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The first consistent phenomenological theory for two- and three-dimensional Rayleigh-Taylor (RT) turbulence has recently been presented by Chertkov Phys. Rev. Lett. 91, 115001 (2003). By means of direct numerical simulations, we confirm the spatiotemporal prediction of the theory in two dimensions and explore the breakdown of the phenomenological description due to intermittency effects. We show that small-scale statistics of velocity and temperature follow Bolgiano-Obukhov scaling. At the level of global observables, we show that the time-dependent Nusselt and Reynolds numbers scale as the square root of the Rayleigh number. These results point to the conclusion that RT turbulence in two and three dimensions, thanks to the absence of boundaries, provides a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection."
Celani et al. (2006) studied this question.