Experiments in Surface Gravity–Capillary Wave Turbulence

Abstract

The last decade has seen a significant increase in the number of studies devoted to wave turbulence. Many deal with water waves, as modeling of ocean waves has historically motivated the development of weak turbulence theory, which addresses the dynamics of a random ensemble of weakly nonlinear waves in interaction. Recent advances in experiments have shown that this theoretical picture is too idealized to capture experimental observations. While gravity dominates much of the oceanic spectrum, waves observed in the laboratory are in fact gravity–capillary waves, due to the restricted size of wave basins. This richer physics induces many interleaved physical effects far beyond the theoretical framework, notably in the vicinity of the gravity–capillary crossover. These include dissipation, finite–system size effects, and finite nonlinearity effects. Simultaneous space-and-time-resolved techniques, now available, open the way for a much more advanced analysis of these effects. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 54 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence

“…Such quantitative analogy between Alfvén waves in plasma and surface waves on magnetic fluids would deserve further studies in particular theoretically, and could lead to a better understanding of plasma by studying them more easily. The analogy discovered here could be pushed forward to explore open questions in wave turbulence such as the properties of large scales [30], or the critical balance separating weak turbulence from strong turbulence [21]. The phenomenon reported here could also be observed experimentally using a ferrofluid with a high magnetic susceptibility and a high saturation magnetization.…”

“…The energy spectrum is E c (k) = (γ/ρ)k 2 S c (k). To date, the KZ spectrum has been very well confirmed for capillary waves both experimentally (e.g., see [27][28][29][30]) and numerically [31][32][33][34][35] for weakly nonlinear capillary waves. For B = 0, no weak turbulence prediction for magneto-capillary waves exists so far, only dimensional analysis has been done [23,24].…”

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].…”

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].…”