• Accepted Paper

Scaling effect on vortex formation and mixing in Richtmyer-Meshkov instability

Lidong Cheng, Gengxin Zhan, Haoyang Liu, Bin Yu, Xiaoyuan Zhang, and Bin Zhang

Phys. Rev. Fluids - Accepted 23 October, 2026

DOI: https://doi.org/10.1103/41gb-2xc2

Abstract

The dynamics of a single-mode Richtmyer–Meshkov instability (RMI) is investigated numerically across characteristic length scales spanning millimeters to microns, using two-dimensional Navier–Stokes simulations of a . As the scale is reduced, the increasing dominance of viscous diffusion over inertial forces fundamentally alters both the vortex formation and the global mixing efficiency. This transition is quantified by a dimensionless vortex breakdown number μ*=(ν1+ν2)u′ρ′/(ΔpW), which delineates three regimes: an inviscid regime (μ*<10−3, high Reynolds number), where coherent spiral vortices drive efficient entrainment; a transient regime (10−3<μ*<10−1, moderate Reynolds number), where incipient viscous diffusion suppresses vortex roll-up while molecular diffusion remains insufficient, resulting in a pronounced mixing minimum; and a viscous regime (μ*>10−1, low Reynolds number), where vortex formation is completely inhibited and mixing is dominated by rapid molecular diffusion. Analysis of the circulation budget reveals that the baroclinic production of vorticity is essentially scale-invariant, whereas the viscous dissipation term grows dramatically with decreasing scale, becoming the dominant contribution in the viscous regime. The non-monotonic variation of the global mixing degree with μ* is thereby traced to the interplay between an inviscid stirring mechanism that saturates at large scales and a diffusion-driven mechanism that becomes efficient only at very small scales. These findings provide a unified framework for understanding the scale-dependent mixing transition in RMI flows, offering guiding principles for the design of microfluidic mixing devices and for interpreting instability behaviour in high-energy-density environments.

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