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Indexed by:期刊论文

Date of Publication:2014-01-01

Journal:WAVE MOTION

Included Journals:SCIE、EI

Volume:51

Issue:1

Page Number:157-167

ISSN No.:0165-2125

Key Words:Fermi-Pasta-Ulam-Tsingou-problem; Recurrence; Energy equipartition; Soliton ensemble; Boussinesq equation; Water wave

Abstract:Beginning with the first mode as the initial condition, long-term evolutions of gravity waves in shallow water are simulated based on the full nonlinear Boussinesq model. Evident recurrence is observed in long basins with appropriate initial amplitudes. Equipartition can be obtained in the case of a long basin, large initial amplitude or a long evolution time. Well-defined solitary waves are present during the recurrence stage and completely lost at the equipartition stage. The transition from regular to chaotic motion is conjectured to be related to the ratio of the dispersion and nonlinearity of the initial condition. For short basins with small initial amplitudes, nonlinearity is much smaller than dispersion, energy transfer is weak, and no recurrence can be observed. If dispersion and nonlinearity are chosen to be the same order in the initial condition, recurrence clearly emerges. However, if nonlinearity is chosen to be larger than dispersion, recurrence is absent and the system reaches equipartition rapidly. (C) 2013 Elsevier B.V. All rights reserved.