Drifting breathers and Fermi–Pasta–Ulam paradox for water waves

One physical mechanism that is responsible for the focusing of uni-directional water waves is the modulation instability. This occurs when side-bands around the main frequency are excited either deterministically or randomly and subsequently grow exponentially. In physical space, the periodically-pe...

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Bibliographic Details
Published in:Wave motion 2019-08, Vol.90, p.168-174
Main Authors: Chabchoub, A., Hoffmann, N., Tobisch, E., Waseda, T., Akhmediev, N.
Format: Article
Language:English
Subjects:
Breathers
Fluid dynamics
Fluid flow
Fluid mechanics
Group velocity
Hydrodynamics
Initial conditions
Modulation
Nonlinear dynamics
Nonlinear waves
Paradoxes
Phase velocity
Propagation
Velocity
Water waves
Wave packets
Wave power
Wave propagation
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Summary:One physical mechanism that is responsible for the focusing of uni-directional water waves is the modulation instability. This occurs when side-bands around the main frequency are excited either deterministically or randomly and subsequently grow exponentially. In physical space, the periodically-perturbed wave group can reach significant wave amplifications and in the case of infinite modulation period even three times the initial amplitude of the regular Stokes wave train. These periodic wave groups propagate in deep-water with a group velocity half the wave’s phase speed. In this experimental study, we investigate the dynamics of modulationally unstable wave groups that propagate with a velocity that is higher than the packet’s group velocity in deep-water. It is shown that when this additional velocity to the wave group is marginal, a very good agreement with nonlinear Schrödinger hydrodynamics is reached at all stages of propagation and the characteristic wave energy cascade remains symmetric and stationary. Otherwise, a significant deviation is observed only at the stage of large wave focusing of the isolated wave packet. In this case, the wave field experiences an almost perfect return to the initial conditions after the compression, a particular dynamics also known as the Fermi–Pasta–Ulam paradox. •Drifting rogue waves.•Fermi–Pasta–Ulam paradox.•Stationary soliton dynamics.•Interdisciplinary nonlinear wave propagation.
ISSN:0165-2125
1878-433X
DOI:10.1016/j.wavemoti.2019.05.001