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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Linear instability in Rayleigh-stable Taylor-Couette flow.

Kengo Deguchi1

  • 1School of Mathematical Sciences, Monash University, VIC 3800, Australia.

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|March 17, 2017
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Summary
This summary is machine-generated.

Rayleigh's stability criterion is challenged by new findings in rotating fluid dynamics. A linear instability was discovered in cyclonic rapid rotation Taylor-Couette flow, even when deemed stable by Rayleigh's criterion.

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Area of Science:

  • Fluid dynamics
  • Hydrodynamic stability

Background:

  • Rayleigh's stability criterion is a foundational concept for inviscid rotating fluid flows.
  • It has been traditionally considered a universal barrier against instability in rapidly rotating systems.
  • Previous studies assumed Rayleigh stability implied flow stability.

Purpose of the Study:

  • To investigate the stability of Taylor-Couette flow under rapid rotation.
  • To re-evaluate the applicability of Rayleigh's stability criterion in specific flow regimes.
  • To identify potential instabilities overlooked by classical criteria.

Main Methods:

  • Linear stability analysis of the Navier-Stokes equations for Taylor-Couette flow.
  • Numerical simulations exploring the cyclonic rapid rotation regime.
  • Systematic variation of the radius ratio between the cylinders.

Main Results:

  • A linear instability was identified in Taylor-Couette flow that is stable according to Rayleigh's criterion.
  • This instability occurs in the cyclonic rapid rotation regime.
  • The instability is present across nearly all radius ratios of the cylinders.

Conclusions:

  • Rayleigh's stability criterion is not a universally sufficient condition for stability in all rapidly rotating flows.
  • The identified instability in cyclonic Taylor-Couette flow necessitates a revision of classical stability paradigms.
  • Further research is needed to fully characterize the dynamics and implications of this newly found instability.