Hydrodynamic modes in a confined granular fluid

Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states thanks to energy injection mechanisms that take place throughout the system. These states can be stable even at high densities and inelasticities allowing for a detailed analysis of the hydrodynamic modes that govern the dynamics of granular fluids. Analyzing the decay of the time correlation functions it is shown that there is a crossover between a quasielastic regime in which energy evolves as a slow mode, to a inelastic regime, with energy slaved to the other conserved fields. The two regimes have well differentiated transport properties and, in the inelastic regime, the dynamics can be described by a reduced hydrodynamics with modified longitudinal viscosity and sound speed. The crossover between the two regimes takes place at a wavevector that is proportional to the inelasticity. A two dimensional granular model, with collisions that mimic the energy transfers that take place in a confined system is studied by means of microscopic simulations. The results show excellent agreement with the theoretical framework and allows the validation of hydrodynamic-like models.