Римановы волны в динамике оползней над плоским откосом
Nonlinear dynamics of the landslides moved from the mountain slope is studied in the framework of co-called “fluid” models of ideal and viscous layers of weak thickness (shallow-water approximation). Friction is described by the Coulomb (“dry”) law. In general, the basic equations are hyperbolic equations allowing using the classic approaches of the modern wave theory. Rigorous analytical solutions – Riemann waves described the evolution of the nonlinear perturbations in opposite directions from the landslide centre are obtained within both models. The particle velocity in the ideal flow is determined via the landslide height, meanwhile in the viscous flow the particle velocity is determined by the integral expression from the landslide height. The speed of front deformation is different in ideal and viscous fluids; it is higher for a flow with uniform vertical distribution of velocity. At the same time, the speed of landslide top deformation is almost the same in both models.