612 research outputs found
Rayleigh--Taylor turbulence in two dimensions
The first consistent phenomenological theory for two and three dimensional
Rayleigh--Taylor (RT) turbulence has recently been presented by Chertkov [Phys.
Rev. Lett. {\bf 91} 115001 (2003)]. By means of direct numerical simulations we
confirm the spatio/temporal 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 Rayleigh-Taylor
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''.Comment: 4 pages, 5 figure
The large-scale structure of passive scalar turbulence
We investigate the large-scale statistics of a passive scalar transported by
a turbulent velocity field. At scales larger than the characteristic
lengthscale of scalar injection, yet smaller than the correlation length of the
velocity, the advected field displays persistent long-range correlations due to
the underlying turbulent velocity. These induce significant deviations from
equilibrium statistics for high-order scalar correlations, despite the absence
of scalar flux.Comment: 4 pages, 6 figure
Going forth and back in time: a fast and parsimonious algorithm for mixed initial/final-value problems
We present an efficient and parsimonious algorithm to solve mixed
initial/final-value problems. The algorithm optimally limits the memory storage
and the computational time requirements: with respect to a simple forward
integration, the cost factor is only logarithmic in the number of time-steps.
As an example, we discuss the solution of the final-value problem for a
Fokker-Planck equation whose drift velocity solves a different initial-value
problem -- a relevant issue in the context of turbulent scalar transport.Comment: 12 pages, 4 figure
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