A new approach to the Rayleigh-Taylor instability
| Autor: | László Székelyhidi, Björn Gebhard, József J. Kolumbán |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Gravity (chemistry) Mechanical Engineering 010102 general mathematics Mechanics 01 natural sciences Instability Article 010101 applied mathematics Physics::Fluid Dynamics Mathematics (miscellaneous) Mathematics - Analysis of PDEs Differential inclusion Atwood number Relaxation (physics) Rayleigh–Taylor instability 0101 mathematics Constant (mathematics) Analysis Mixing (physics) |
| Zdroj: | Archive for Rational Mechanics and Analysis |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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