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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Linearized Richtmyer-Meshkov flow analysis for impulsively accelerated incompressible solids.

A López Ortega¹, D J Hill, D I Pullin

¹Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 28, 2010

Summary

This study analyzes the Richtmyer-Meshkov instability in elastic solids. We found that material properties stabilize the interface, leading to standing waves or oscillating decay, unlike unstable gas behavior.

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Area of Science:

Fluid Dynamics
Solid Mechanics
Plasma Physics

Background:

The Richtmyer-Meshkov instability is crucial in fluid dynamics.
Prior studies on compressible elastic materials suggest bounded interface amplitude.
Instability in gases typically shows unbounded growth.

Purpose of the Study:

To analytically investigate linearized impulsive Richtmyer-Meshkov flow in incompressible elastic solids.
To understand the long-term behavior of the interface amplitude.
To identify the role of material properties in flow stabilization.

Main Methods:

Linearization of conservation equations around a base unperturbed flow.
Solution of the initial and boundary value problem using Laplace transform techniques.
Analysis of singularities in the Laplace domain for parametric study.

Main Results:

Identified two long-term interface patterns: standing wave and oscillating decay, dependent on material properties.
Demonstrated that shear stiffness stabilizes the interface.
Showed shear stiffness influences the period of interface oscillations.

Conclusions:

The study provides an analytical framework for Richtmyer-Meshkov flow in elastic solids.
Material shear stiffness is key to stabilizing the interface and controlling oscillations.
Results contrast with the typically unstable behavior observed in gases.