Unified decomposition method to study Rayleigh-Taylor instability in liquids and solids

Area of Science:

• Physics
• Continuum Mechanics
• Fluid Dynamics

Background:

• Rayleigh-Taylor instability is crucial in various physical phenomena.
• Previous studies employed diverse methods to model elasticity, viscosity, and magnetic field effects.
• A unified approach is needed for comprehensive analysis.

Purpose of the Study:

• To validate a unified method for analyzing Rayleigh-Taylor instability across different physical models.
• To incorporate nonconservative forces and constitutive relations into instability analysis.
• To derive new analytical solutions for solid-solid and solid-fluid interfaces.

Main Methods:

• Decomposition of the unstable mode into irrotational and rotational parts.
• Application of interface boundary conditions to recover previous results.
• Derivation of approximate analytical solutions for growth rates.

Main Results:

• The unified method successfully models Rayleigh-Taylor instability in solids and fluids.
• Previous findings on solid-liquid interfaces with/without magnetic fields and finite thickness are reproduced.
• New, highly accurate analytical solutions for semi-infinite solid-solid and solid-fluid interfaces are obtained.

Conclusions:

• The validated unified method provides a versatile framework for studying interfacial instabilities.
• The derived analytical solutions enhance the predictive capability for solid-fluid and solid-solid systems.
• This work offers a more accurate and unified approach to understanding complex interfacial phenomena.