Growth rate of Rayleigh-Taylor turbulent mixing layers from first principles

Details Growth rate of Rayleigh-Taylor turbulent mixing layers from first principles Growth rate of Rayleigh-Taylor turbulent mixing layers from first principles

2009-04-03

arxiv.org/abs/0904.0557v2

Physics

Fluid Dynamics

Scientific paper

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. Here we show, from first principles, that an analytical expression of the growth rate, compatible with both mechanisms, can be derived 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.

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