Immiscible Rayleigh-Taylor turbulence using mesoscopic lattice Boltzmann algorithms

TL;DR

This study uses a multicomponent lattice Boltzmann method on GPUs to analyze 2D immiscible Rayleigh-Taylor turbulence, comparing results with theoretical predictions and exploring interface dynamics and enstrophy growth.

Contribution

It extends lattice Boltzmann simulations to 2D immiscible RT turbulence and compares findings with phenomenological theories, providing validation for future 3D studies.

Findings

Quadratic growth of mixing layer observed

Linear growth of typical velocity confirmed

Enstrophy grows approximately as t^{3/2}

Abstract

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.