Observation of gravity-capillary wave turbulence

We report the observation of the cross-over between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes

Observation of intermittency in wave turbulence

We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density function of the local slope increments of the surface waves strongly changes across the time scales. The related structure functions and the flatness are found to be power laws of the time scale on more than one decade. The exponents of these power laws increase nonlinearly with the order of the structure function. All these observations show the intermittent nature of the increments of the local slope in wave turbulence. We discuss the possible origin of this intermittency.Comment: new version to Phys. Rev. Let

Freely decaying weak turbulence for sea surface gravity waves

We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler equations for gravity waves in infinitely deep water. In agreement with the theory of Zakharov and Filonenko, we find the formation of a power spectrum characterized by a power law of the form of $|{\bf k}|^{-2.5}$.Comment: 4 pages, 3 figure

A Laboratory Study of Nonlinear Surface Waves on Water

This paper describes an experimental investigation in which a large number of water waves were focused at one point in space and time to produce a large transient wave group. Measurements of the water surface elevation and the underlying kinematics are compared with both a linear wave theory and a second-order solution based on the sum of the wave-wave interactions identified by Longuet-Higgins & Stewart (1960). The data shows that the focusing of wave components produces a highly nonlinear wave group in which the nonlinearity increases with the wave amplitude and reduces with increasing bandwidth. When compared with the first- and second-order solutions, the wave-wave interactions produce a steeper wave envelope in which the central wave crest is higher and narrower, while the adjacent wave troughs are broader and less deep. The water particle kinematics are also strongly nonlinear. The accumulated experimental data suggest that the formation of a focused wave group involves a significant transfer of energy into both the higher and lower har¬monics. This is consistent with an increase in the local energy density, and the development of large velocity gradients near the water surface. Furthermore, the nonlinear wave-wave interactions are shown to be fully reversible. However, when compared to a linear solution there is a permanent change in the relative phase of the free waves. This explains the downstream shifting of the focus point (Longuet-Higgins 1974), and appears to be similar to the phase changes which result from the nonlinear interaction of solitons travelling at different velocities (Yuen & Lake 1982)

Understanding rogue waves: Are new physics really necessary? 14th Aha Huliko'a Hawaiian Winter Workshop

Abstract. The standard model of ocean waves describes them as the superposition of many wavelets with different frequencies and directions of travel. Nonlinearities are assumed to be small enough that they can be handled by a perturbation expansion. This model has served us well, leading to accurate predictions of directional wave spectra, wave statistics, and wave kinematics. Yet there remain some observations which are difficult to explain with the standard model. Strongly nonlinear physical processes have been invoked to explain the existence of very large, or rogue waves. Are these new models really necessary to explain the observations? There are several reasons why we may not need to invoke new physics. First, measuring rare events in extreme conditions in the ocean is very difficult. There is a significant possibility of substantial instrument error. There are well- documented cases where carefully calibrated wave recorders on the same platform gave very different readings. The most striking examples of rogue waves in the recent literature are unusually asymmetrical with high crests compared to the depth of their troughs. Second order perturbation theory produces crests in steep waves that are at least 10 % higher than those given by the Rayleigh distribution, and higher order approximations show further increases. If only the short record in which a large wave occurs is considered, then it will stand out as an outlier. When more data is considered, these very large waves seem less aberrant. Sometimes waves are measured over an area, as by remote sensing, or estimated over an area, as by damage observed on the deck of a platform. In such cases, statistical theory shows that we should expect higher maximum wave crests than those measured at a point measurement since more waves are effectively sampled