Tikan Alexey, Bonnefoy Félicien, Ducrozet Guillaume, Prabhudesai Gaurav, Michel Guillaume, Cazaubiel Annette, Falcon Éric, Copie Francois, Randoux Stéphane, Suret Pierre
Univ. Lille, CNRS, UMR 8523, PhLAM - Physique des Lasers Atomes et Molécules, F-59000, Lille, France.
Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), 1015, Lausanne, Switzerland.
Sci Rep. 2022 Jun 20;12(1):10386. doi: 10.1038/s41598-022-14209-7.
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.
我们通过数值和实验研究了一维水箱中部分相干波传播背景下的非线性色散关系（NDR）概念。非线性随机波具有窄带傅里叶频谱，并由一维非线性薛定谔方程在主导阶进行描述。该问题是在可积湍流的框架下考虑的，其中孤子起着关键作用。通过使用有限数量的波传感器，我们精确测量了深水波缓慢变化包络的NDR。这使得能够精确表征NDR的频移和展宽，同时还揭示了孤子的存在。此外，我们的分析表明，NDR的形状和展宽提供了实验中由高阶效应引起的偏离可积湍流的特征。我们还将实验观测结果与狄斯特方程和欧拉方程的数值模拟进行了比较。
