  We studied turbulence induced by the Rayleigh-Taylor (RT) instability for 2D
immiscible two-component flows by using a multicomponent lattice Boltzmann
method with a Shan-Chen pseudopotential implemented on GPUs. We compare our
results with the extension to the 2D case of the phenomenological theory for
immiscible 3D RT studied by Chertkov and collaborators ({\it Physical Review E
71, 055301, 2005}). Furthermore, we compared the growth of the mixing layer,
typical velocity, average density profiles and enstrophy with the equivalent
case but for miscible two-component fluid. Both in the miscible and immiscible
cases, the expected quadratic growth of the mixing layer and the linear growth
of the typical velocity are observed with close long-time asymptotic prefactors
but different initial transients. In the immiscible case, the enstrophy shows a
tendency to grow like $\propto t^{3/2}$, with the highest values of vorticity
concentrated close to the interface. In addition, we investigate the evolution
of the typical drop size and the behavior of the total length of the interface
in the emulsion-like state, showing the existence of a power law behavior
compatible with our phenomenological predictions. Our results can also be
considered as a first validation step to extend the application of lattice
Boltzmann tool to study the 3D immiscible case.
