Development of roll waves in power-law fluids with non-uniform initial conditions.

The paper investigates the spatial evolution of a disturbance in an open-channel flow of a power-law fluid at non-uniform accelerated and decelerated initial profiles, up to the occurrence of roll-waves in mild and steep slope channels. Both theoretical and numerical analyses are applied to the depth averaged continuity and momentum conservation equations, deduced from the von Kármán’s integral method. For the theoretical investigation, the non-linear near-front expansion technique has been applied. Then, the full non-linear problem in its conservative formulation has been numerically solved. Independently on the rheology of the flowing medium, non-uniform initial conditions strongly influence the perturbation celerity, the disturbance evolution and the roll-waves development. For mild slope channels, an initially decelerated profile of shear-thinning fluids has a stabilizing effect, while the opposite is found for accelerated profiles. For shear-thickening fluids, only the stabilizing effect caused by a decelerated profile is observed. In steep slope channels, independently of the fluid rheology, decelerated initial conditions promote the roll-wave occurrence, while accelerated ones inhibit the perturbation growth. Although experimental verifications are needed, present results have to be properly accounted in defining roll-waves prediction methods and in assigning appropriate boundary conditions to enhance or to reduce their formation.