Study and Simulation of Nonlinear Surface Gravity Waves
under Shallow-Water Conditions

I. B. Abbasov

Taganrog State University of Radio Engineering, Nekrasovskii per. 44, Taganrog, 347928 Russia

e-mail: mkk@egf.tsure.ru

Received February 18, 2002; in final form, June 24, 2002

Abstract—Nonlinear processes during the propagation of surface gravity waves under shallow-water condi-
tions are described with the method of successive approximations. The energy characteristics of the occurring
wave processes are considered. On the basis of the analytic expressions obtained for the horizontal velocity of
medium particles, the graphs of distortion of the profile of a surface wave during its propagation under shallow-
water conditions are given. The graphs of variations in the energy of the fundamental wave and higher harmon-
ics with respect to their path lengths are also given.

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