Dense granular flows are ubiquitous in nature and industrial applications, and significant effort has gone into developing continuum-level constitutive equations for the steady-state rheology of dense granular materials. The most widely used rheology for dense granular flow is the local inertial rheology of MiDi (2004), which has had success in describing steady, dense, rapid flows down chutes or in silos. Recent work (Barker et al., 2015) has shown that the inertial rheology displays a linear instability against short wavelength perturbations – i.e., Hadamard instability – in particular, in the slow, quasi-static flow regime. It is expected that the inclusion of higher-order gradients into the rheology can restore linear stability, and indeed, Goddard and Lee (2017) have shown that higher-order velocity gradients can have a stabilizing effect. In our recent work, we have proposed a nonlocal rheology – called the nonlocal granular fluidity (NGF) model – which has been shown to quantitatively describe a wide variety of steady, dense flows. In this talk, we consider the linear stability of the NGF model in its steady-state form under planar shear flow. Our results show that the NGF model is linearly stable against short wavelength perturbations.
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