Growth rate of Rayleigh-Taylor turbulent mixing layers with the foliation approach

Abstract

For years, astrophysicists, plasma fusion and fluid physicists have puzzled over Rayleigh-Taylor turbulent mixing layers. In particular, strong discrepancies in the growth rates have been observed between experiments and numerical simulations. Although two phenomenological mechanisms (mode-coupling and mode-competition) have brought some insight on these differences, convincing theoretical arguments are missing to explain the observed values. In this paper, we provide an analytical expression of the growth rate compatible with both mechanisms and is valide for a self-similar, low Atwood Rayleigh-Taylor turbulent mixing subjected to a constant or time-varying acceleration. The key step in this work is the introduction of {\it foliated} averages and {\it foliated} turbulent spectra highlighted in our three dimensional numerical simulations. We show that the exact value of the Rayleigh-Taylor growth rate not only depends upon the acceleration history but is also bound to the power-law exponent of the {\it foliated} spectra at large scales.

References in corpus (3)

• The Formation of Massive Star Systems by Accretion
• Kolmogorov scaling and intermittency in Rayleigh-Taylor turbulence
• Rayleigh-Taylor turbulence is nothing like Kolmogorov turbulence in the self similar regime

Cited by in corpus (3)

• Late-time growth rate, mixing and anisotropy in the multimode narrowband Richtmyer--Meshkov Instability: the $\theta$-Group Collaboration
• Gas expulsion in massive star clusters? Constraints from observations of young and gas-free objects
• Modeling late-time sensitivity to initial conditions in Boussinesq Rayleigh-Taylor turbulence