The Zakharov integral equation for surface gravity waves is modified to include higher-order (quintet) interactions, for water of constant (finite or infinite) depth. This new equation is used to study some aspects of class I (4-wave) and class II (5-wave) instabilities of a Stokes wave.

[1] Unidirectional random waves generated by a wavemaker in a 300-m-long wave tank are investigated experimentally. Spatial evolution of numerous statistical wavefield parameters is studied. Three series of experiments are carried out for different values of the nonlinear parameter e. It is found that the frequency spectrum of the wavefield undergoes significant variation in the course of the wavefield evolution along the tank. The initially narrow Gaussian spectrum becomes wider at the early stages of the evolution and then narrower again, although it still remains wider than the initial spectrum at the most distant measuring location. It is found that the values of all the statistical wave parameters are strongly related to the local spectral width. The deviations of various statistical parameters from the Gaussian statistics increase with the width of the spectrum so that the probability of extremely large (the so-called freak) waves is highest when the local spectral width attains maximum. The deviations from the Rayleigh distribution also become more pronounced when the nonlinearity parameter e is higher. It is found that the Tayfun and Fedele 3rd order random wavefield model provides an appropriate description of the observed phenomena. An attempt is made to relate the spatial variations of the wavefield statistics reported here to the wavefield recurrence, as suggested recently.Citation: Shemer, L., and A. Sergeeva (2009), An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield,

Despite a significant progress and numerous publications over the last few decades a comprehensive understanding of the process of waves' excitation by wind still has not been achieved. The main goal of the present work was to provide as comprehensive as possible set of experimental data that can be quantitatively compared with theoretical models. Measurements at various air flow rates and at numerous fetches were carried out in a small scale, closed-loop, 5 m long wind wave flume. Mean airflow velocity and fluctuations of the static pressure were measured at 38 vertical locations above the mean water surface simultaneously with determination of instantaneous water surface elevations by wave gauges. Instantaneous fluctuations of two velocity components were recorded for all vertical locations at a single fetch. The water surface drift velocity was determined by the particle tracking velocimetry (PTV) method. Evaluation of spatial growth rates of waves at various frequencies was performed using wave gauge records at various fetches. Phase relations between various signals were established by cross-spectral analysis. Waves' celerities and pressure fluctuation phase lags relative to the surface elevation were determined. Pressure values at the water surface were determined by extrapolating the measured vertical profile of pressure fluctuations to the mean water level and used to calculate the form drag and consequently the energy transfer rates from wind to waves. Directly obtained spatial growth rates were compared with those obtained from energy transfer calculations, as well as with previously available data.

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We observe the propagation dynamics of surface gravity water waves, having an Airy function envelope, in both the linear and the nonlinear regimes. In the linear regime, the shape of the envelope is preserved while propagating in an 18-m water tank, despite the inherent dispersion of the wave packet. The Airy wave function can propagate at a velocity that is slower (or faster if the Airy envelope is inverted) than the group velocity. Furthermore, the introduction of the Airy wave packet as surface water waves enables the observation of its position-dependent chirp and cubic-phase offset, predicted more than 35 years ago, for the first time. When increasing the envelope of the input Airy pulse, nonlinear effects become dominant, and are manifested by the generation of water-wave solitons.

This paper is dedicated to Professor Gad Hetsroni on the occasion of his 65th birthday. Gad, through his leadership and devotion to science in general and multiphase¯ows in particular, has been the beacon of this ®eld. As the Founder and the Editor of the International Journal of Multiphase Flow, Gad has marched this ®eld forward at a rapid pace and positioned it at the focus of science and engineering. We would like to express our deep gratitude to Gad for all he has done for the ®eld of multiphase¯ow and we wish him many more productive and enjoyable years. AbstractThe motion of a single elongated (Taylor) bubble propagating in a transparent vertical pipe is studied experimentally in stagnant liquid, as well as in upward and downward liquid¯ow. Digital image processing of a sequence of video images serves as the main experimental method for the study of the Taylor bubble motion. In addition, the distribution of the velocities in front of the bubble and in the liquid ®lm is measured using Particle Image Velocimetry. The relation between the Taylor bubble motion and the velocity ®eld in front of it is discussed. #

An experimental investigation of the flow field around a single Taylor bubble rising in a vertical pipe filled with stagnant water is presented. The Reynolds number of the flow based on the Taylor bubble rise velocity and the pipe diameter is 4350. The velocity field around the bubble was determined by Particle Image Velocimetry (PIV). The mean velocity fields in front of the bubble, in the liquid film, and in the wake region were calculated by ensemble-averaging the instantaneous velocity fields measured around 100 different bubbles. Ensemble-averaged velocities become negligible at 0.5D from the bubble nose and at $12 D from the bubble tail. However, notable instantaneous velocity fluctuations were found to exist up to 50D from the Taylor bubble tail. These residual vortices may influence the shape and the propagation velocity of the trailing bubble even at large separation distances. Ó

Results of experiments on the evolution of the Peregrine breather (PB) in a wave tank are presented and compared with numerical simulations based on the Nonlinear Schrödinger (NLS) and the Dysthe equations. The experiments demonstrate notable deviation from the NLS solution due to significant asymmetric widening of the spectrum. Good agreement of measurements with the solutions of the Dysthe equation is obtained. Contrary to the PB NLS soliton, no return to the initial undisturbed wave train can be expected.