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Hydrodynamics of Tsunami Waves


Mathematical Modeling of Hydrodynamics Guiding the Evolution of Catastrophic Tsunami Waves

Tech Area / Field

  • PHY-NGD/Fluid Mechanics and Gas Dynamics/Physics

3 Approved without Funding

Registration date

Leading Institute
VNIITF, Russia, Chelyabinsk reg., Snezhinsk

Supporting institutes

  • Institute of Computational Technologies, Russia, Novosibirsk reg., Novosibirsk


  • University of Washington, USA, WA, Seattle

Project summary

The objective of the project is to simulate mathematically tsunami waves (including those caused by space body impact on the Earth), tidal flows, and other wave phenomena at coast, as well as propagation of contamination in seas and oceans. To solve these problems the project proposes to develop special analytical and mathematical models of wave hydrodynamics.

Tsunami is classified as a unique phenomenon because of vast variety of causes resulting in these waves, propagation at long distances in open ocean, and catastrophic effects of their interaction with objects on coast. Key thrust areas are defined by the facts that there are no highly reliable means for tsunami prediction and protection of settlements and industrial facilities against the waves. Major effort is focused on determining the relative effectiveness of different mechanisms governing tsunami generation and adequate description of wave effects on underwater and coast structures.

Tsunami research projects were initiated by severe consequences of some particular events (Kamchatka, 1952; Japan, 1983, 1993; Nicaragua, 1992; and others) resulted in deaths of people and destruction of commercial facilities.

During the last years the probability has significantly grown that tsunami would become a global disaster because of construction at coat of great energetic facilities including atomic power plants (APP), commercial enterprises using new high-risk technologies, military and dual-use facilities, new settlements.

Analysis of recent publications allows concluding that mathematical modeling is used more and more widely in the study of different aspects of tsunami. And activities of Russian scientists including those performed by the project participants are often of the pioneer character. In addition, if earlier the community of the Pacific countries contributed mostly, then now scientists of Mediterranean and Caribbean countries, Western Europe joined them.

The development of a hybrid mathematical model covering the entire process of tsunami evolution could be a direction capable to provide a breakthrough in the understanding of tsunami physics.

In the project implementation a great part of activities will be devoted to mathematical modeling of tsunamis caused by space body impact on the Earth. These tsunamis we will call impact tsunamis. The project implies the development of integrated models for the above phenomena and a system of computational codes for their realization. In the ocean wave energy dissipation is much lower than in the seismic one generated by space body impact on dry land. Therefore, it is of great interest to model impact on ocean of the space bodies able to generate a tsunami wave which run-up on coast may lead to severe consequences. To describe generation of tsunami resulted from a space body impact on the Earth, we propose to use a 2-D model of matter motion allowing for some states of asteroid and water: solid, liquid, and water vapour. Earlier VNIITF specialists simulated the impact of a 2-km-diam stone asteroid on ocean at velocity of 22 km/s. The development of an overall model describing generation and propagation of impact tsunamis is complicated, at first, by the fact that typical times of the processes are incomparable, specifically, propagation of the wave is slower than generation. And second, tsunami generation is mainly a vertical process.

That is why in the study of impact tsunamis by mathematical modeling the entire process is pided into three steps:

1. wave generation nearby place of impact;
2. wave propagation in open ocean from place of impact to coast;
3. interaction between tsunami and ocean shelf, and tsunami run-up on coast.

Each of the steps exploits different mathematical models and methods. For impact tsunamis, unlike seismic ones, essentially non-linear processes are typical for all the three steps.

Authors of the project headed by academician Y. I. Shokin (Institute for Computational Technologies, Novosibirsk) investigated tsunamis within the framework of national and international programs including those under contracts with UNESCO Intergovernmental Oceanographic Commission, programs "Ocean", "Wave".

Results of the investigation into tsunami kinematics performed by the project authors allowed to develop mathematical models, computational algorithms and code packages for computing the time of tsunami propagation, compute and transmit to international community Atlas of maps used in practice by the Pacific Tsunami Warning System (PTWS). The algorithms and codes developed by the project authors constitute the basis of an automated tsunami service of Sakhalin Tsunami Center.

Fundamental and applied studies performed by the authors in the area of tsunami wave field dynamics within the scope of approximate hydrodynamic models allowed implementation of computational experiments on tsunami zoning for some Kurily, Kamchatka and Primorsky regions, research of wave characteristics of some Far East bays, formulation of a concept for Local Tsunami Warning System and estimation of its parameters.

Implementation of the project will provide:

1. gain new fundamental knowledge on tsunami hydrodynamics and validate approaches to the design of hybrid wave hydrodynamics models;
2. develop, investigate and improve physico-mathematical and computational models to study abnormal wave phenomenon - tsunami in ocean and sea and its run-up on coast;
3. carry out computational experiments to test models and gain our knowledge on how tsunami waves transform in the process of their propagation from origin to coast;
4. solve particular tsunami problems to improve the work of warning services and enhance efficiency of safety measures for public and commercial objects, both operating and being designed.

The project results can be most effectively used in fundamental research, development of expertise systems, automated tsunami warning systems of local and global scale, and automated systems for facility design including hydrotechnical and hydroenergetic ones.

Mathematical results and modeling algorithms can also be used in other spheres of ocean geophysics described by equations of relative structure.

Project results are proposed for publishing and presenting at conferences.

Potential Role of Foreign Collaborators

The areas for potential collaboration with foreign scientists are:

- study hydrodynamic aspects of tsunami waves and search for methods which could be used for developing hybrid models of wave hydrodynamics;
- develop, study and improve physical, mathematical and computational models;
- perform computational experiments to test the models;
- exchange scientific information on the problem.

The proposal was formally supported by Prof. Harry H.-J.Yeh (Department of Civil Engineering, University of Washington) and Prof. Mohammed I. El-Sabh (President of Natural Hazards Society, Centre Oceanographique de Rimousqui).


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