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A water cylinder deposited on a heated channel levitates on its own generated vapor film owing to the Leidenfrost effect. This experimental setup permits the study of the one-dimensional propagation of surface waves in a free-to-move liquid system. We report the observation of gravity-capillary waves under a dramatic reduction of gravity (up to a factor 30), leading to capillary waves at the centimeter scale. The generated nonlinear structures propagate without deformation and undergo mutual collisions and reflections at the boundaries of the domain. They are identified as Korteweg-de Vries solitons with negative amplitude and subsonic velocity. The typical width and amplitude-dependent velocities are in excellent agreement with theoretical predictions based on a generalized Korteweg-de Vries equation adapted to any substrate geometry. When multiple solitons are present, they interact and form a soliton turbulencelike spectrum. [ABSTRACT FROM AUTHOR]

After a bubble bursts at a liquid surface, the collapse of the cavity generates capillary waves, which focus on the axis of symmetry to produce a jet. The cavity and jet dynamics are primarily controlled by a nondimensional number that compares capillary inertia and viscous forces, i.e., the Laplace number La=ργR_{0}/μ^{2}, where ρ, μ, γ, and R_{0} are the liquid density, viscosity, interfacial tension, and the initial bubble radius, respectively. In this Letter, we show that the time-dependent profiles of cavity collapse (tt_{0}) both obey a |t-t_{0}|^{2/3} inviscid scaling, which results from a balance between surface tension and inertia forces. Moreover, we present a scaling law, valid above a critical Laplace number, which reconciles the time-dependent scaling with the recent scaling theory that links the Laplace number to the final jet velocity and ejected droplet size. This leads to a self-similar formula which describes the history of the jetting process, from cavity collapse to droplet formation.

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

This work presents direct numerical simulations of capillary wave turbulence solving the full three-dimensional Navier-Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after few forcing periods. Smaller wave scales are generated by nonlinear interactions, and the wave height spectrum is found to obey a power law in both wave number and frequency, in good agreement with weak turbulence theory. By estimation of the mean energy flux from the dissipated power, the Kolmogorov-Zakharov constant is evaluated and found to be compatible with the exact theoretical value. The time scale separation between linear, nonlinear interaction, and dissipative times is also observed. These numerical results confirm the validity of the weak turbulence approach to quantify out-of equilibrium wave statistics.

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a liquid by changing its viscosity. We observe that the frequency power-law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the liquid. Here we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be nonconstant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.

We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent as the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by a viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state.