Modal model mean field self-similar solutions to the asymptotic evolution of Rayleigh-Taylor and Richtmyer-Meshkov instabilities and its dependence on the initial conditions

Yonatan Elbaz, Dov Shvarts

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

The evolution of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for incompressible and immiscible fluids and their dependence on the initial perturbation spectrum is evaluated using a new mean field formulation of the Haan-Ofer-Shvarts mode coupling model. The height of the lighter fluid bubbles penetrating into the denser fluid is shown to reach asymptotic, universal, self-similar behavior when the initial spectrum is dominated by short wavelengths and at least 3-4 mode coupling generations have occurred. For RT, the model yields h = αRT Agt2 for the bubble front penetration height, in good agreement with experimental data and 3D numerical simulations for various initial conditions. For RM, the lack of a natural length scale leads to a 2nd type self-similar solution h = α R M t θ and θ is rigorously determined from a detailed solution of the model equation, while αRM retains knowledge of the initial spectrum. The value of θRM in two dimensions is θ2 D = 2/5, consistent with the Alon-Shvarts bubble-merger model and numerical simulations, and in three dimensions, it is θ3 D = 1/3. We find that the smaller value θ3 D ∼ 0.25 ± 0.05 obtained in numerical simulations and experiments [Dimonte and Schneider, Phys. Fluids 12, 304 (2000)] results from the lack of enough mode coupling generations needed to reach the RM asymptotic self-similar stage. The feasibility of a true self-similar RM experiment on NIF is discussed.

Original languageEnglish
Article number062126
JournalPhysics of Plasmas
Volume25
Issue number6
DOIs
StatePublished - 1 Jun 2018

ASJC Scopus subject areas

  • Condensed Matter Physics

Fingerprint

Dive into the research topics of 'Modal model mean field self-similar solutions to the asymptotic evolution of Rayleigh-Taylor and Richtmyer-Meshkov instabilities and its dependence on the initial conditions'. Together they form a unique fingerprint.

Cite this