Free surface instability of non-Newtonian laminar flows

The mechanism of free surface instability of non-Newtonian laminar flows is studied theoretically and experimentally in the paper. Development of surface waves and roll waves of non-Newtonian flow has been reported in many cases, such as the river clogging in the hyperconcentrated flows, intermittent viscous debris flows and fluctuation in mudflows. Theoretical analysis from the equation of motion incorporating the non-Newtonian nature of the fluid demonstrated that the free surface instability is essentially caused by the yield stress. Two dimensionless numbers, S-y and S-vis, representing the effects of yield stress and viscosity are calculated and compared for various flows. It is concluded that the free surface is unstable and roll waves may develop even at constant incoming flow rate if S-y is much larger than S-vis and is stable if S-y is smaller than S-vis. Experiments were conducted to study the phenomena of river clogging, development of a perturbation wave in non-Newtonian laminar flow, and development of roll waves. The results agree well with the theoretical formula showing exponential law of growth of wave height. The growth rate of wave height depends essentially on the parameter S-y. if S-y is large enough a series of roll waves develop from stable flow and the larger is the parameter, the higher the waves.