Waves dynamics in a linearized mud-flow shallow model

The study of formation and evolution of waves in mud-flows is strongly motivated by their destructive power. The rheology of these flows, which involve massive solid transport, is often described using linear or non-linear viscoplastic models. The paper analyzes the wave dynamics of mud-flows, presenting the linearized response of the 1D uniform flow of a viscoplastic fluid with yield stress, i.e. Herschel & Bulkley fluid, to a pointwise impulsive forcing term. The solution in either linearly stable or unstable conditions is found, for both subcritical and supercritical flows, through the bilateral inverse Laplace transform. The analysis offers a unified description of the behaviour of different non-newtonian fluids, recovering as particular cases both the Bingham and the power-law models. The influence of the dimensionless governing numbers and of the rheological parameters on the shape and peak of waves is investigated.