Low-frequency oscillations in a granular column

A vertically vibrated granular bed exhibits many phenomena, such as convection and Faraday-like surface waves. However, when the lateral dimensions of the bed are confined such that a quasi-one-dimensional geometry is formed, the only phenomena that remain are the bouncing bed and granular Leidenfrost states, where in the latter a dense cluster is floating on top of a dilute, gaseous layer of particles. This setup thus permits the observation of the granular Leidenfrost state for a wide range of energy injection parameters and more specifically allows for a thorough characterization of the low-frequency oscillation (LFO) that is present in this state. We experimentally and numerically determine the LFO frequency from the power spectral density of the center-of-mass signal of the grains, varying many parameters of the system. We find that the LFO frequency (i) is inversely proportional to the fast inertial timescale and (ii) decorrelates with a typical decay time proportional to the slow dissipative timescale in the system. Using a Langevin approach, we show that the latter is consistent with the view that the LFO is driven by the inherent noise that is present in the granular Leidenfrost state with a low number of particles.