Tsunami Modelling with Unstructured Grids. Interaction between Tides and Tsunami Waves

  • Alexey Androsov
  • Jörn Behrens
  • Sergey Danilov
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 115)


After the destructive event of December 26, 2004, many attempts have been made to accurately simulate the generation and propagation of tsunami waves in the Indian Ocean. In support of the Tsunami Early Warning System for the Indian Ocean, a very high-resolution finite element model (TsunAWI) has been developed for simulations of the wave propagation. It offers geometrical flexibility by working on unstructured triangular grids and is based on finite-element \(P_1^{NC}-P_1\) discretization. The paper presents a brief description of the model, with a focus on its verification and validation. The key issue in modelling the tsunami is wetting and drying. The original algorithm to solve this problem is discussed. Full and reduced formulation of the momentum advection for \(P_1^{NC}-P_1\) elements and parameterization of horizontal diffusion are presented. Using the well-known Okushiri test case, the influence of nonlinearity on the wave propagation is demonstrated. Numerical experiments simulating the Indian Ocean Tsunami on December 26, 2004 have been conducted. For the whole Indian Ocean, the comparison of simulation results with observational (coast gauge) data is carried out.

A typical tsunami wave is much shorter than tidal waves which are usually neglected in tsunami modelling. However, in coastal areas with strong tidal activity, dynamic nonlinear interaction of tidal and tsunami waves can amplify the magnitude of inundation. To study this effect, water level change due to tide is included in the general scheme.


Indian Ocean Tsunami Wave Tidal Wave Unstructured Grid Indian Ocean Tsunami 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kienle, J., Kowalik, Z., Murty, T.S.: Tsunamis generated by eruptions from Mount St. Augustine Volcano, Alaska. Science 236, 1442–1447 (1987)CrossRefGoogle Scholar
  2. 2.
    Greenberg, D.A., Murty, T.S., Ruffman, A.: A numerical model for the Halifax Harbor tsunami due to the 1917 explosion. Marine Geodesy 16, 153–167 (1987)CrossRefGoogle Scholar
  3. 3.
    Baptista, A.M., Priest, G.R., Murty, T.S.: Field survey of the 1992 Nicaragua Tsunami. Marine Geodesy 16, 1692–1703 (1993)CrossRefGoogle Scholar
  4. 4.
    Hanert, E., Le Roux, D.Y., Legat, V., Delesnijder, E.: An efficient Eulerian finite element method for the shallow water equations. Ocean Model 10, 115–136 (2005)CrossRefGoogle Scholar
  5. 5.
    Myers, E.P., Baptista, A.M.: Inversion for Tides in the Eastern North Pacific Ocean. Advances Water Resources 24(5), 505–519 (2001)CrossRefGoogle Scholar
  6. 6.
    Weisz, R., Winter, C.: Tsunami, tides and run-up: a numerical study. In: Papadopoulos, G.A., Satake, K. (eds.) Proceedings of the International Tsunami Symposium, Chania, Greece, June 27-29, p. 322 (2005)Google Scholar
  7. 7.
    Kowalik, Z., Proshutinsky, T., Proshutinsky, A.: Tide-tsunami interactions. Science of Tsunami Hazards 24(5), 242–256 (2006)Google Scholar
  8. 8.
    Dao, M.H., Tkalich, P.: Tsunami propagation modelling - a sensitivity study. Natur. Hazards Earth System Sci. 7, 741–754 (2007)CrossRefGoogle Scholar
  9. 9.
    Mofjeld, H.O., Gonzalez, F.I., Titov, V.V., Venturato, A.J., Newman, J.C.: Effects of Tides on Maximum Tsunami Wave Heights: Probability Distributions. J. Atmos. Oceanic Technol. 24(1), 117–123 (2007)CrossRefGoogle Scholar
  10. 10.
    Oliger, J., Sundstrom, A.: Theoretical and practical aspects of some initial boundary value problems in fluid dynamics. SIAM J. Appl. Math. 35, 419–446 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Androsov, A.A., Klevanny, K.A., Salusti, E.S., Voltzinger, N.E.: Open boundary conditions for horizontal 2-D curvilinear-grid long-wave dynamics of a strait. Adv. Water Resour. 18, 267–276 (1995)CrossRefGoogle Scholar
  12. 12.
    Lynett, P.J., Wu, T.-R., Liu, P.L.-F.: Modeling wave runup with depth-integrated equations. Coastal Eng. 46, 89–107 (2002)CrossRefGoogle Scholar
  13. 13.
    Carrier, G.F., Greenspan, H.P.: Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4, 97–109 (1958)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Siden, G.L.D., Lynch, D.R.: Wave Equation Hydrodynamics on Deforming Elements. Int. J. Numer. Meth. Fluids 8, 1071–1093 (1988)zbMATHCrossRefGoogle Scholar
  15. 15.
    Harig, S., Chaeroni, C., Pranowo, W.S., Behrens, J.: Tsunami simulations on several scales: Comparison of approaches with unstructured meshes and nested grids. Ocean Dynamics 58, 429–440 (2008)CrossRefGoogle Scholar
  16. 16.
    Egbert, G.D., Erofeeva, S.Y.: Efficient inverse modeling of barotropic ocean tides. J. Atmos Oceanic Technol. 19(2), 183–204 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Alexey Androsov
    • 1
  • Jörn Behrens
    • 2
  • Sergey Danilov
    • 1
  1. 1.Alfred Wegener Institute for Polar and Marine ResearchBremerhavenGermany
  2. 2.University of HamburgHamburgGermany

Personalised recommendations