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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.
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.
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