Experimental quasi-1D capillary-wave turbulence

Abstract

Wave turbulence in quasi-1D geometry is usually not investigated experimentally since low-order resonant wave interactions are theoretically prohibited. Here, we report on the first observation of unidirectional capillary-wave turbulence on the surface of a fluid in a canal. We also show that five-wave interactions are the lowest-order resonant process subsisting at small scales, and are thus probably the one generating such quasi-1D capillary wave turbulence. We show that the wave spectrum is compatible with the corresponding dimensional analysis prediction. The main assumptions of weak turbulence theory are also verified experimentally. Quasi-1D wave turbulence could be thus highlighted in other fields of wave turbulence.

Experimental Periodic Korteweg--de Vries Solitons along a Torus of Fluid

“…Here, using this technique, we experimentally discover unreported periodic KdV solitons along a stable torus of liquid whose properties are fully characterized (profile, velocity, collision, and dissipation), and described with an experimentally validated model taking into account both the curved and periodic conditions. Our work thus paves the way to observe other nonlinear phenomena such as wave turbulence [15,16], and soliton gas [17][18][19][20][21] in this specific geometry. Note that KdV solitons can be reached experimentally in curved geometries without periodicity (e.g., along the border of a liquid cylinder [22][23][24]), whereas trials have been attempted for periodic conditions in plane geometry (e.g., in an annular water tank [25,26]), as well as for a curved and periodic system but only in a nonstationary regime and by applying a strong constraint to the liquid ring [27][28][29].…”

Transition from wave turbulence to acousticlike shock-wave regime

“…However, the finite size of our experimental system and the nonvanishing viscosity of the fluid used here will lead to work in the intermediatefrequency scales and thus to an entanglement of the gravity and capillary effects [9]. Indeed, for a 1D gravity-capillary system, we previously reported experimentally a power-law spectrum in S η ∼ ω −3.3±0.2 in the intermediate-scale range as a result of the occurrence of three-wave interactions [29] [see also the purple curve in Fig. 7(a)].…”

“…For example, in one dimension, pure gravity waves dominated by five-wave resonant interactions are predicted to have a power spectrum of the surface elevation η as S η ∼ ω −17/4 [40]. It has been also observed experimentally that 1D capillary waves are dominated by five-wave resonant interactions and follow a power spectrum in S η ∼ ω −31/12 [29]. Thus, for a 1D gravity-capillary system (with no magnetic field), these two asymptotic spectra are thus expected, the pure gravity spectrum for large enough scales (f 5 Hz) and the pure capillarity one for small enough scales (f 50 Hz) [9].…”

“…Here, we use a one-dimensional (1D) canal filled with a magnetic fluid subjected to an external horizontal magnetic field to tune the dispersivity of the wave system within a deep-water regime. At a low magnetic field, the classical quasi-1D dispersive gravity-capillary wave turbulence is observed [29], whereas at a high enough field a nondispersive regime is reached. In the latter, we observe the emergence of random shock waves, keeping their shape over time, with a very steep profile close to the one derived from the 1D Burgers equation [30], although not reaching a fully vertical front.…”

Feynman rules for forced wave turbulence

“…The next-to-leading order corrections to the correlation functions that we computed should, in principle, be measurable quantities. This may be a fruitful avenue to pursue, given the extensive recent experimental work on wave turbulence [91,35,92,93] and prethermalization [54][55][56].…”