Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Kienle, J., Kowalik, Z., Murty, T.S.: Tsunamis generated by eruptions from Mount St. Augustine Volcano, Alaska. Science 236, 1442–1447 (1987)
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)
Baptista, A.M., Priest, G.R., Murty, T.S.: Field survey of the 1992 Nicaragua Tsunami. Marine Geodesy 16, 1692–1703 (1993)
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)
Myers, E.P., Baptista, A.M.: Inversion for Tides in the Eastern North Pacific Ocean. Advances Water Resources 24(5), 505–519 (2001)
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)
Kowalik, Z., Proshutinsky, T., Proshutinsky, A.: Tide-tsunami interactions. Science of Tsunami Hazards 24(5), 242–256 (2006)
Dao, M.H., Tkalich, P.: Tsunami propagation modelling - a sensitivity study. Natur. Hazards Earth System Sci. 7, 741–754 (2007)
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)
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)
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)
Lynett, P.J., Wu, T.-R., Liu, P.L.-F.: Modeling wave runup with depth-integrated equations. Coastal Eng. 46, 89–107 (2002)
Carrier, G.F., Greenspan, H.P.: Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4, 97–109 (1958)
Siden, G.L.D., Lynch, D.R.: Wave Equation Hydrodynamics on Deforming Elements. Int. J. Numer. Meth. Fluids 8, 1071–1093 (1988)
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)
Egbert, G.D., Erofeeva, S.Y.: Efficient inverse modeling of barotropic ocean tides. J. Atmos Oceanic Technol. 19(2), 183–204 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Androsov, A., Behrens, J., Danilov, S. (2011). Tsunami Modelling with Unstructured Grids. Interaction between Tides and Tsunami Waves. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds) Computational Science and High Performance Computing IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17770-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-17770-5_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17769-9
Online ISBN: 978-3-642-17770-5
eBook Packages: EngineeringEngineering (R0)