Free surface from convective flow in a vibrated granular medium

Abstract Vertical vibration of a granular medium with greater acceleration than g creates a pair of convection rolls with opposite rotation propagating along its edges. For 2D monodisperse disks, the top free surface bends downward for inclined walls with angles with respect to the horizontal axis. It remains flat for , identical to rotational invariance of the hexagonal close packing, and bends upward for . Grain boundaries of alternating 5- and 7-fold disclinations emerge at the center of a container to separate two hexagonal lattices, on the left and right halves of a container, with different orientation. When the opening angle of inclined walls is equal to an integral multiple of , namely and , such grain boundaries disappear. For 2D bidisperse disks, the top free surface is still smooth but is less deformed from a flat profile. Hexagonal close packing exists only locally in small plaquettes without grain boundaries for all angles θ . In hydrodynamic description the monodisperse free surface is well described by a contour of the constant pressure calculated from the Navier-Stokes equation.