Scientific article
Open access

Stabilization of uni-directional water-wave trains over an uneven bottom

Published inNonlinear Dynamics
Publication date2020

We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr"odinger equation (NLSE) with coefficients varying in space along propagation is used as a reference model. Based on a low-dimensional approximation obtained by considering only three complex harmonic modes, we discuss how to stabilize a one-dimensional pattern in the form of train of large peaks sitting on a background and propagating over a significant distance. Our approach is based on a gradual depth variation, while its conceptual framework is the theory of autoresonance in nonlinear systems and leads to a quasi-frozen state. Three main stages are identified: amplification from small sideband amplitudes, separatrix crossing, and adiabatic conversion to orbits oscillating around an elliptic fixed point. Analytical estimates on the three stages are obtained from the low-dimensional approximation and validated by NLSE simulations. Our result will contribute to understand dynamical stabilization of nonlinear wave packets and the persistence of large undulatory events in hydrodynamics and other nonlinear dispersive media.

  • arxiv : nlin.PS
Citation (ISO format)
ARMAROLI, Andrea et al. Stabilization of uni-directional water-wave trains over an uneven bottom. In: Nonlinear Dynamics, 2020. doi: 10.1007/s11071-020-05819-9
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Article (Published version)
ISSN of the journal0924-090X

Technical informations

Creation08/10/2020 3:32:00 PM
First validation08/10/2020 3:32:00 PM
Update time03/15/2023 10:24:19 PM
Status update03/15/2023 10:24:19 PM
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