Roll waves on a shallow layer of debris modelled as a dilatant fluid

A shallow layer of dilatant fluid (tau = alpha(partial derivativeu/partial derivativey)(n) with n = 2) in laminar motion is considered to study finite amplitude roll waves down a slope, simplified by Karman's momentum integral approach. The existence of a condition of a periodic discontinuous solution is derived, neglecting the finite length of the shock, the curvature of trajectories and surface tension effects. Energy dissipation in the body of the stream and in the discontinuity are analyzed and discussed.