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Coupling effects and thin-shell corrections for surface instabilities of cylindrical fluid shells.

Shuai Zhang1, Hao Liu2, Wei Kang1

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Physical Review. E
|March 15, 2020
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Linear perturbations on fluid shells reveal three instability stages: strongly coupled, transition, and uncoupled. The ratio of outer to inner radius to the mode number (α^m) predicts coupling effects and experimental outcomes.

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Area of Science:

  • Fluid dynamics
  • Plasma physics
  • Instability analysis

Background:

  • Understanding fluid shell instabilities is crucial for inertial confinement fusion.
  • Existing models often simplify the complex coupling effects between shell surfaces.

Purpose of the Study:

  • To analyze linear azimuthal perturbations on fluid shells.
  • To identify and categorize different terms contributing to shell instability.
  • To define stages of instability evolution based on coupling effects.

Main Methods:

  • Regrouping linear azimuthal perturbations using the index α^m (ratio of R_out to R_in, raised to the power of mode number m).
  • Analyzing the contributions of Bell model terms, coupling terms, and thin-shell correction terms.

Main Results:

  • Introduced α^m as a key index for coupling effects in fluid shell instabilities.
  • Identified three distinct stages of instability: strongly coupled (α^m < 6), transition, and uncoupled (α^m ~ 36).
  • Demonstrated that thin-shell corrections are significant in the strongly coupled stage.

Conclusions:

  • The α^m index provides an intuitive framework for understanding fluid shell instability.
  • The identified stages and coupling dynamics can guide experimental design and interpretation.
  • Results offer a simplified yet comprehensive view of instability evolution in fluid shells.