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Updated: Oct 15, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
A New Approach to the Rayleigh-Taylor Instability
Björn Gebhard1, József J Kolumbán1, László Székelyhidi1
1Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Germany.
Abstract:
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the constitutive laws we formulate a general criterion for the existence of infinitely many weak solutions which reflect the turbulent mixing of the two fluids. Our criterion can be verified in the case that initially the fluids are at rest and separated by a flat interface with the heavier one being above the lighter one-the classical configuration giving rise to the Rayleigh-Taylor instability. We construct specific examples when the Atwood number is in the ultra high range, for which the zone in which the mixing occurs grows quadratically in time.
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