Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-26T12:20:12.168Z Has data issue: false hasContentIssue false
  • English
  • Français

Landslide tsunamis propagating around a conical island

Published online by Cambridge University Press:  18 March 2010

E. RENZI  and
P. SAMMARCO
E. RENZI
Affiliation:
Dipartimento di Ingegneria Civile, Università degli Studi di Roma Tor Vergata, Via del Politecnico 1, 00133 Roma, Italy
P. SAMMARCO*
Affiliation:
Dipartimento di Ingegneria Civile, Università degli Studi di Roma Tor Vergata, Via del Politecnico 1, 00133 Roma, Italy
*
†Email address for correspondence: sammarco@ing.uniroma2.it
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical forced two-horizontal-dimension model is derived to investigate landslide tsunamis propagating around a conical island lying on a flat continental platform. Separation of variables and Laplace transform are used to obtain the free-surface elevation in the whole domain and the runup at the shoreline in terms of confluent Heun functions. The main properties of these functions and their asymptotic behaviour for large parameters are investigated. Expression of the transient leading wave travelling offshore is also derived. The distinguishing physical features of landslide tsunamis propagating in a round geometry are then pointed out and compared with those of landslide tsunamis propagating along a straight coast. Analytical results satisfactorily agree with available experimental data.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 650 , 10 May 2010 , pp. 251 - 285
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions, Applied Mathematics Series, vol. 55. National Bureau of Standards.Google Scholar
Bardet, J.-P., Synolakis, C. E., Davies, H. L., Imamura, F. & Okal, E. A. 2003 Landslide tsunamis: recent findings and research directions. Pure Appl. Geophys. 160, 1793–1809.CrossRefGoogle Scholar
Bender, C. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientist and Engineers. McGraw-Hill.Google Scholar
Bruins, H. J., MacGillivray, J. A., Synolakis, C. E., Benjamini, C., Keller, J., Kisch, H. J., Klgel, A. & van der Plicht, J. 2008 Geoarchaeological tsunami deposits at Palaikastro (Crete) and the Late Minoan IA eruption of Santorini. J. Archeological Sci. 35 (1), 191–212.CrossRefGoogle Scholar
Di Risio, M., Bellotti, G., Panizzo, A. & De Girolamo, P. 2009 a Three-dimensional experiments on landslide generated waves at a sloping coast. Coast. Engng 56 (5–6), 659–671.CrossRefGoogle Scholar
Di Risio, M., De Girolamo, P., Bellotti, G., Panizzo, A., Aristodemo, F., Molfetta, M. & Petrillo, A. F. 2009 b Landslide-generated tsunamis runup at the coast of a conical island: new physical model experiments. J. Geophys. Res. 114 (C01009).Google Scholar
Fujima, K., Yuliadi, D., Goto, C., Hayashi, K. & Shigemura, T. 1995 Characteristics of long waves trapped by conical island. Coast. Engng Japan 38 (2), 111–132.CrossRefGoogle Scholar
Guza, R. T. & Davis, R. E. 1974 Excitation of edge waves by waves incident on a beach. J Geophys. Res. 79, 1285–1291.CrossRefGoogle Scholar
Heun, K. 1899 Zur Theorie der Riemann'schen Functionen zweiter Ordnung mit vier Verzweigungspunkten. Mathematische Annalen 33, 161–179.CrossRefGoogle Scholar
Kanoglu, U. & Synolakis, C. E. 1998 Long wave runup on piecewise linear topographies. J. Fluid Mech. 374, 1–28.CrossRefGoogle Scholar
Lautenbacher, C. C. 1970 Gravity wave refraction by islands. J. Fluid Mech. 41 (3), 655–672.CrossRefGoogle Scholar
Liu, P. L.-F., Cho, Y.-S., Briggs, M. J., Kanoglu, U. & Synolakis, C. E. 1995 Runup of solitary waves on a circular island. J. Fluid Mech. 302, 259–285.CrossRefGoogle Scholar
Liu, P. L.-F., Lynett, P. & Synolakis, C. E. 2003 Analytical solutions for forced long waves on a sloping beach. J. Fluid Mech. 478, 101–109.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1967 On the trapping of wave energy round islands. J. Fluid Mech. 29 (4), 781–821.CrossRefGoogle Scholar
Lynett, P. & Liu, P. F. 2005 A numerical study of the runup generated by three-dimensional landslides. J. Geophys. Res. 110 (C003006).Google Scholar
Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005 Theory and Applications of Ocean Surface Waves. World Scientific.Google Scholar
Meyer, R. E. 1971 Resonance of unbounded water bodies. In Mathematical Problems in the Geophisical Sciences (ed. Reid, W. H.), Lectures in Applied Mathematics, vol. 13. American Mathematical Society.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1986 Numerical Recipes in Fortran 77. Cambridge University Press.Google Scholar
Sammarco, P. & Renzi, E. 2008 Landslide tsunamis propagating along a plane beach. J. Fluid Mech. 598, 107–119.CrossRefGoogle Scholar
Slavyanov, S. Y. 1995 Confluent Heun equation. In Heun's Differential Equation (ed. Ronveaux, A.), pp. 87–127. Oxford Science Publications.Google Scholar
Smith, R. & Sprinks, T. 1975 Scattering of surface waves by a conical island. J. Fluid Mech. 72 (2), 373–384.CrossRefGoogle Scholar
Summerfield, W. 1971 Circular islands as resonators of long-wave energy. Phil. Trans. R. Soc. Lond. Ser. A 272, 361–402.Google Scholar
Synolakis, C. E., Bernard, E. N., Titov, V. V., Kanoglu, U. & Gonzalez, F. I. 2008 Validation and verification of tsunami numerical models. Pure Appl. Geophys. 165 (11–12), 2197–2228.CrossRefGoogle Scholar
Tinti, S., Maramai, A., Armigliato, A., Graziani, L., Mannucci, A., Pagnoni, G. & Zaniboni, F. 2005 Observations of physical effects from tsunamis of December 30, 2002 at Stromboli volcano, southern Italy. Bull. Volcanol. 68 (5), 450–461.CrossRefGoogle Scholar
Tinti, S. & Vannini, C. 1995 Tsunami trapping near circular islands. Pure Appl. Geophys. 144 (3/4), 595–619.CrossRefGoogle Scholar
Tuck, E. O. & Hwang, L. S. 1972 Long wave generation on a sloping beach. J. Fluid Mech. 51, 449–461.Google Scholar
Yeh, H., Liu, P. L.-F., Briggs, M. & Synolakis, C. E. 1994 Tsunami catastrophe in Babi island. Nature 372, 6503–6508.Google Scholar
Zhang, Y. & Zhu, S. 1994 New solutions for the propagation of long water waves over variable depth. J. Fluid Mech. 278, 391–406.CrossRefGoogle Scholar