Linear stability analysis of a vertically oscillated granular layer

We present a linear stability analysis of an oscillating granular layer, tr eating it as an isothermal incompressible fluid with zero surface tension, which undergoes periodic collisions with and separations from an oscillatin g plate. Because the viscosity of the granular layer is unknown, we use the experimental value of the critical acceleration for the transition from a flat to patterned layer as input for the theory, and use the analysis to ca lculate the granular viscosity and the wavelength of the most unstable mode . The wavelength compares favorably with the experimental pattern wavelengt h. Further, we find that the wavelengths are controlled by the viscosity of the granular layer. [S1063-651X(99)11112-7].