Abrupt changes in water depth are known to lead to abnormal free-surface wave statistics. The present study considers whether this translates into abnormal loads on offshore infrastructure. A fully non-linear numerical model is used which is carefully validated against experiments. The wave kinematics from the numerical model are used as input to a simple wave loading model. We find enhanced overturning moments, an increase of approximately 20%, occur over a distance of a few wavelengths after an abrupt depth transition. We observe similar results for 1:1 and 1:3 slopes. This increase does not occur in linear simulations.@en

An increased number of rogue waves, relative to standard distributions, can be induced by unidirectional waves passing over abrupt decreases in water depth. We investigate this phenomenon in a more general setting of multidirectional waves. We examine the influence of the directionality on the occurrence probability of rogue waves using laboratory experiments and fully nonlinear potential flow simulations. Based on the analysis of the statistics of random waves, we find that directional spreading reduces the formation probability of rogue waves relative to unidirectional seas. Nevertheless, for typical values of directional spreading in the ocean (15∘–30∘), our numerical results suggest that there is still a significant enhancement to the number of rogue waves just beyond the top of a depth discontinuity.@en

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. @en

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. @en

Wave breaking is the main mechanism that dissipates energy from ocean waves by wind. Its effects on the frequency spectrum cause a downshift of the spectral peak and dissipation of the total energy of the spectrum. Various reduced-form wave breaking models have been developed to capture wave breaking in envelope-based wave evolution equations for perturbed plane-wave systems, but their applicability to waves with a continuous spectrum has not been examined. In this paper we perform modified nonlinear Schrödinger equation simulations to study four existing wave breaking models and compare the results with new experimental data for breaking unidirectional wave groups. We first compare the different wave breaking models for perturbed plane-wave simulations and then examine their potential extension to waves with a continuous spectrum. We find that most existing models are able to model breaking in perturbed plane waves, but none produce the correct spectral dissipation for focused wave groups. We propose a modification to the breaking model by Kato and Oikawa [J. Phys. Soc. Jpn. 64, 4660 (1995)0031-901510.1143/JPSJ.64.4660] in order to model breaking in focused wave groups. The modified model incorporates both a breaking criterion, which activates and deactivates the dissipation term proposed by Kato and Oikawa, and a heuristic spectral weighting function that is obtained by fitting to experimental data. The modified model also predicts breaking in perturbed plane waves well. @en

When making directional surface gravity waves in a wave tank or when initialising numerical simulations of the ocean, the wave spectrum is often curtailed suppressing higher frequencies and wavenumbers. We consider the impact of doing this by numerically simulating two seminal experiments, those of Onorato et al. (J. Fluid Mech., vol. 627, 2009, pp. 235–257, R2) and Latheef & Swan (Proc. R. Soc. A, vol. 469, no. 2152, 2013, p. 20120696). We simulate waves using a fully nonlinear potential-flow model. We find that curtailing the spectrum can have a significant impact on the subsequent evolution. In particular, for cases where the spectrum has been curtailed, the nonlinear physics produces significantly more extreme or rogue waves than are observed in the case where the full spectral tail was included in the initial conditions, and this difference persists over tens of periods after the waves are initialised. This suggests that sea states that are ‘out of equilibrium’ (i.e. with their tails removed) can produce a greater number of rogue waves. We show this can also have an impact on predicted loads on offshore infrastructure.@en

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.@en

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.@en