Abrupt depth transitions (ADTs) have recently been identified as potential causes of 'rogue' ocean waves. When stationary and (close-to-) normally distributed waves travel into shallower water over an ADT, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show, by comparing to new experiments and numerical simulations, that the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the ADT, and new second-order free waves generated due to the ADT.@en

Recent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown that the key physics underlying these increases can be captured by a weakly dispersive and weakly nonlinear Boussinesq-type model. In the present paper, a numerical model based on an alternative Boussinesq-type formulation is used to repeat these earlier simulations. Although qualitative agreement is achieved, the present model is found to be unable to reproduce accurately the findings of the earlier study. Model parameter tests are then used to demonstrate that the present Boussinesq-type formulation is not well-suited to modelling the propagation of waves over sudden depth transitions. The present study nonetheless provides useful insight into the complexity encountered when modelling this type of problem and outlines a number of promising avenues for further research.

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Recent experimental and numerical studies of surface gravity waves propagating over a sloping bottom have shown that an increase in the probability of extreme waves can be triggered by depth variations in sufficiently shallow waters. This phenomenon is studied here by means of a boundary element method with fast multipole acceleration to solve the fully nonlinear water wave equations. We focus on the case of a random, unidirectional wave field with prescribed statistical properties propagating over a submerged slope and consider different depth variations, including a step. Validation is provided by comparing with experiments by Trulsen, Zeng, and Gramstad [Phys. Fluids 24, 097101 (2012)PHFLE61070-663110.1063/1.4748346]. Strongly non-Gaussian statistics are observed in a region localized near the depth transition, beyond which the statistics settle rapidly to the steady statistical state of finite-depth random wave fields. Using a harmonic separation technique, we show that the second-order terms are responsible for the change in the statistical properties near the depth transition. We explore in detail the effects of peak frequency, significant wave height, the inclination of the slope, and the depth of the shallower water side on the kurtosis, skewness, and the excess probability of the crest height, including their spatial distributions.

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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.

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