Abstract
Runup of irregular waves, modeled as superposition of Furrier harmonics with random phases, is studied in frames of nonlinear shallow water theory. The possibility of appearance of freak waves on a beach is analyzed. The distribution functions of runup characteristics are computed. An incident wave represents an irregular sea state with Gaussian spectrum. The asymptotic of probability functions in the range of large amplitudes for estimation of freak wave formation in the shore is studied. It is shown that the average runup height of waves with wide spectrum is higher than of waves with narrow spectrum.
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Brocchini M, Gentile R (2001) Modelling the run-up of significant wave groups. Cont Shelf Res 21:1533–1550
Carrier GF, Greenspan HP (1958) Water waves of finite amplitude on a sloping beach. J Fluid Mech 4:97–109
Carrier GF, Wu TT, Yeh H (2003) Tsunami run-up and draw-down on a plane beach. J Fluid Mech 475:79–99
Chien H, Kao C-C, Chuang LZH (2002) On the characteristics of observed coastal freak waves. Coast Eng J 44(4):301–319
Denissenko P, Didenkulova I, Rodin A, Listak M, Pelinovsky E (2013) Experimental statistics of long wave runup on a plane beach. J Coast Res SI 65:195–200
Didenkulova I (2009) New trends in the analytical theory of long sea wave runup. In: Quak E, Soomere T (eds) Applied wave mathematics: selected topics in solids, fluids, and mathematical methods. Springer, pp 265-296
Didenkulova I (2011) Shapes of freak waves in the coastal zone of the Baltic sea (Tallinn Bay). Boreal Environ Res 16(Suppl. A): 138-148
Didenkulova I, Pelinovsky E (2011) Rogue waves in nonlinear hyperbolic systems (shallow-water framework). Nonlinearity 24:R1–R18
Didenkulova II, Slunyaev AV, Pelinovsky EN, Charif Ch (2006a) Freak waves in 2005. Nat Hazards Earth Syst Sci 6:1007–1015
Didenkulova II, Zahibo N, Kurkin AA, Levin BV, Pelinovsky EN, Soomere T (2006b) Runup of nonlinearly deformed waves on a coast. Dokl Earth Sci 411(8):1241–1243
Didenkulova II, Kurkin AA, Pelinovsky EN (2007a) Run-up of solitary waves on slopes with different profiles. Izv Atmos Ocean Phys 43(3):384–390
Didenkulova I, Pelinovsky E, Soomere T, Zahibo N (2007b) Runup of nonlinear asymmetric waves on a plane beach. In: Kundu A (ed) Tsunami and nonlinear waves, pp 173-188
Dysthe K, Krogstad HE, Muller P (2008) Oceanic rogue waves. Annu Rev Fluid Mech 40:287–310
Kânoğlu U (2004) Nonlinear evolution and runup-rundown of long waves over a sloping beach. J Fluid Mech 513:363–372
Kânoğlu U, Synolakis C (2006) Initial value problem solution of nonlinear shallow water-wave equations. Phys Rev Lett 97:148501
Kharif Ch, Pelinovsky E (2003) Physical mechanisms of the rogue wave phenomenon. Eur J Mech / B-Fluid 22(6):603–634
Kharif Ch, Pelinovsky E, Slunyaev A (2009) Rogue waves in the ocean. Springer, Berlin
Massel SR (1996) Ocean surface waves: their physics and prediction. World Scientific, Singapore
Nikolkina I, Didenkulova I (2011) Rogue waves in 2006–2010. Nat Hazards Earth Syst Sci 11:2913–2924
Nikolkina I, Didenkulova I (2012) Catalogue of rogue waves reported in media in 2006–2010. Nat Hazards 61(3):989–1006
Olagnon M, Athanassoulis GA (eds) (2001) Rogue waves 2000. Ifremer, France
Pedersen G, Gjevik B (1983) Runup of solitary waves. J Fluid Mech 142:283–299
Pelinovsky E, Mazova R (1992) Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles. Nat Hazards 6:227–249
Rosenthal W (2003) Rogue waves: forecast and impact on marine structures. GKSS Research Center, Geesthacht, Germany
Sand SE, Hansen NE, Klinting P, Gudmestad OT, Sterndorff MJ (1990) Freak wave kinematics. In: Torum A, Gudmestad OT (eds) Water wave kinematics. Kluwer, Dordrecht, pp 535–549
Sergeeva AV, Didenkulova II (2005) Runup of irregular waves on a plane beach. Izv Russ Acad Eng Sci 14:98–105
Slunyaev A, Didenkulova I, Pelinovsky E (2011) Rogue waters. Contemp Phys 52(6):571–590
Spielfogel LO (1976) Runup of single waves on a sloping beach. J Fluid Mech 74:685–694
Synolakis CE (1987) The runup of solitary waves. J Fluid Mech 185:523–545
Synolakis CE (1991) Tsunami runup on steep slopes: how good linear theory really is. Nat Hazards 4:221–234
Tadepalli S, Synolakis CE (1994) The Runup of N-waves. Proc R Soc Lond A445:99–112
Tinti S, Tonini R (2005) Analytical evolution of tsunamis induced by near-shore earthquakes on a constant-slope ocean. J Fluid Mech 535:33–64
Torum A, Gudmestad OT (eds) (1990) Water wave kinematics. Kluwer, Dordrecht
Acknowledgments
This study was supported by the basic part of the state contract No 2014/133 and RFBR grants (14-02-00983, 14-05-00092, 15-35-20563). Ira Didenkulova acknowledges grant MK-1146.2014.5. Anna Sergeeva thanks Volkswagen Foundation.
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Didenkulova, I., Pelinovsky, E., Sergeeva, A. (2016). Runup of Long Irregular Waves on Plane Beach. In: Pelinovsky, E., Kharif, C. (eds) Extreme Ocean Waves. Springer, Cham. https://doi.org/10.1007/978-3-319-21575-4_8
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DOI: https://doi.org/10.1007/978-3-319-21575-4_8
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