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Updated: Sep 7, 2025

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
Published on: January 9, 2017
Nonlinear dispersion relation in integrable turbulence
Alexey Tikan1,2, Félicien Bonnefoy3, Guillaume Ducrozet3
1Univ. Lille, CNRS, UMR 8523, PhLAM - Physique des Lasers Atomes et Molécules, F-59000, Lille, France.
Abstract:
We investigate numerically and experimentally the concept of nonlinear dispersion relation (NDR) in the context of partially coherent waves propagating in a one-dimensional water tank. The nonlinear random waves have a narrow-bandwidth Fourier spectrum and are described at leading order by the one-dimensional nonlinear Schrödinger equation. The problem is considered in the framework of integrable turbulence in which solitons play a key role. By using a limited number of wave gauges, we accurately measure the NDR of the slowly varying envelope of the deep-water waves. This enables the precise characterization of the frequency shift and the broadening of the NDR while also revealing the presence of solitons. Moreover, our analysis shows that the shape and the broadening of the NDR provides signatures of the deviation from integrable turbulence that is induced by high order effects in experiments. We also compare our experimental observations with numerical simulations of Dysthe and of Euler equations.
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