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Rayleigh-Taylor instability in accelerated elastic-solid slabs.

S A Piriz1, A R Piriz1, N A Tahir2

  • 1Instituto de Investigaciones Energéticas (INEI), E.T.S.I.I., and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain.

Physical Review. E
|January 20, 2018
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Summary
This summary is machine-generated.

Researchers studied the Rayleigh-Taylor instability in accelerated solid slabs over fluids. They found a stability threshold dependent on material properties and acceleration, revealing conditions where the slab remains stable regardless of perturbation wavelength.

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Area of Science:

  • Fluid Dynamics
  • Solid Mechanics
  • Instability Theory

Background:

  • The Rayleigh-Taylor instability is crucial in various physical phenomena.
  • Previous studies focused on specific Atwood numbers (AT=1).
  • Understanding instability in accelerated solids over fluids requires further investigation.

Purpose of the Study:

  • To develop a linear theory for the asymptotic growth of Rayleigh-Taylor instability.
  • To extend existing theories to arbitrary Atwood numbers (AT).
  • To identify stability thresholds for accelerated elastic-solid slabs.

Main Methods:

  • Linear stability analysis.
  • Asymptotic growth rate calculations.
  • Theoretical modeling of incompressible fluid and elastic solid interactions.

Main Results:

  • A generalized linear theory for Rayleigh-Taylor instability is presented.
  • An instability threshold was identified, below which the slab is stable for all wavelengths.
  • The condition for slab stability was determined as ρ₂gh/G ≤ 2(1-AT)/AT.

Conclusions:

  • The study provides a comprehensive theory for Rayleigh-Taylor instability in accelerated solids.
  • A critical stability threshold exists, offering new insights into material behavior under acceleration.
  • The findings are applicable to systems involving accelerated elastic solids over fluids.