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Nonlinear Rayleigh-Taylor growth in converging geometry.
1Lawrence Livermore National Laboratory, University of California, Livermore, California 94550, USA. clark90@llnl.gov
Summary
This study generalizes the Layzer model for Rayleigh-Taylor growth to spherical implosions. It reveals that bubble rise accelerates during late-stage implosion, differing from constant-velocity models.
Area of Science:
- Fluid dynamics
- Plasma physics
- Astrophysics
Background:
- The Layzer model describes early nonlinear Rayleigh-Taylor growth for planar interfaces.
- This model does not account for spherical convergence effects relevant to fusion and astrophysics.
Purpose of the Study:
- Generalize the Layzer nonlinear bubble rise model for self-similar, spherically converging flows.
- Investigate bubble amplitude and rise rate dynamics in converging systems.
Main Methods:
- Developed a generalized Layzer model for spherical convergence.
- Derived a simple formula for bubble amplitude.
- Compared results with numerical hydrodynamics simulations.
Main Results:
- The generalized model predicts an initial constant bubble rise velocity, consistent with the Layzer result.
- A significant acceleration in bubble rise rate is observed during the late phase of implosion.
- The derived bubble amplitude formula captures this late-phase acceleration.
Conclusions:
- The classic Layzer model is insufficient for spherically converging interfaces.
- A modified understanding of bubble dynamics, including acceleration, is crucial for inertial confinement fusion and astrophysical phenomena.
- Numerical simulations validate the generalized model's predictions.