
This paper theoretically studies, using depth-averaged equations with Wyart-Cates rheology, the instability mechanism at the origin of the surface waves that develop when a shear-thickening suspension flows down an incline (Darbois Texier Comm Phys 2020). While at low concentration we recover the familiar Kapitza (roll-wave) instability of inertial origin, new instability branches appear above the discontinuous shear-thickening transition, due to the negative slope of the suspension flow rule. Analysis of the role of inertia in this regime shows that the waves experimentally observed arise from a purely non-inertial mechanism, coined `Oobleck waves’, which results from the coupling between the free-surface deformation and the negatively-sloped rheology. This result might be relevant to free-surface flows of other complex fluids displaying velocity-weakening rheology (Download the paper here).