Evolution of disturbances on shallow layers of non-Newtonian fluids

We study the stability of shallow layers of non-Newtonian fluids considered in the frame of the two-parametric power-law model of Ostwald–de Waele, taking into account the surface tension effect, which gives rise to decreasing domains of unstable wave modes. For the weak nonlinearities two equations, valid in the limits of small and large Ostwald–de Waele numbers, are derived. They are analytically studied and the evolution of some finite disturbance is solved numerically by making use of the upwind explicit finite-difference scheme.