Title:        Rayleigh-Taylor instability in two dimensions


Abstarct:

Rayleigh-Taylor instability is a well-known mixing mechanism 
occuring when a light fluid is accelerated into heavy fluid. This 
instability plays a crucial role in many fields of science (
i.e., supernovae explosions).
The final stage of instability necessarily leads to the so-called 
Rayleigh-Taylor turbulence. Despite the long
history of this instability, it was been discovered by Lord Rayleigh in 
the 1880s, a first consistent phenomeno-
logical theory for the turbulent stage has been presented very recently 
by Chertkov for the miscibile case [Phys.
Rev. Lett. 91, 115001 (2003)] and by Chertkov et al. for the immiscible 
case [Phys. Rev E 71, 055301(R)
(2005)]. With reference to these works, we concentrate on the 
two-dimensional problem and our main aim is
to investigate, by means of direct simulations, the statistical 
properties of the flow in the mixing region. Regar-
ding the miscible case, the confirmation of the theoretical 
spatio/temporal prediction and the breakdown of the
phenomenology description due to intermittency effects are discussed. 
For immiscible case, the surface ten-
sion raises serious problems in describing numerically the instability. 
The numerical method (the Phase-field
method) that overcomes these problems is described and some of our 
preliminary results are shown.