Dynamics of spiral patterns in vertically vibrated thin granular layer system

Formation dynamics of transient spiral and target patterns are studied for vertically oscillated thin granular layer systems. When the dimensionless acceleration amplitude is changed from 2.5 of a flat pattern state to 3.0 of a steady stripe pattern state by linearly ramping the oscillation amplitude in time at a constant oscillation frequency, two different routes to the stripe pattern are observed depending on the ramping time. For small ramping time, spiral or target patterns are formed as an intermediate state before the stripe pattern. For large ramping time, however, stripe patterns are formed without the transient spiral or target pattern. Furthermore, we study the short time dynamics of spiral and target patterns.