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Spectra of nonlinear shallow water waves  

Zahibo, Narcisse (Physics Department, University of Antilles Guyane)
Didenkulova, Ira (Applied Mathematics Department, State Technical University, and Department of Nonlinear Geophysical Processes, Institute of Applied Physics)
Pelinovsky, Efim (Applied Mathematics Department, State Technical University, and Department of Nonlinear Geophysical Processes, Institute of Applied Physics)
Publication Information
Journal of Korean Society of Coastal and Ocean Engineers / v.19, no.4, 2007 , pp. 355-360 More about this Journal
Abstract
The process of the nonlinear shallow water wave transformation in a basin of a constant depth is studied. Characteristics of the first breaking of the wave are analyzed in details. The Fourier spectrum and steepness of the nonlinear wave are calculated. It is shown that the spectral amplitudes can be expressed using the wave front steepness, which allows the practical estimations.
Keywords
Nonlinear deformation; wave breaking; Fourier spectrum; steepness; shallow water theory;
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1 Engelbrecht, J.K., Fridman, V.E. and Pelinovsky, E.N. (1988). Nonlinear Evolution Equations (Pitman Research Notes in Mathematics Series, No. 180). London: Longman
2 Gurbatov, S., Malakhov, A. and Saichev, A. (1991). Nonlinear random waves and turbulence in nondispersive media: waves, rays and particles. Manchester University Press, Manchester
3 Rudenko, O. and Soluyan, S. (1977). Theoretical background of nonlinear acoustics. Plenum, N.-Y
4 Shuto, N. (1985). The Nikhonkai-Chubu earthquake tsunami on the North Akita coast. Coastal Engineering in Japan, vol. 28, 255-264   DOI
5 Stoker, J.J. (1957). Water waves. Willey Inter Science, NY
6 Zahibo, N., Pelinovsky, E., Talipova, T., Kozelkov, A., and Kurkin, A. (2006). Analytical and numerical study of nonlinear effects at tsunami modelling. Applied Mathematics and Computation. vol. 174, No. 2, 795-809   DOI   ScienceOn
7 Voltsinger, N.E., Klevanny, K.A. and Pelinovsky, E.N. (1989). Long wave dynamics of the coastal zone, Hydrometeoisdat, Leningrad (in Russian)
8 Whitham, G.B. (1974). Linear and Nonlinear Waves. Wiley, N.Y
9 Tsuji, Y., Yanuma, T., Murata, I. and Fujiwara, C. (1991). Tsunami ascending in rivers as an undular bore. Natural Hazards, vol. 4, 257-266   DOI
10 Hammack, J.L. (1973). A note on tsunamis: their generation and propagation in an ocean of uniform depth. J. Fluid Mech., vol. 60, 769-799   DOI
11 Pelinovsky, E.N. (1982). Nonlinear Dynamics of Tsunami Waves. Applied Physics Institute Press, Gorky (in Russian)
12 Wu, Y.H. and Tian, J.-W. (2000). Mathematical analysis of long-wave breaking on open channels with bottom friction. Ocean Engineering, vol. 26, 187-201
13 Ostrovsky, L. and Pelinovsky, E. (1976). Nonlinear evolution of tsunami waves. Bull. Roy. Soc. New Zealand, vol. 15, 203-211
14 Arseniev, A.C. and Shelkovnikov, N.K. (1991). Dynamics of sea long waves. Moscow State University Press, Moscow (in Russian)
15 Pelinovsky, E.N. and Troshina, E.N. (1994). Propagation of long waves in straits. Phys. Oceanography, vol. 5, N. 1, 43-48   DOI
16 Tan, W.Y. (1992). Shallow water hydrodynamics. Elsevier, N.Y
17 Pelinovsky, E.N. (1976). Spectral analysis of simple waves. Radiophysics and Quantum Electronics, vol. 19, N. 3, 262-270
18 Murty, T. (1977). Seismic sea waves – Tsunamis. Canada
19 Caputo, J.-G. and Stepanyants, Y.A. (2003). Bore formation, evolution and disintegration into solitons in shallow inhomogeneous channels. Nonlinear Processes in Geophysics, vol. 10, 407-424   DOI   ScienceOn