Simulation of tsunami waves generated by submarine landslides in the Black Sea

Abstract

Numerical technique for studying surface waves appearing under the motion of a submarine landslide is discussed. This technique is based on the application of the model of a quasi-deformable landslide and two shallow water models, namely, the classic (dispersion free) one and the completely nonlinear dispersive model of the second hydrodynamic approximation. Numerical simulation of surface waves generated by a large model landslide on the continental slope of the Black Sea near the Russian coast is performed. It is shown that the dispersion has a signi cant impact on the picture of propagation of tsunami waves on su ciently long paths.The water area of the Black Sea is speci c for its high seismic activity [37] and is exposed to potential risk of tsunami waves [43, 49] generated not only by strong earthquakes, but also by submarine landslides [45] that may be caused by even weak seismic events. Bottom sediments sometimes lose their strength and begin movement over an underwater slope even without the impact of any earthquake [1, 24, 38].Geophysical and hydrographic studies of the continental slope of the Black Sea show [10] that its large part is exposed to e ects of submarine landslides and hence the waves generated in this process should be taken into account in risk estimation in the densely populated Black Sea coast, as well as for submarine pipelines intended to oil and gas transportation. The authors of [38] explain the anomalous uctuations of the Black Sea level occurred at the Bulgarian coast on May 7, 2007 by just the landslide mechanism of surface waves generation.Under the lack of data on the parameters of bottom sediments, the only source of some quantitative information about the wave processes arising in the case of potential submarine landslides is a computational experiment. The results of numerical simulation of landslide processes can be used in the design of engineering structures on the shelf and the continental slope, and also in evaluation of tsunami risk in particular areas of the coast.In numerical experiments, a landslide is usually represented either as a rigid body moving over a at slope [8, 9, 18, 48], or as a certain volume of near bottom uid di ering from water by a greater density [5, 14], or as a motion of some elasto-plastic medium [15]. In some papers (see, e.g., [24]) the motion of landslide was not modelled, but the surface waves generated by a landslide in its initial stage of motion were determined from empirical formulas derived on the base of numerous numerical and eld studies [17]. The free surface obtained by empirical formulas was taken as an initial condition for calculation of surface waves under the assumption that the uid under the initial wave was in its rest state. However, we have to note that the empirical formulas used in this case are valid only for the model of rigid landslide motion over a at slope. The numerical experiments [4] have shown that the motion of a landslide over an uneven bottom results in a quite another picture of generated surface waves. The...

New Algorithm for Numerical Simulation of Surface Waves Within the Framework of the Full Nonlinear Dispersive Model

“…Thus, the equations of the weakly nonlinear dispersion model obtained in [7] and the classical (nondispersive) shallow water model on a sphere have the same form as the equations of the FNLD-model on a sphere. The differences appear in the expression for the kinetic energy and in the calculations of the pressure terms (6). We provide the single form of the equations of the entire hierarchical chain of long-wave models in spherical and planar geometries [3], that made it possible to construct the uniform numerical algorithm for them.…”

“…The similar algorithm can be applied also to the solution of the FNLD-equations in plane geometry [6].…”

“…The second task is to solve the system of hyperbolic type consisting of the equations of continuity and motion in the dispersion-free shallow water model. The decomposition of the original system on two subproblems allows us to solve numerically the NLD-equations using the well known finite difference predictor-corrector type scheme for classical shallow water model modified so that the pressure is calculated additionally at each time step [6]. The corrected stability conditions and new knowledge on the dispersion properties of the modified predictor-corrector scheme are obtained.…”

A two-layer shallow flow model with two axes of integration, well-balanced discretization and application to submarine avalanches

“…On one hand, to correctly capture the generated wave and its latter propagation, it is essential to consider dispersive effects in the fluid model as it has been widely observed (e.g. [38,36,2,13,25]). On the other hand, for the granular mass the difficulty mainly lies in defining the appropriate rheology including pore pressure effects [16,15,7].…”

“…Other attempts consider a Boussinesq or a nonhydrostatic shallow water model to include dispersive effects, following the same idea and results (see e.g. [3,13,25,37]).…”