We study a singular limit of tumbled granular flows in quasi-two- dimensional rotating drums, demonstrating that the limiting dynamical system, as the shear layer vanishes, belongs to a class of discrete discontinuous mappings called piecewise isometries. In doing so, we identify a mechanism of mixing, in the absence of the usual streamline crossing mediated by the flowing layer. By considering the exceptional case of a 50% full square tumbler, this mechanism (streamline jumping) is related to the horizontal motion of the free surface of the flow in non-half-full tumblers. The limiting dynamics are quite complex, if not (technically) chaotic.
|Original language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Apr 12 2010|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics