2020/02/24 by Björn Gebhard, József J. Kolumbán, László Székelyhidi +1 · 22 citations
Engineering · Mathematics · #Compressibility #Computational Fluid Dynamics and Aerodynamics #Constant (computer programming) #Euler equations #Euler's formula #Fluid Dynamics and Turbulent Flows #Instability #Mixing (physics) #Navier-Stokes equation solutions #Quadratic growth #Rest (music) #math.AP
paper · pdf · open access · doi:10.1007/s00205-021-01672-1
published in Archive for Rational Mechanics and Analysis 241(3), 1243-1280 (Springer Science+Business Media)
arxiv created 2020/02/24 · openalex created_date 2020/03/06 · openalex publication_date 2021/06/12 · arxiv updated 2021/06/15 · openalex updated_date 2026/08/05
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.