Denissenko, Petr, Didenkulova, I., Pelinovskiĭ, E. N. and Pearson, Jonathan M.. (2011) Influence of the nonlinearity on statistical characteristics of long wave runup. Nonlinear Processes in Geophysics, Vol.18 (No.6). pp. 967-975. ISSN 1023-5809

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Abstract

Runup of long irregular waves on a plane beach is studied experimentally in the water flume at the University of Warwick. Statistics of wave runup (displacement and velocity of the moving shoreline and their extreme values) is analyzed for the incident wave field with the narrow band spectrum for different amplitudes of incident waves (different values of the breaking parameter Brσ). It is shown experimentally that the distribution of the shoreline velocity does not depend on Brσ and coincides with the distribution of the vertical velocity in the incident wave field as it is predicted in the statistical theory of nonlinear long wave runup. Statistics of runup amplitudes shows the same behavior as that of the incident wave amplitudes. However, the distribution of the wave runup on a beach differs from the statistics of the incident wave elevation. The mean sea level at the coast rises with an increase in Brσ causing wave set-up on a beach, which agrees with the theoretical predictions. At the same time values of skewness and kurtosis for wave runup are similar to those for the incident wave field and they might be used for the forecast of sea floods at the coast.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Water waves -- Statistical methods
Journal or Publication Title:	Nonlinear Processes in Geophysics
Publisher:	Copernicus GmbH
ISSN:	1023-5809
Date:	2011
Volume:	Vol.18
Number:	No.6
Page Range:	pp. 967-975
Identification Number:	10.5194/npg-18-967-2011
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Estonia. Haridus- ja Teadusministeerium [The Ministry of Education and Science], Estonian Science Foundation (ESF), Rossiĭskiĭ fond fundamentalʼnykh issledovaniĭ [Russian Foundation for Basic Research] (RFFI), Russia (Federation)
Grant number:	SF0140007s11 (HT), 8870 (ESF), 11-05-00216 (RFFI), 11-02-00483 (RFFI), 11-05-92002 (RFFI), 11-05-97006 (RFFI), MK-1440.2012.5 (Russia), MK-4378.2011.5 (Russia)
References:	Bowen, A. J., Inman, D. L., and Simmons, V. P.: Wave “set-down” and “set-up”, J. Geophys. Res., 73, 2569–2577, 1968. Carrier, G. F. and Greenspan, H. P.: Water waves of finite amplitude on a sloping beach, J. Fluid Mech., 4, 97–109, 1958. Choi, B. H., Kim, D. C., Pelinovsky, E. and Woo, S. B.: Threedimensional simulation of tsunami run-up around conical island, Coast. Eng., 54, 618–629, 2007. Choi, B. H., Pelinovsky, E., Kim, D. C., Didenkulova, I., and Woo, S.-B.: Two- and three-dimensional computation of solitary wave runup on non-plane beach, Nonlin. Processes Geophys., 15, 489– 502, doi:10.5194/npg-15-489-2008, 2008. Dean, R. G. andWalton, T. L.: Wave setup, in: Handbook of coastal and ocean engineering, edited by: Kim, Y. C.,World Sci., Singapore, 2009. Didenkulova, I., Pelinovsky, E., and Sergeeva, A.: Statistical characteristics of long waves nearshore, Coast. Eng., 58, 94–102, 2011. Didenkulova, I., Pelinovsky, E., and Soomere, T.: Run-up characteristics of tsunami waves of “unknown” shapes, Pure Appl. Geophys., 165, 2249–2264, 2008. Didenkulova, I., Pelinovsky, E., Soomere, T., and Zahibo, N.: Runup of nonlinear asymmetric waves on a plane beach, Tsunami and Nonlinear Waves, edited by: Anjan Kundu, Springer, 173–188, 2007. Didenkulova, I. I., Zahibo, N., Kurkin, A. A., Levin, B. V., Pelinovsky, E. N., and Soomere, T.: Runup of nonlinearly deformed waves on a coast, Doklady Earth Sci., 411, 1241–1243, 2006b. Fuhrman, D. R. and Madsen, P. A.: Simulation of nonlinear wave run-up with a high-order Boussinesq model, Coast. Eng., 55, 139–154, 2008. Goda, Y. and Suzuki, Y.: Estimation of Incident and Reflected Waves in Random Wave Experiments. Proceedings, 15th Internation Conference on Coastal Engineering, Honolulu, Hawaii., 1, 828–845, 1976. Guza, R. T. and Thornton, E. B.: Local and shoaled comparisons of sea surface elevations, pressures, and velocities, J. Geophys. Res., 85, 1524–1530, 1980. Holman, R. A.: Extreme value statistics for wave run-up on a natural beach, Coast. Eng., 9, 527–544, 1986. Holman, R. A. and Sallenger, A. H.: Setup and Swash on a Natural Beach, J. Geophys. Res., 90, 945–953, 1985. Huntley, D. A., Guza, R. T., and Bowen, A. J.: A universal form for shoreline run-up spectra, J. Geophys. Res., 82, 2577–2581, 1977. Kendall, M. G. and Stuart, A.: The advanced theory of statistics, Volume I., Distribution theory, London, 439 pp., 1969. Kennedy, A. B., Chen, Q., Kirby, J. T., and Dalrymple, R. A.: Boussinesq modeling of wave transformation, breaking and runup, J. Waterway, Port Coast. Ocean Eng. 126, 39–47, 2000. Le Mehaute, B., Koh, R. C., and Hwang, L. S.: A synthesis of wave run-up, J. Waterways Port Harbor Coast. Eng., 94, 77–92, 1968. Liu, P. L.-F., Cho, Y.-S., Briggs, M. J., Kanoglu, U., and Synolakis, C.: Runup of solitary waves on a circular island, J. Fluid Mech., 302, 259–285, 1995. Mansard, E. P. D. and Funke E. R.: The measurement of incident and reflected spectra using a least square method, in: Proc. 17th Coastal Eng. Conf., ASCE, 154–172, 1980, Massel, S. R.: Hydrodynamics of coastal zones, Elsevier, Amsterdam, 1989. Massel, S. R.: Ocean surface waves: their physics and prediction, World Scientific Publ., Singapore, 492 pp., 1996. Raubenneimer, B. and Guza, R. T.: Observations and predictions of run-up, J. Geophys. Res., 101, 25575–25587, 1996. Raubenneimer, B., Guza, R. T., and Elgar, S.: Field observations of wave-driven setdown and setup, J. Geophys. Res., 106, 4639– 4638, 2001. Stockdon, H. F., Holman, R. A., Howd, P. A., and Sallenger, A. H.: Empirical parameterization of setup, swash, and runup, Coast. Eng., 53, 573–588, 2006. Spinneken, J. and Swan, C.: Second-order wave maker theory using force-feedback control, Part I. A new theory for regular wave generation, Ocean Eng., 36, 539–548, 2009. Synolakis, C .E.: Tsunami runup on steep slopes: How good linear theory really is, Nat. Hazards, 4, 221–234, 1991. Zahibo, N., Didenkulova, I., Kurkin, A., and Pelinovsky, E.: Steepness and spectrum of nonlinear deformed shallow water wave, Ocean Eng., 35, 47–52, 2008.
URI:	http://wrap.warwick.ac.uk/id/eprint/42200

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