Richtmyer-Meshkov instability: theory of linear and nonlinear evolution

Area of Science:

• Fluid dynamics
• Plasma physics
• Astrophysical phenomena

Background:

• Richtmyer-Meshkov instability (RMI) occurs when a shock wave interacts with a perturbed interface between fluids.
• The instability involves the generation and evolution of vorticity at the interface.
• Understanding RMI is crucial for fields ranging from inertial confinement fusion to astrophysics.

Purpose of the Study:

• To develop a comprehensive theoretical framework for analyzing both linear and nonlinear regimes of RMI.
• To elucidate the fundamental mechanisms driving instability growth, including vorticity deposition and acoustic effects.
• To provide analytical models for predicting RMI evolution in various scenarios.

Main Methods:

• Development of an exact analytical model for the asymptotic linear growth rate of RMI.
• Formulation of an analytical model for the nonlinear phase of RMI in incompressible, irrotational fluids.
• Utilizing molecular dynamics simulations to investigate RMI in solids and liquids for planar and cylindrical geometries.

Main Results:

• The study identifies two primary drivers of RMI: initial vorticity deposition and subsequent variations due to acoustic fields.
• An analytical model for linear growth rate is derived, showing dependence on key parameters.
• A model for nonlinear RMI is presented, describing the decrease in perturbation velocity as amplitude increases.
• Molecular dynamics simulations confirm vorticity generation in viscous materials.

Conclusions:

• The presented framework accurately describes RMI phenomena across different regimes.
• The interplay between shock dynamics and fluid properties governs instability evolution.
• The findings have implications for understanding and controlling instabilities in diverse physical systems.