Revista Recursos Hdricos
Volume 33, Nmero 2, novembro 2012

DOI: 10.5894/rh33n2-2
O texto deste artigo foi submetido para reviso e possvel publicao em outubro de 2012, tendo sido aceite pela Comisso de Editores Cientficos Associados em outubro de 2012. Este artigo parte integrante da Revista Recursos Hdricos, Vol. 33, N 2, 25-35, novembro de 2012.

Simulating the 1755 tsunami propagation in present-day Lisbon with a shallow-water model

Simulao da propagao do tsunami de 1755 na atual frente ribeirinha de Lisboa com equaes do tipo Saint-Venant

D. Conde ¹, R. Canelas ², J. Murillo ³, R.M.L. Ferreira ⁴

---

1 - CEHIDRO /// Instituto Superior Tcnico - UTL
2 - CEHIDRO /// Instituto Superior Tcnico - UTL
3 - University of Zarazoza /// Fluid Mechanics C.P.S.
4 - CEHIDRO /// Instituto Superior Tcnico - UTL

---

ABSTRACT: A recent revision of the catalogue of tsunamis in Portugal has shown that Tagus estuary has been affected by catastrophic tsunamis numerous times over the past two millennia. This justifies the modelling efforts aimed at quantifying potential inundation areas for present-day altimetry and bathymetry of Tagus estuary. The purpose of this work is to present a 2DH mathematical model applicable to discontinuous shallow flows over complex geometries such as tsunami propagation overland. The conceptual model and the discretization scheme are presented and validation tests are described. The propagation of a tsunami with the magnitude of that of 1755 is simulated for the bathymetric and altimetry conditions of present day Tagus estuary. The study shows that some locations of Tagus estuary are vulnerable to tsunami impacts, as they may register 1 to 2m flow depths and velocities of 5ms–1.

Keywords: mathematical modelling, tsunami, Tagus estuary.

RESUMO: Uma reviso recente do histrico de tsunamis em Portugal mostrou que o esturio do Tejo foi afetado por vrios tsunamis catastrficos nos dois milnios mais recentes. Tal facto justifica os esforos de modelao com o objetivo de quantificar reas de potencial inundao no esturio do Tejo, considerando as suas condies altimtricas e batimtricas atuais. O propsito deste trabalho apresentar um modelo matemtico 2DH aplicvel a escoamentos descontnuos em guas pouco profundas com geometrias de fundo complexas, como o caso da propagao em terra de um tsunami. Apresenta-se neste artigo o modelo conceptual e o esquema de discretizao, bem como uma descrio dos testes de validao efetuados. Foi efetuada a simulao de um tsunami com a mesma magnitude do que destruiu Lisboa em 1755, considerando no entanto as condies de altimetria e batimetria do presente. Este estudo mostra que alguns locais do esturio do Tejo esto vulnerveis ao impacto de um tsunami de tal proporo, com alturas de escoamento de 1 a 2m e velocidades da ordem de 5m/s.

Keywords: modelao matemtica, tsunami, esturio do Tejo.

 

Alcrudo, F. & Benkhaldoun, F. (2001). Exact solutions to the Riemann problem of the shallow water equations with a bottom step. Computers and Fluids, 30, 643–671.

Antunes do Carmo (2000). Tsunamis: gerao e riscos. Territorium, 7: 15-24.

Baptista M.A.; Miranda, J.M.; Omira, R.; Antunes, C. (2011). Potential inundation of Lisbon downtown by a 1755-like tsunami. Natural Hazards and Earth System Science. 11, 3319-3326. doi:10.5194/nhess-11-3319-2011.

Baptista, M.A. & Miranda J.M. (2009). Revision of the Portuguese catalog of tsunamis. Natural hazards and earth system sciences, 9 (1): 25-42.

Baptista, M. A.; Soares, P. M.. ; Miranda, J. M. & Luis, J. F. (2006). Tsunami propagation along Tagus estuary (Lisbon, Portugal). Preliminary results, Science of Tsunami Hazards, 24(5), 329-328

Conde, D. (2012). A tsunami in Lisbon. Where to run?. MSc dissertation, Instituto Superior Tcnico, TU Lisbon.

Ferreira, R. M. L. (2005). River Morphodynamics and Sediment Transport. Conceptual Model and Solutions. Ph.D. thesis, Instituto Superior Tcnico - Universidade Tcnica de Lisboa, Lisboa.

Ferreira, R. M., Franca, M. J., Leal, J. G. & Cardoso, A. H. (2009). Mathematical modelling of shallow flows: Closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics. Canadian Journal of Civil Engineering, 36, 1604–1621.

Kanoglu, U. & Synolakis, C.E. (1998). Long wave runup on piecewise linear topographies, Journal of Fluid Mechanics, 374, 1-28.

Leveque, R. (2002). Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.

Liu, P. L.-F.; Wu, T.-R.; Raichlen, F.; Synolakis, C.E., & Borrero, J.C. (2005). Runup and rundown generated by three-dimensional sliding masses. J. Fluid Mech., vol. 536, pp. 107–144.

Luis, J.F. (2007). Mirone: A multi-purpose tool for exploring grid data. Computers & Geosciences, 33, 31-41.

Murillo, J. & Garcia-Navarro, P. (2010). Weak solutions for partial differential equations with source terms: application to the shallow water equations. J. Comp. Physics 229(11), 4327–4368.

Murillo, J.; Garca-Navarro, P., Brufau, P. & Burguete, J. (2010). 2d modelling of erosion/deposition processes with suspended load using. Journal of Hydraulic Research, 46(1), 99–112.

Pope, S. B. (2000). Turbulent Flows. Cambridge University Press.
Roe, P. (1981). Approximate Riemann solvers, parameter vectors and difference schemes. J. Comp. Physics 43, 357–372.

Stoker, J.J. (1957). Water waves. The mathematical with applications. Willey Classic Library, (reprint of 1957 edition).

Toro, E. (2001). Shock-Capturing Methods for Free Surface Shallow Flows. Wiley, New York.

Vzquez-Cendn, M. (1999). Improved treatment of source terms in upwind schemes for the shallow water equations with irregular geometry. J. Comp. Physics, 148,497.

Viana-Baptista, M.A.; Miranda, J.M.; Omira, R.; Antunes, C. (2011). Potential inundation of Lisbon downtown by a 1755-like tsunami. Natural Hazards and Earth System Science. 11, 3319-3326. doi:10.5194/nhess-11-3319-2011.

Whitham, G. B. (1974). Linear and Non-Linear Waves. John Willey and Sons, Willey-Interscience. ISBN 0-471-94090-9.

Yeh, H.H. (1991). Tsunami bore runup. Natural Hazards 4(2-3), 209–220. DOI: 10.1007/BF00162788.

.