Continuum modeling of secondary vortex flow driven by dilatancy in sheared granular media

Shear-induced dilatancy – the tendency of slowly sheared dense granular media to undergo change in density – has been shown to couple strongly with the kinematics. In this study, we investigate its role in driving complex secondary flows, including persistent vortex structures. We employ a continuum framework using the non-local constitutive model of Dsouza and Nott (J. Fluid Mech., 2020) to analyse transient secondary flows in a plane shear configuration under the influence of gravity. Unlike other constitutive models that assume granular materials to be incompressible, the model of Dsouza and Nott incorporates dilatancy and has previously shown excellent agreement with discrete element method (DEM) simulations and experimental data for simple flows. Our current simulations capture the emergence and evolution of secondary vortices observed in DEM studies, providing direct evidence that shear dilatancy, coupled with gravity, can sustain such flows when the directions of velocity gradient and gravity are not collinear. This work provides critical mechanistic insight into the role of non-locality and dilatancy in driving kinematics in dense granular flows, thereby advancing our fundamental understanding of slow granular dynamics.