Understanding the effect of wind forcing on steep unidirectional waves is important for the study of wind-wave interaction. In this paper, unidirectional random wave experiments are carried out in a large-scale wave tank in which waves interacted with turbulent wind generated by wind fans. The properties and evolution of deep-water gravity waves subject to following wind forcing are investigated through parametric laboratory experiments. The effect of wind forcing on the significant wave height varies with the initial wave steepness. Wind forcing increases the growth of waves of small initial steepness but attenuates large, steep waves as a result of the vertical angle of the wind to the free surface in our experiments. The energy input by wind forcing increases the high-frequency tail of the wave spectra, and this effect increases with fetch. The mean frequency increases under wind forcing. The effect of wind forcing on the probability of extreme events is investigated. Wind forcing enhances wave steepness, resulting in a deviation of the exceedance probability from first-order and second-order theoretical distributions and an increased value of kurtosis but not skewness.

We study the evolution of unidirectional water waves from a randomly forced input condition with uncorrelated Fourier components. We examine the kurtosis of the linearised free surface as a convenient proxy for the probability of a rogue wave. We repeat the laboratory experiments of Onorato et al. (Phys. Rev. E, vol. 70, 2004, 067302), both experimentally and numerically, and extend the parameter space in our numerical simulations. We consider numerical simulations based on the modified nonlinear Schrödinger equation and the fully nonlinear water wave equations, which are in good agreement. For low steepness, existing analytical models based on the nonlinear Schrödinger equation (NLS) are found to be accurate. For cases which are steep or have very narrow bandwidths, these analytical models over-predict the rate at which excess kurtosis develops. In these steep cases, the kurtosis in both our experiments and numerical simulations peaks before returning to an equilibrium level. Such transient maxima are not predicted by NLS-based analytical models. Above a certain threshold of steepness, the steady-state value of kurtosis is primarily dependent on the spectral bandwidth. We also examine how the average shape of extreme events is modified by nonlinearity over the evolution distance, showing significant asymmetry during the initial evolution, which is greatly reduced once the spectrum has reached equilibrium. The locations of the maxima in asymmetry coincide approximately with the locations of the maxima in kurtosis.

Many ocean engineering problems involve bound harmonics which are slaved to some underlying assumed close to linear time series. When analyzing signals we often want to remove the bound harmonics so as to "linearise" the data or to extract individual bound harmonic components so that they may be studied. For even moderately broadbanded systems filtering in the frequency domain is not sufficient to separate components as they overlap in frequency. One way to overcome this difficulty is to use input signals with the same linear envelope but with different phases and then use simple addition and subtraction of the resulting signals to extract different harmonics. This approach has been established for the analysis of wave groups. In this paper we examine whether this approach can be used on random time series as well. We analyse random wave time series of wave elevation from the towing tank in Shanghai Jiao Tong University and force measurements on a cylinder taken in the Kelvin tank at the University of Strathclyde.