Transformation of Nonlinear Surface Gravity Waves under Shallow-Water Conditions

References

[1] D. H. Peregrine, “Long Waves on a Beach,” Journal of Fluid Mechanics, Vol. 27, No. 0404, 1967, pp. 815-827.

[2]
N. Е. Voltsinger, К. А. Klevanniy and Е. Н. Pelinovskiy, “Long-Wave Dynamics of Coastal Zone,” Gidrometeoizdat, 1989, p. 272.

[3]
P. I. Naumkin and I. А. Shishmarev, “On the Existence and Breaking the Waves Described by the Whitham Equation,” Soviet Physics-Doklady, Vol. 384, No. 31, 1986, pp. 90-95.

[4] V. G. Galenin and V. V. Kuznetsov, “Simulation of Wave Transformation in Coastal Zone,” Water Resources, Vol. 7, No. 1, 1980, pp. 156-165.

[5]
U. Kanoglu, “Nonlinear Evolution and Run Up-Run Down of Long Waves over a Sloping Beach,” Journal of Fluid Mechanics, Vol. 513, 2004, pp. 363-372.

[6] I. I. Didenkulova, N. Zaibo, А. А. Kurkin and Е. N. Peli-novskiy, “Steepness and Spectrum of Nonlinear Deformed Wave under Water Conditions,” Izvestiya RAN Atmos-pheric and Oceanic Physics, Vol. 42, No. 6, 2006, pp. 839-842.

[7]
N. А. Kudryashov, Yu. I. Sytsko and S. А. Chesnokov, “Mathematic Simulation of Gravity Waves in the Ocean in ‘Shallow Water’ Approximation,” Pisma v ZhETF, Vol. 77, No. 10, 2003, p. 649.

[8] А. А. Litvinenko and G. А. Khabakhpashev, “Computer Simulation of Nonlinear Considerably Long Two-dimensional Waves under Water Conditions in Basins with Sloping Floor,” Computer technologies, Vol. 4, No. 3, 1999, pp. 95-105.

[9]
S. Yu. Kuznetsov and Ya. V. Saprykina, “Experimental Researches of Wave Group Evolution in the Coastal Sea Zone,” Oceanology, Vol. 42, No. 3, 2002, p. 356-363.

[10]
I. B. Abbasov, “Study and Simulation of Nonlinear Surface Waves under Shallow-Water Conditions,” Izvestiya RAN. Atmospheric and Oceanic Physics, Vol. 39, No. 4, 2003, pp. 506-511.

[11]
H. Lamb, “Hydrodynamics,” Dover, New York, 1930, p. 524.

[12]
G. Whitham, “Linear and Nonlinear Waves,” Wiley, New York, 1974, p. 622.

[13]
L. М. Brekhovskikh and V. V. Goncharov, “Introduction to the Mechanics of Continuous Media,” Nauka, 1982, p. 325.

[14]
М. B. Vinogradova, О. V. Rudenko and А. P. Sukhorukov, “Wave Theory,” Nauka, 1979, p. 383.

[15]
А. K. Monin and V. P. Krasitskiy, “Phenomena at the Ocean Surface,” L. Gidrometeoizdat, 1985, p. 375.

[16] I. О. Leontiev, “Coastal Dynamics: Waves, Streams, Burden Streams,” M.: GEOS, 2001, p. 272.

[17]
R. E. Flick, R. T. Guza and D. L. Inman, “Elevation and Velocity Measurements of Laboratory Shoaling Waves,” Journal of Geophysical Research, Vol. 86, No. 5, 1981, pp. 4149-4160.

[18]
M. S. Lonquet-Higgins, “Grest Instabilities of Gravity Waves, Part 1,” Journal of Fluid Mechanics, Vol. 258, No. 1, 1994, pp. 115-129.

[19]
V. Zaharov, “Weakly Non-Linear Waves on the Surface of an Ideal Finite Depth Fluid,” American Mathematical Society Transactions, Series 2, Vol. 182, 1998, pp. 167- 197.

[20]
S. А. Gabov, “Introduction to the Theory on Nonlinear Waves,” Moscow State Unversity, 1988, p.176.

[21] Y. Goda and K. Morinobu, “Breaking Wave Heights on Horizontal Bed Affected by Approach Slope,” Coastal Engineering Journal, Vol. 40, No. 4, 1998, pp. 307-326.

[22]
Ya. V. Saprykina, S. Yu. Kuznetsov, Zh. Tcherneva and N. Andreeva, “Space-Time Unsteadiness of the Amplitude-Phase Structure of Storm Waves in the Coastal Sea Zone,” Oceanology, Vol. 49, No. 2, 2009, pp. 198-208.

[23]
K. Kawasaki, “Numerical Simulation of Breaking and Post-Breaking Wave Deformation Process around a Submerged Breakwater,” Coastal Engineering Journal, Vol. 41, No. 3-4, 1999, pp. 201-223.