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Experiments by Invited Researchers

 

Experimental study of a random nonlinear wave field in a tank

Project acronym: HyIII-FZK-11
Name of Group Leader: Lev Shemer, Tel - Aviv University
User-Project Title: Experimental study of a random nonlinear wave field in a tank
Facility: Large Wave Flume, GWK
Proceedings TA Project: Effect of the initial spectral shape on the evolution of random unidirectional wave field along the tank
Data Management Report: There is no Data Management Report available for this project

User-Project Objectives

Summary:

Nonlinear interactions of ocean waves are usually statistical in nature. Kinetic theory of random ocean wave field is based on two fundamental assumptions: weak nonlinearity of waves and randomness of their phases. The random phase approximation is an essential assumption used for turbulent closures for all stochastic wave systems and even for a much broader range of turbulent systems.

Numerous attempts have been made to explore the possibility to use nonlinear wave theories for forecast of evolution of a random wave field. These works reveal the crucial role of non-resonant interactions in the evolution of nonlinear random water waves.

Experiments in a wave tank, where no exact resonances may exist since only near-esonantinteractions between unidirectional waves are possible, serve as an ideal vehicle to study nonlinear random waves in laboratory conditions. The problem of unusually steep (the so-called freak, or rogue) waves attracts particular interest. Such waves, often dubbed killer-waves, appear and disappear fast and unexpectedly, and have a potential of causing substantial damage to marine traffic.

The relatively high occurrence of those waves that exceeds the predictions based on the adopted statistical descriptions suggests that freak waves are abnormal and should be investigated in depth. Thus the objective of the project is to investigate variation along the tank of various statistical properties of the wave field that are of relevance to appearance of those waves.

In the course of this project we have different spectral shapes of random wave fields, ranging from very narrow to relatively wide, as observed in the ocean (the so-called JONSWAP spectrum). For each spectral shape, experiments were performed for the same level of nonlinearity, which is characterized by the r.m.s. values of the surface elevation.

The effects of both the spectral shape and the spectral width could thus be analyzed for fixed value of the nonlinearity parameter. In addition, for 3 spectral shapes experiments were carried at higher amplitudes, thus allowing examining the effect of nonlinearity. For stronger nonlinearity, wave breaking occurred in some realizations.

For every set of experimental parameters, about 50 independent realizations of identical spectra, with random initial phases of each frequency harmonics, were generated by the GWK wavemaker. Convenient graphic interface was written allowing fast adjustment of the wavemaker driving signal to obtain the required shape.

For each set of experimental parameters the variation along the tank of numerous statistical parameters of the random wave field were analysed, including the frequency spectra, the spectral width, the r.m.s values of the surface elevation, the higher moments (skewness and kurtosis), and the probability distributions of the wave heights, wave crests and wave troughs.

It appears that the character of variation of those parameters with the distance from the wavemaker is strongly affected by the initial spectral width. For narrow initial spectrum, the statistical parameters vary significantly along the tank. The spectrum widens at the initial stage of the evolution; while the values of skewness and in particular of kurtosis are increasing significantly.

The widening of the spectrum and increase in kurtosis are accompanied by notable increase in the probability of extremely large (freak) waves. Farther away from the wavemaker, the spectrum becomes narrower, and the deviation of all other parameters from Gaussianity also decreases. As the initial spectrum becomes wider, the variation of all statistical parameters along the tank, while still significant in most cases, becomes less dramatic.

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