Preprint 6/2023

Scale invariant bounds for mixing in the Rayleigh-Taylor instability

Konstantin Kalinin, Govind Menon, and Bian Wu

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Submission date: 06. Mar. 2023
Pages: 23
MSC-Numbers: 35Q35, 35Q35, 35Q35
Keywords and phrases: Rayleigh-Taylor instability, Saffman-Taylor instability, fluid mixing
Link to arXiv: See the arXiv entry of this preprint.

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.

06.07.2023, 02:10