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 average runup height of waves with wide spectrum is higher than that of waves with narrow spectrum.
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References
Brocchini M, Gentile R (2001) Modelling the run-up of significant wave groups. Continental 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. Coastal Eng J 44(4):301–319
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. Doklady Earth Sci 411(8):1241–1243
Didenkulova II, Kurkin AA, Pelinovsky EN (2007a) Run-up of solitary waves on slopes with different profiles. Izvestiya 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. Springer, Berlin Heidelberg New York, pp 173–188
Kânoǧlu U, Synolakis C (2006) Initial value problem solution of nonlinear shallow water-wave equations. Phys Rev Lett 97:148501
Kharif C, Pelinovsky E (2003) Physical mechanisms of the rogue wave phenomenon. Eur J Mech B: Fluid 22(6):603–634
Massel SR (1996) Ocean surface waves: Their physics and prediction. World Scientific, Singapore
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. Izvestiya Russian Acad Eng Sci 14:98–105
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 A 445:99–112
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
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Didenkulova, I., Pelinovsky, E., Sergeeva, A. (2008). Runup of Long Irregular Waves on Plane Beach. In: Pelinovsky, E., Kharif, C. (eds) Extreme Ocean Waves. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8314-3_5
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DOI: https://doi.org/10.1007/978-1-4020-8314-3_5
Publisher Name: Springer, Dordrecht
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