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.