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We study here the spontaneous clustering of a submonolayer of grains underhorizontal circular shaking. The clustering of grains occurs when increasingthe oscillation amplitude beyond a threshold. The dense area travels in acircular fashion at the driving frequency, even exceeds the speed of driving.It turns out that the observed clustering is due to the formation of densitywave. The analysis of a phenomenological model shows that the instability ofthe uniform density profile arises by increasing the oscillation amplitude andcaptures the non-monotonic dependence of the transition amplitude of theclustering on the global density of the system. Here, the key ingredient isthat the velocity of individual grains increases with the local density. Theinterplay of dissipative particle-particle interaction and the frictionaldriving of the substrate results into this dependence, which is tested withdiscrete element method simulations.

Spontaneous formation of density waves in granular matter under swirling excitation