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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Scale Invariant Bounds for Mixing in the Rayleigh–Taylor Instability
Konstantin Kalinin, Govind Menon and Bian WuAbstract
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:
- 03.07.23
- Published:
- 06.07.23
- MSC Codes:
- 35Q35, 35Q35, 35Q35
- Keywords:
- Rayleigh-Taylor instability, Saffman-Taylor instability, fluid mixing