title: Nonlinear dynamics of an interface between shear bands.
abstract: We study numerically the nonlinear dynamics of a shear banding interface in two-dimensional planar shear flow, within the nonlocal Johnson-Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for a sufficiently small ratio of the interfacial width l to cell length L(x). The instability saturates in finite amplitude interfacial fluctuations. For decreasing l/L(x) these undergo a nonequilibrium transition from simple traveling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.
authors.affiliation: School of Mathematics, University of Manchester, Booth Street East, Manchester M13 9EP, United Kingdom.
authors.forename: S M
authors.initials: SM
authors.lastname: Fielding
authors.forename: P D
authors.initials: PD
authors.lastname: Olmsted