Scaling law of structure function of Richtmyer–Meshkov turbulence

This work investigates the compressible turbulence induced by Richtmyer–Meshkov (RM) instability using high-resolution Navier–Stokes simulations. Special attention is paid to the characteristics of RM turbulence including the mixing width growth, the turbulent kinetic energy (TKE) decay, the mixing degree, inhomogeneity and anisotropy. Three distinct initial perturbation spectra are designed at the interface to reveal the initial condition imprint on the RM turbulence. Results show that cases with initial large-scale perturbations present a stronger imprint on statistical characteristics and also a quicker growth of mixing width, whereas cases with small-scale perturbations present a faster TKE decay, greater mixing level, higher isotropy and homogeneity. A thorough analysis on the inter-scale energy transfer in RM turbulence is also presented with the coarse-graining approach that exposes the two subfilter-scale (SFS) energy fluxes (i.e. deformation work and baropycnal work). A strong correlation between the nonlinear model of baropycnal work (Fluids, 4(2), 2019) and the simulation results is confirmed for the first time, demonstrating its potential in modelling the RM turbulence. Two primary mechanisms of baropycnal work (the straining and baroclinic generation processes) are explored with this nonlinear model. The evolutions of two SFS energy fluxes exhibit distinct behaviours at various filter scales, in different flow regions and under various flow motions (strain and rotation). It is found that all three cases share the common inter-scale energy transfer dynamics, which is important for modelling the RM turbulence.

Section: Characteristics Of the Mixing Layersupporting

confidence: 59%

Section: Characteristics Of the Mixing Layermentioning

confidence: 99%

Section: Numerical Set-upmentioning

confidence: 99%

Section: Inter-scale Energy Transfermentioning

confidence: 99%

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Mixing and inter-scale energy transfer in Richtmyer–Meshkov turbulence

Zhou,

Ding,

Cheng

2024

“…Anomalous scalings of active scalars in homogeneous turbulence were developed by Ching & Cheng (2008). Kinetic and scalar structure function scaling laws for RMI turbulence have been investigated through simulations and theory by Zhou et al (2023). The Batchelor spectrum of passive scalar isotropic turbulence was discussed by Donzis, Sreenivasan & Yeung (2010).…”

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

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.

Freeze-out of perturbation growth for shocked heavy fluid layers by eliminating reverberating waves

Cong,

Guo,

Zhou

et al. 2024

The shock wave accelerating a heavy fluid layer can induce reverberating waves that continuously interact with the first and second interfaces. In order to manipulate the perturbation growths at fluid-layer interfaces, we present a theoretical framework to eliminate the reverberating waves. A model is established to predict the individual freeze-out (i.e. stagnation of perturbation growth) for the first and second interfaces under specific flow conditions determined based on the shock dynamics theory. The theoretical model quantifies the controllable parameters required for freeze-out, including the initial amplitudes of the first and second interfaces, the interface coupling strength and the maximum initial layer thickness preventing the second interface's phase reversal. The effectiveness of the model in predicting individual freeze-out for the first and second interfaces is validated numerically over a wide range of initial conditions. The upper and lower limits of initial amplitudes for the freeze-out of the whole fluid-layer width growth are further predicted. Within this amplitude range, a slightly higher initial amplitude for the second interface is specified, effectively arresting the growth of the entire fluid-layer width before the phase reversal of the second interface.