtmyer–Meshkov Instability Upon Reshock

The scaling law of the structure function of Richtmyer–Meshkov (RM) turbulence is investigated both numerically and theoretically. High-fidelity simulations with a minimum-dispersion, adaptive-dissipation scheme are first performed. Results show that the mixing width experiences an exponential growth and the turbulent kinetic energy has a visible $-3/2$ spectrum. The scalar field exhibits a greater degree of intermittency than the velocity field, and also the small-scale statistics suffer a larger influence of large scales. Visible differences in the scaling law of the structure function among the RM turbulence and other types of turbulence are observed, which reveal the unique characteristic of RM turbulence. A phenomenological theory, which gives the spatial and temporal scaling laws of the structure functions of velocity and scalar of RM turbulence, is developed for the first time by introducing an external agent. The spatial scaling exponents of structure functions from simulation deviate from the Kolmogorov exponents, but are quite close to the RM-modified anomalous exponents. This demonstrates the validity of the present phenomenological theory. The temporal scaling exponents of structure functions first meet the RM-modified anomalous exponents, and then approach the Kolmogorov–Obukhov–Corrsin non-intermittent ones.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scaling law of structure function of Richtmyer–Meshkov turbulence

Zhou,

Ding,

Cheng

et al. 2023

“…2014; Noble et al. 2020 a , b ). The high-speed (HS) series is composed of 20 individual experiments, while the single-shot (SS) series is composed of 71 individual experiments.…”

Section: Experiments Detailsmentioning

confidence: 99%

“…Previous high-speed PLIF experiments (Noble et al. 2020 a , b ) using this IC lacked direct measurement of the velocity field so they were not suitable to extract individual production and transport terms. This is remedied in the present work, where the production and flux terms can be separately evaluated.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock

Noble,

Ames,

McConnell

et al. 2023

Self Cite

The Richtmyer–Meshkov instability (Richtmyer, Commun. Pure Appl. Maths, vol. 13, issue 2, 1960, pp. 297–319; Meshkov, Fluid Dyn., vol. 4, issue 5, 1972, pp. 101–104) of a twice-shocked gas interface is studied using both high spatial resolution single-shot (SS) and lower spatial resolution, time-resolved, high-speed (HS) simultaneous planar laser-induced fluorescence and particle image velocimetry in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. This IC is accelerated by a shock of nominal strength Mach number $M = 1.75$ , and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An ensemble of experiments is analysed after reshock while the interface mixing width grows linearly with time. The kinetic and scalar energy spectra and the terms of their evolution equation are calculated and compared between SS and HS experiments. The inertial range scaling of the scalar power spectrum is found to follow Gibson's relation (Gibson, Phys. Fluids, vol. 11, issue 11, 1968, pp. 2316–2327) as a function of Schmidt number when the effective turbulent Schmidt number is used in place of the material Schmidt number that controls equilibrium scaling. Further, the spatially integrated scalar flux follows similar behaviour observed for the kinetic energy in large eddy simulation studies by Zeng et al. (Phys. Fluids, vol. 30, issue 6, 2018, 064106) while the spatially varying scalar flux exhibits back scatter along the centre of the mixing layer and forward energy transfer in the spike and bubble regions.

“…In recent decades, the RM instability has received increasing attention due to its significance in scientific research (e.g. compressible turbulence) (Noble et al 2023) and practical applications (e.g. supernova explosion) (Musci et al 2020), and comprehensive reviews have been reported (Ranjan, Oakley & Bonazza 2011;Zhou 2017).…”

Section: Introductionmentioning

confidence: 99%

Divergent Richtmyer–Meshkov instability under different shock strengths

Ding,

Zhang,

Luo

2024

Richtmyer–Meshkov (RM) instability at a single-mode interface impacted by a cylindrical divergent shock with low to moderate Mach numbers is investigated experimentally. The motion of an unperturbed interface is first examined to obtain the background flow. The shocked interface moves uniformly at the early stage, but later decelerates. The stronger the incident shock, the larger the interface deceleration, which is reasonably predicted by a one-dimensional model considering the effect of postshock non-uniformity. Such a deceleration greatly inhibits the growths of harmonics of an initially perturbed interface and, consequently, the divergent RM instability presents very weak nonlinearity from early to late stages. Particularly, higher-Mach-number cases present weaker nonlinearity due to larger deceleration there. This abnormal linear growth regime is reported for the first time. Benefiting from this, the incompressible linear model holds validity at all stages of divergent RM instability. It is also found that compressibility inhibits the initial growth rate, but produces a weak influence on the subsequent instability growth.