Energy transfer in the Richtmyer-Meshkov instability

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Computational Physics

Background:

• Richtmyer-Meshkov instability (RM) drives turbulent mixing layers.
• Understanding energy transfer in these layers is crucial for predicting mixing.
• Parallels exist between RM and Rayleigh-Taylor (RT) instability dynamics.

Purpose of the Study:

• To present the variable-density spectral kinetic energy budget for RM-induced turbulent mixing.
• To analyze energy transfer mechanisms and their evolution.
• To compare RM mixing layer dynamics with RT instability.

Main Methods:

• Utilized a 512^3 implicit large eddy simulation (ILES).
• Analyzed the kinetic energy budget at multiple time instants and spatial locations.
• Computed spectral numerical dissipation for the self-similar layer.

Main Results:

• Energy transfer spectra are asymmetric, concentrated on the spike side.
• Vortex rings identified as key sources of alternating energy transfer.
• Quadratic and pressure terms largely cancel in spike regions; dilatational terms are negligible.
• Numerical dissipation is small at low wavenumbers but significant and analogous to eddy viscosity at high wavenumbers.

Conclusions:

• Vortex rings play a critical role in energy transfer, explaining similarities with RT instability.
• Numerical dissipation effects are minimal in resolved scales but significant in underresolved scales.
• The study provides detailed spectral insights into RM turbulent mixing layer evolution.