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MiS Preprint
6/2023

Scale invariant bounds for mixing in the Rayleigh-Taylor instability

Konstantin Kalinin, Govind Menon and Bian Wu

Abstract

We study the Rayleigh-Taylor instability for two miscible, incompressible, inviscid fluids. Scale-invariant estimates for the size of the mixing zone and coarsening of internal structures in the fully nonlinear regime are established following techniques introduced for the Saffman-Taylor instability in [Otto and Menon, Commun.Math.Phys., 2005]. These bounds provide optimal scaling laws and reveal the strong role of dissipation in slowing down mixing.

Received:
Jul 3, 2023
Published:
Jul 6, 2023
MSC Codes:
35Q35, 35Q35, 35Q35
Keywords:
Rayleigh-Taylor instability, Saffman-Taylor instability, fluid mixing

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Preprint
2023 Repository Open Access
Konstantin Kalinin, Govind Menon and Bian Wu

Scale invariant bounds for mixing in the Rayleigh-Taylor instability