Fastest growing linear Rayleigh-Taylor modes at solid/fluid and solid/solid interfaces

Area of Science:

• Physics
• Materials Science
• Fluid Dynamics

Background:

• Previous Rayleigh-Taylor instability analyses for elastic solids were limited to specific conditions (Atwood number A=1) and focused on cutoff wavelengths.
• Understanding instability dynamics at interfaces is crucial for various physical phenomena and material behaviors.

Purpose of the Study:

• To rigorously derive and systematically investigate dispersion relations for solid/fluid and solid/solid interfaces across all Atwood numbers.
• To compute the most unstable modes (maximum growth rate) and associated wavelengths for all unstable disturbances.
• To provide a comprehensive understanding of Rayleigh-Taylor instability in elastic solids.

Main Methods:

• Derivation of dispersion relations for solid/fluid and solid/solid interfaces.
• Rationalization of dispersion relations into multivariable polynomials.
• Systematic computation of wavelengths and growth rates for all unstable disturbances as a function of material properties and acceleration.

Main Results:

• Instability onset occurs via monotonically growing disturbances at these interfaces.
• The locus of most unstable wavelength (lambda(m)) and growth rate (sigma(m)) pairs were calculated for the entire dimensionless space.
• A unique behavior was observed at solid/fluid interfaces where two configurations with different Atwood numbers can exhibit the same most unstable wavelength.

Conclusions:

• The derived results are applicable to finite thickness layers (h > lambda/2) for estimating key instability parameters.
• A plausible mechanism for wavelength selection in magnetically imploded liners is proposed, linking theoretical findings to experimental observations.
• This work provides a generalized framework for analyzing Rayleigh-Taylor instability in elastic solids, applicable to a wide range of conditions.