Model for pattern formation of granular matter on vibratory conveyors

Recently, Götzendorfer et al. [Götzendorfer A, Kruelle CA, Rouijaa M. Granular surface waves in a vibratory conveyor. In: Garcia-Rojo R, Herrmann HJ, McNamara S, editors. Powders and grains, Stuttgart; 2005. p. 1185] have observed subharmonic propagating surface wave patterns if granular material on a trough is subject to a combination of vertical and horizontal periodic driving. The observed structures are non-stationary in space, drift with a constant mean velocity along the trough and oscillate subharmonically with half the driving frequency. We present a phenomenological model for the surface evolution of the granular material that qualitatively reproduces and explains important aspects of the experimentally observed patterns.