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Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
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Stability boundaries for the Rayleigh-Taylor instability in accelerated elastic-plastic solid slabs.
A R Piriz1, S A 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 23, 2020
Summary
This study presents a linear theory for Rayleigh-Taylor instability in elastic-plastic solid slabs, providing analytical expressions for stability and plastic flow boundaries under acceleration. It simplifies the model to focus on average perturbation growth for accurate predictions.
Area of Science:
- Solid Mechanics
- Fluid Dynamics
- Materials Science
Background:
- Rayleigh-Taylor instability is crucial in various physical phenomena.
- Understanding the behavior of elastic-plastic materials under acceleration is complex.
- Previous models often simplified material behavior or instability dynamics.
Purpose of the Study:
- To develop a linear theory for incompressible Rayleigh-Taylor instability in elastic-plastic solid slabs.
- To establish analytical expressions for the boundaries of stability and plastic flow.
- To provide a simplified yet comprehensive model for this phenomenon.
Main Methods:
- Developed a linear theory based on a constitutive model with linear elastic and rigid-plastic phases.
- Applied the theory to a solid slab under constant acceleration, overlaying an ideal fluid.
- Assumed instability is dominated by average perturbation amplitude growth, neglecting higher frequencies.
Main Results:
- Obtained complete analytical expressions for the boundaries of stability and plastic flow.
- The results are valid for arbitrary Atwood numbers and slab thicknesses.
- The simplified approach effectively captures the dominant instability dynamics.
Conclusions:
- The developed linear theory accurately predicts the stability and plastic flow boundaries for elastic-plastic slabs.
- The model offers a valuable analytical tool for studying acceleration-driven instabilities in materials.
- This work contributes to a fundamental understanding of material behavior under dynamic conditions.
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