A new approach to the Rayleigh-Taylor instability

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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Cited by in corpus (7)

• H-principle for the 2D incompressible porous media equation with viscosity jump
• On bounded two-dimensional globally dissipative Euler flows
• A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation
• Scale invariant bounds for mixing in the Rayleigh-Taylor instability
• Entropy solutions to macroscopic IPM
• The Rayleigh-Taylor instability with local energy dissipation
• On the energy-constrained optimal mixing problem for one-dimensional initial configurations