Immiscible Rayleigh-Taylor turbulence using mesoscopic lattice Boltzmann algorithms

We studied turbulence induced by the Rayleigh-Taylor (RT) instability for two-dimensional (2D) immiscible two-component flows by using a multicomponent lattice Boltzmann method with a Shan-Chen pseudopotential implemented on graphics processing units. We compare our results with the extension to the 2D case of the phenomenological theory for immiscible 3D RT turbulence studied by Chertkov and collaborators [Phys. Rev. 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. In both 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 proportional to t3/2, 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 emulsionlike state, showing the existence of a power-law behavior compatible with our phenomenological predictions. Our results can also be considered as a validation step to extend the application of the lattice Boltzmann tool to study the 3D immiscible case.