Simulation of landslide tsunami in the Russian Far East based on 3D Navier–Stokes equations

The paper presents the results of modeling landslide tsunamis near the Kamchatka Peninsula in part of the Pacific Ocean. The paper describes the model based on the three-dimensional (3D) Navier–Stokes equations. The model is supplemented with the rheological relation based on the Bingham model to account for the rheology of landslide masses. The paper proposes a modification of the classical Bingham model with a non-zero yield strength, which implies that the medium is at rest or it moves as a solid (body) in the absence of a tension in the medium exceeding this limit. The application of the classical model is impossible within the framework of the used equation system. The paper proposes its modification, which consists in the possibility of changing the yield strength to zero value by adding a linear function to a given shear rate, until which the fluid flows as Newtonian and after reaching it, the flow conditions of the substance obeys Bingham’s law. An original algorithm is used to simulate waves in real water areas, it implements open boundary conditions. The algorithm is based on the use of a damping boundary layer that absorbs the kinetic energy of the incoming wave, which is taken into account using an additional source in the angular momentum equation. A method is proposed for determining the resistance coefficient, the value of which determines the intensity of absorption of the kinetic energy of the wave. The used mathematical model makes it possible to model in a single way the occurrence, propagation and rolling on shore of tsunami waves of landslide origin. The results of modeling of an underwater landslide in the waters of the Kamchatka Bay near the city of Ust-Kamchatsk are presented, taking into account bathymetric date. The paper includes the analysis of dependence of wave heights on the volume of landslide in the zone of its initial position and at several points of the coast, as well as sections of the coast (in particular on Bering Island), which may be most severely affected by the occurrence of landslide tsunamis in this water area.