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Landslide tsunamis in lakes

  • Louis-Alexandre Couston (a1), Chiang C. Mei (a2) and Mohammad-Reza Alam (a1)

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.

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Airy G. B. 1841 Tides and waves. In Encyclopaedia Metropolitana (ed. Rose H. J. et al. ), Mixed Sciences, vol. 3, pp. 18171845. London.
Ataie-Ashtiani B. & Nik-Khah A. 2008 Impulsive waves caused by subaerial landslides. Environ. Fluid Mech. 8 (3), 263280.
Balzano A. 1998 Evaluation of methods for numerical simulation of wetting and drying in shallow water flow models. Coast. Engng 34, 83107.
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.
Bryant E.2008 Tsunami, The Underrated Hazard. Springer.
Carrier G. F. & Greenspan H. P. 1958 Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4 (1), 97109.
Carrier G. F., Wu T. T. & Yeh H. 2003 Tsunami run-up and draw-down on a plane beach. J. Fluid Mech. 475, 7999.
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.
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.
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.
Didenkulova I. I. & Pelinovsky E. N. 2007 Phenomena similar to tsunami in Russian internal basins. Russian J. Earth Sci. 8 (6), 19.
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.
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.
Frits H. M., Mohammed F. & Yoo J. 2009 Lituya bay landslide impact generated mega-tsunami 50th anniversary. Pure Appl. Geophys. 166 (1–2), 153175.
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.
Fujima K. 2007 Tsunami runup in Lagrangian description. In Tsunami and Nonlinear Waves (ed. Kundu A.), pp. 191207. Springer.
Gardner J. V., Mayer L. A. & Hughs Clarke J. E. 2000 Morphology and processes in Lake Tahoe. Geol. Soc. Amer. Bull. 112 (5), 736746.
Geist E. L., Lynett P. J. & Chaytor J. D. 2009 Hydrodynamic modeling of tsunamis from the Currituck landslide. Mar. Geol. 264 (1–2), 4152.
Genevois R. & Ghirotti M. 2005 The 1963 Vaiont Landslide. Giorn. Geol. Appl. 1 1, 4152.
Goto C. 1979 Nonlinear equation of long waves in the Lagrangian description. In Coastal Engineering in Japan, 22, pp. 19.
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).
Goto C. & Shuto N. 1980 Run-up of tsunamis by linear and nonlinear theories. Coast. Engng Proc. 1 (17), 695707.
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.
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.
Johnsgard H. & Pedersen G. 1997 A numerical model for three-dimensional runup. Intl J. Numer. Meth. Fluids 24 (9), 913931.
Jorstad F. A.1968 Waves generated by landslides in norwegian fjords and lakes. Norwegian Geotechnical Institute Publ 79, pp. 13–32.
Kamphuis J. W. & Bowering R. J.1970 Impulse waves generated by landslides. In Coastal Engineering Proceedings 1 (12), 575–588.
Kânoğlu U. 2004 Nonlinear evolution and runup–rundown of long waves over a sloping beach. J. Fluid Mech. 513, 363372.
Lamb H. 1932 Hydrodynamics. Cambridge University Press.
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.
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.
Lockridge P. A. 1990 Nonseismic phenomena in the generation and augmentation of tsunamis. Nat. Hazards 3, 403412.
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.
Lynett P. & Liu P. L.-F. 2005 A numerical study of the run-up generated by three-dimensional landslides. J. Geophys. Res. 110, 116.
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.
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.
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.
Meyer R. E. 1986a On the shore singularity of water waves. I. The local model. Phys. Fluids 29 (10), 31523163.
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.
Miche A. 1944 Mouvements ondulatoires de la mer en profondeur croissante ou décroissante. Ann. des Ponts et Chaussees 114 (1), 131164.
Panizzo A., De Girolamo P. & Petaccia A. 2005a Forecasting impulse waves generated by subaerial landslides. J. Geophys. Res. 110 (C12), C12025.
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.
Pedersen G. & Gjevik B. 1983 Run-up of solitary waves. J. Fluid Mech. 135, 283299.
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.
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.
Sammarco P. & Renzi E. 2008 Landslide tsunamis propagating along a plane beach. J. Fluid Mech. 598, 107119.
Satake K. 1995 Linear and nonlinear computations of the 1992 Nicaragua earthquake tsunami. In Tsunamis: 1992–1994, vol. 144, pp. 455470. Birkhäuser.
Shuto N. 1967 Run-up of long waves on a sloping beach. Coastal Engineering in Japan 10, 2338.
Shuto N. 1968 Three-dimensional behaviour of long waves on a sloping beach. Coastal Engineering in Japan, JSCE 11, 5357.
Shuto N.1972 Standing waves in front of a sloping dike. In Coastal Engineering Proceedings 1 (13), pp. 1629–1647.
Shuto N. & Goto C. 1978 Numerical simulation of tsunami run-up. Coast. Engng Japan 21, 1320.
Spielvogel L. Q. 1975 Single-wave run-up on sloping beaches. J. Fluid Mech. 74 (4), 685694.
Synolakis C. E. 1987 The runup of solitary waves. J. Fluid Mech. 185, 523545.
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.
Tadepalli S. & Synolakis C. E. 1994 The run-up of N-waves on sloping beaches. Proc. R. Soc. Lond. A 445 (1923), 99112.
Tchamen G. W. & Kahawita R. A. 1998 Modelling wetting and drying effects over complex topography. Hydrol. Process. 1182 (February), 11511182.
Tuck E. O. & Hwang L. S. 1972 Long wave generation on a sloping beach. J. Fluid Mech. 51 (3), 449461.
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.
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).
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.
Yeh H. H., Liu P. L.-F. & Synolakis C. E. 1996 Long-wave Runup Models: Friday Harbor, USA, 12–17 September 1995. World Scientific.
Zabusky N. J. 1962 Exact solution for the vibrations of a nonlinear continuous model string. J. Math. Phys. 3 (5), 10281039.
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.
Zelt J. A.1986 Tsunamis, the response of harbours with sloping boundaries to long wave excitation, PhD thesis, California Institute of Technology.
Zelt J. A. & Raichlen F. 1990 A Lagrangian model for wave-induced harbour oscillations. J. Fluid Mech. 213, 203225.
Zelt J. A. 1991 The run-up of nonbreaking and breaking solitary waves. Coast. Engng 15 (3), 205246.
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