Streamline jumping: A mixing mechanism

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.