Competition between merging and bifurcation in the generalized Rayleigh-Taylor instability

The nonlinear evolution of bubble and spike fronts growing through the generalized Rayleigh-Taylor instability are studied by numerical simulations and by solving an extension of Alon's [Phys. Rev. E 48, 1008 (1993)2470-004510.1103/PhysRevE.48.1008] statistical model based on the asymptotic velocity of a single-mode bubble and the merging bubble process. In this work, the generalized Rayleigh-Taylor instability includes a frictional force due to collision with a secondary fluid. Depending on its strength the behavior during the nonlinear stage leads to two different regimes: the first is the classical inertial case where the bubble front is known to grow as h∝t^{2} and evolves towards large structures, and the second is the collisional case where the front grows as h∝t and maintains structures of relatively constant size. In this new regime, the importance of adding the bifurcation process, the opposite process of merging, is highlighted.