The Translatory Wave Model for Landslides

Abstract

The Saint-Venant equations are usually the basis of numerical models for landslide flows. They are nonstationary and nonlinear. The theory for translatory waves in a prismatic channel and a funneling channel can be used for landslides using the assumption of either turbulent or laminar flow in the slide. The mathematics of translatory waves traveling over dry land or superimposed on another flow are developed. This results in a new slope factor controlling the flow velocity, together with the Chezy coefficient used in previous applications of the translatory wave theory. Flow times for the slide to reach a given destination, slide depth, and velocity can be calculated using the initial magnitude of the flow in the slide. The instabilities of the wave tail are discussed. Three case studies are presented: a submarine slide that started the Tohoku tsunami in Japan, the Morsárjökull rock avalanche in SE Iceland, and the Móafellshyrna slide in central N Iceland.