Hostname: page-component-758b78586c-wkjwp Total loading time: 0 Render date: 2023-11-30T05:50:22.968Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

Landslide tsunamis in lakes

Published online by Cambridge University Press:  11 May 2015

Louis-Alexandre Couston
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
Chiang C. Mei
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Mohammad-Reza Alam*
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
Email address for correspondence:


Landslides plunging into lakes and reservoirs can result in extreme wave runup at the shores. This phenomenon has claimed lives and caused damage to near-shore properties. Landslide tsunamis in lakes are different from typical earthquake tsunamis in the open ocean in that (i) the affected areas are usually within the near field of the source, (ii) the highest runup occurs within the time period of the geophysical event, and (iii) the enclosed geometry of a lake does not let the tsunami energy escape. To address the problem of transient landslide tsunami runup and to predict the resulting inundation, we utilize a nonlinear model equation in the Lagrangian frame of reference. The motivation for using such a scheme lies in the fact that the runup on an inclined boundary is directly and readily computed in the Lagrangian framework without the need to resort to approximations. In this work, we investigate the inundation patterns due to landslide tsunamis in a lake. We show by numerical computations that Airy’s approximation of an irrotational theory using Lagrangian coordinates can legitimately predict runup of large amplitude. We also demonstrate that in a lake of finite size the highest runup may be magnified by constructive interference between edge waves that are trapped along the shore and multiple reflections of outgoing waves from opposite shores, and may occur somewhat after the first inundation.

© 2015 Cambridge University Press 

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.)


Airy, G. B. 1841 Tides and waves. In Encyclopaedia Metropolitana (ed. Rose, H. J. et al. ), Mixed Sciences, vol. 3, pp. 18171845. London.Google Scholar
Ataie-Ashtiani, B. & Nik-Khah, A. 2008 Impulsive waves caused by subaerial landslides. Environ. Fluid Mech. 8 (3), 263280.Google Scholar
Balzano, A. 1998 Evaluation of methods for numerical simulation of wetting and drying in shallow water flow models. Coast. Engng 34, 83107.Google Scholar
Bernatskiy, A. V. & Nosov, M. A. 2012 The role of bottom friction in models of nonbreaking tsunami wave runup on the shore. Izv. Atmos. Ocean. Phys. 48 (4), 427431.Google Scholar
Bryant, E.2008 Tsunami, The Underrated Hazard. Springer.Google Scholar
Carrier, G. F. & Greenspan, H. P. 1958 Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4 (1), 97109.Google Scholar
Carrier, G. F., Wu, T. T. & Yeh, H. 2003 Tsunami run-up and draw-down on a plane beach. J. Fluid Mech. 475, 7999.Google Scholar
Didenkulova, I. & Pelinovsky, E. 2013 Analytical solutions for tsunami waves generated by submarine landslides in narrow bays and channels. Pure Appl. Geophys. 170 (9–10), 16611671.Google Scholar
Didenkulova, I., Pelinovsky, E., Soomere, T.  & Zahibo, N. 2007a Runup of nonlinear asymmetric waves on a plane beach. In Tsunami and Nonlinear Waves (ed. Kundu, A.), pp. 175190. Springer.Google Scholar
Didenkulova, I. I., Kurkin, A. A. & Pelinovsky, E. N. 2007b Run-up of solitary waves on slopes with different profiles. Izv. Atmos. Ocean. Phys. 43 (3), 384390.Google Scholar
Didenkulova, I. I. & Pelinovsky, E. N. 2007 Phenomena similar to tsunami in Russian internal basins. Russian J. Earth Sci. 8 (6), 19.Google Scholar
Di Risio, M., De Girolamo, P., Bellotti, G., Panizzo, A., Aristodemo, F., Molfetta, M. G. & Petrillo, A. F. 2009 Landslide-generated tsunamis runup at the coast of a conical island: new physical model experiments. J. Geophys. Res. 114 (C1), 116.Google Scholar
Di Risio, M., De Girolamo, P. & Beltrami, G. M. 2011 Forecasting landslide generated tsunamis: a review. In The Tsunami Threat – Research and Technology (ed. Marner, N.-A.), Forecastin InTech.Google Scholar
Frits, H. M., Mohammed, F. & Yoo, J. 2009 Lituya bay landslide impact generated mega-tsunami 50th anniversary. Pure Appl. Geophys. 166 (1–2), 153175.Google Scholar
Fritz, H. M., Hager, W. H. & Minor, H.-E. 2004 Near field characteristics of landslide generated impulse waves. J. Waterways Port Coast. Ocean Engng 130 (December), 287302.Google Scholar
Fujima, K. 2007 Tsunami runup in Lagrangian description. In Tsunami and Nonlinear Waves (ed. Kundu, A.), pp. 191207. Springer.Google Scholar
Gardner, J. V., Mayer, L. A. & Hughs Clarke, J. E. 2000 Morphology and processes in Lake Tahoe. Geol. Soc. Amer. Bull. 112 (5), 736746.Google Scholar
Geist, E. L., Lynett, P. J. & Chaytor, J. D. 2009 Hydrodynamic modeling of tsunamis from the Currituck landslide. Mar. Geol. 264 (1–2), 4152.Google Scholar
Genevois, R. & Ghirotti, M. 2005 The 1963 Vaiont Landslide. Giorn. Geol. Appl. 1 1, 4152.Google Scholar
Goto, C. 1979 Nonlinear equation of long waves in the Lagrangian description. In Coastal Engineering in Japan, 22, pp. 19.Google Scholar
Goto, C. & Shuto, N. 1979 Two-dimensional run-up of tsunami by nonlinear theory. In Japanese Conference on Coastal Engineering, 26, pp. 5660. Japan Society of Civil Engineering. Committee on Coastal Engineering (in Japanese).Google Scholar
Goto, C. & Shuto, N. 1980 Run-up of tsunamis by linear and nonlinear theories. Coast. Engng Proc. 1 (17), 695707.Google Scholar
Heller, V., Moalemi, M., Kinnear, R. D. & Adams, R. A. 2012 Geometrical effects on landslide-generated tsunamis. J. Waterways Port Coast. Ocean Engng 138 (August), 286298.Google Scholar
Jensen, A., Pedersen, G. K. & Wood, D. J. 2003 An experimental study of wave run-up at a steep beach. J. Fluid Mech 486, 161188.Google Scholar
Johnsgard, H. & Pedersen, G. 1997 A numerical model for three-dimensional runup. Intl J. Numer. Meth. Fluids 24 (9), 913931.Google Scholar
Jorstad, F. A.1968 Waves generated by landslides in norwegian fjords and lakes. Norwegian Geotechnical Institute Publ 79, pp. 13–32.Google Scholar
Kamphuis, J. W. & Bowering, R. J.1970 Impulse waves generated by landslides. In Coastal Engineering Proceedings 1 (12), 575–588.Google Scholar
Kânoğlu, U. 2004 Nonlinear evolution and runup–rundown of long waves over a sloping beach. J. Fluid Mech. 513, 363372.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google 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, 101109.Google Scholar
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. 536, 107144.Google Scholar
Lockridge, P. A. 1990 Nonseismic phenomena in the generation and augmentation of tsunamis. Nat. Hazards 3, 403412.Google Scholar
Lynett, P. & Liu, P. L.-F. 2002 A numerical study of submarine-landslide-generated waves and run-up. Proc. R. Soc. Lond. A 458 (2028), 28852910.Google Scholar
Lynett, P. & Liu, P. L.-F. 2005 A numerical study of the run-up generated by three-dimensional landslides. J. Geophys. Res. 110, 116.Google Scholar
Madsen, P. A. & Schäffer, H. A. 2010 Analytical solutions for tsunami runup on a plane beach: single waves, N-waves and transient waves. J. Fluid Mech. 645, 2757.Google Scholar
Medeiros, S. C. & Hagen, S. C. 2013 Review of wetting and drying algorithms for numerical tidal flow models. Intl J. Numer. Meth. Fluids 71 (4), 473487.Google Scholar
Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005 Refraction by slowly varying depth. In Theory and Applications of Ocean Surface Waves – Part 1, Advanced edn, chap. 3, pp. 65121. World Scientific.Google Scholar
Meyer, R. E. 1986a On the shore singularity of water waves. I. The local model. Phys. Fluids 29 (10), 31523163.Google Scholar
Meyer, R. E. 1986b On the shore singularity of waterwave theory. II. Small waves do not break on gentle beaches. Phys. Fluids 29 (10), 31643171.Google Scholar
Miche, A. 1944 Mouvements ondulatoires de la mer en profondeur croissante ou décroissante. Ann. des Ponts et Chaussees 114 (1), 131164.Google Scholar
Panizzo, A., De Girolamo, P. & Petaccia, A. 2005a Forecasting impulse waves generated by subaerial landslides. J. Geophys. Res. 110 (C12), C12025.Google Scholar
Panizzo, A., De Girolamo, P., Di Risio, M., Maistri, A. & Petaccia, A. 2005b Great landslide events in Italian artificial reservoirs. Nat. Hazards Earth Syst. Sci. 5, 733740.Google Scholar
Pedersen, G. & Gjevik, B. 1983 Run-up of solitary waves. J. Fluid Mech. 135, 283299.Google Scholar
Pelinovsky, E. N. & Mazova, R. Kh. 1992 Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles. Nat. Hazards 6, 227249.Google Scholar
Rybkin, A., Pelinovsky, E. & Didenkulova, I. 2014 Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier–Greenspan approach. J. Fluid Mech. 748, 416432.Google Scholar
Sammarco, P. & Renzi, E. 2008 Landslide tsunamis propagating along a plane beach. J. Fluid Mech. 598, 107119.Google Scholar
Satake, K. 1995 Linear and nonlinear computations of the 1992 Nicaragua earthquake tsunami. In Tsunamis: 1992–1994, vol. 144, pp. 455470. Birkhäuser.Google Scholar
Shuto, N. 1967 Run-up of long waves on a sloping beach. Coastal Engineering in Japan 10, 2338.Google Scholar
Shuto, N. 1968 Three-dimensional behaviour of long waves on a sloping beach. Coastal Engineering in Japan, JSCE 11, 5357.Google Scholar
Shuto, N.1972 Standing waves in front of a sloping dike. In Coastal Engineering Proceedings 1 (13), pp. 1629–1647.Google Scholar
Shuto, N. & Goto, C. 1978 Numerical simulation of tsunami run-up. Coast. Engng Japan 21, 1320.Google Scholar
Spielvogel, L. Q. 1975 Single-wave run-up on sloping beaches. J. Fluid Mech. 74 (4), 685694.Google Scholar
Synolakis, C. E. 1987 The runup of solitary waves. J. Fluid Mech. 185, 523545.Google Scholar
Synolakis, C. E., Bernard, E. N., Titov, V. V., Kânoğlu, U. & González, F. I. 2008 Validation and verification of tsunami numerical models. Pure Appl. Geophys. 165 (11–12), 21972228.Google Scholar
Tadepalli, S. & Synolakis, C. E. 1994 The run-up of N-waves on sloping beaches. Proc. R. Soc. Lond. A 445 (1923), 99112.Google Scholar
Tchamen, G. W. & Kahawita, R. A. 1998 Modelling wetting and drying effects over complex topography. Hydrol. Process. 1182 (February), 11511182.Google Scholar
Tuck, E. O. & Hwang, L. S. 1972 Long wave generation on a sloping beach. J. Fluid Mech. 51 (3), 449461.Google Scholar
Voight, B., Janda, R. J., Glicken, H. & Douglass, P. M. 1983 Nature and mechanics of the Mount St Helens Rockslide-avalanche of 18 May 1980. Geotechnique 33, 243273.Google Scholar
Walder, J. S., Watts, P., Sorensen, O. E. & Janssen, K. 2003 Tsunamis generated by subaerial mass flows. J. Geophys. Res. 108 (B5), 2236, 19 pages (noted as 2–1 to 2–19 on article).Google Scholar
Weiss, R., Fritz, H. M. & Wünnemann, K. 2009 Hybrid modeling of the mega-tsunami runup in Lituya Bay after half a century. Geophys. Res. Lett. 36 (9), L09602.Google Scholar
Yeh, H. H., Liu, P. L.-F. & Synolakis, C. E. 1996 Long-wave Runup Models: Friday Harbor, USA, 12–17 September 1995. World Scientific.Google Scholar
Zabusky, N. J. 1962 Exact solution for the vibrations of a nonlinear continuous model string. J. Math. Phys. 3 (5), 10281039.Google Scholar
Zahibo, N., Pelinovsky, E. N., Golinko, V. & Osipenko, N. 2006 Tsunami wave runup on coasts of narrow bays. Intl J. Fluid Mech. Res. 33, 118.Google Scholar
Zelt, J. A.1986 Tsunamis, the response of harbours with sloping boundaries to long wave excitation, PhD thesis, California Institute of Technology.Google Scholar
Zelt, J. A. & Raichlen, F. 1990 A Lagrangian model for wave-induced harbour oscillations. J. Fluid Mech. 213, 203225.Google Scholar
Zelt, J. A. 1991 The run-up of nonbreaking and breaking solitary waves. Coast. Engng 15 (3), 205246.Google Scholar