URL: https://www.nature.com/articles/s41598-022-14209-7
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.