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 a cceleration 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 amplitud e in time at a constant oscillation frequency, two different routes to the stripe pattern are observed depending on the ramping time. For small rampin g time, spiral or target patterns an formed as an intermediate state before the stripe pattern. For large ramping time, however, stripe patterns are f ormed without the transient spiral or target pattern. Furthermore, we study the short time dynamics of spiral and target patterns. (C) 2000 Elsevier S cience B.V. All rights resented.