Rogue waves in opposing currents: an experimental study on deterministic and stochastic wave trains

Interaction with an opposing current amplifies wave modulation and accelerates nonlinear wave focusing in regular wavepackets. This results in large-amplitude waves, usually known as rogue waves, even if the wave conditions are less prone to extremes. Laboratory experiments in three independent facilities are presented here to assess the role of opposing currents in changing the statistical properties of unidirectional and directional mechanically generated random wavefields. The results demonstrate in a consistent and robust manner that opposing currents induce a sharp and rapid transition from weakly to strongly non-Gaussian properties. This is associated with a substantial increase in the probability of occurrence of rogue waves for unidirectional and directional sea states, for which the occurrence of extreme and rogue waves is normally the least expected.

Advances in Nonlinear Waves With Emphasis on Aspects for Ship Design and Wave Forensics

Prof. D. Faulkner emphasized the importance of the study of extreme/rogue waves when he noted that the use of sine waves for computing pressures in the design of ships was no longer tenable, primarily because of the large number of cases where extreme structural damage has been encountered due to highly nonlinear large waves. This perspective resulted in the creation of the European program MaxWave and the subsequent program Extreme Seas soon followed. Recently my own studies of nonlinear effects in water waves at Nonlinear Waves Research Corporation (NWRC) have resulted in a number of successes with regard to the fundamental physical understanding of rogue waves. These studies enlarge our ability to understand the requisite impact of extreme waves on the design of ships. Some of these advances are: (1) The determination of analytical techniques for describing rogue wave packets in two dimensions for random sea states which are directionally spread. (2) The description of wave overturning and breaking in directional sea states with the Type II (lateral) instability. (3) The development of hyperfast computer models for the deterministic simulation of directional sea states. (4) The development of a fast approach for computing the full Boltzmann integral (FBI) for the nonlinear wave/wave interactions in wind/wave models. (5) The identification of the actual physical location in the power spectrum for the nonlinear Fourier rogue wave components. (6) The development of nonlinear Fourier techniques for analyzing times series of ocean waves for the presence of rogue wave states. (7) The development of fully nonlinear directional spectra (in terms of frequency and direction) from arrays of instruments. (8) The development of hindcasting and predicting capability for the assessment of the onset of a rogue sea. I also discuss a number of future developments now underway at NWRC.

A Semi-Empirical Wave Crest Distribution of Random Directional Wave Fields

Laboratory data of random directional wave fields have been used to investigate the combined effect of higher order nonlinearity and directional spreading on the wave crest distribution. Different sea states with a variety of combination of steepness and directional spreading have been considered, ranging from long to short crested wave fields. The analysis is also supported by numerical simulations. A 2-parameter Weibull distribution has been fitted to the experimental data and the related parameters have been parameterized as a function of a general version of the Benjamin-Feir Index for directional sea states recently presented by Mori et al. [1]. Long-term distributions of the one-dimensional and two-dimensional Benjamin-Feir Index have been studied based on the hindcast data from the North Atlantic and probabilistic models to describe them are proposed.

On the Estimation of the Kurtosis in Directional Sea States for Freak Wave Forecasting

Based on Monte Carlo simulations of the nonlinear Schrödinger equation in two horizontal dimensions, the dependence of the kurtosis on the directional energy distribution of the initial conditions is examined. The parametric survey is carried out to obtain the behavior of the kurtosis as function of the Benjamin–Feir index and directional spread in directional sea states. As directional dispersion effect becomes significant, the kurtosis monotonically decreases in comparison with the unidirectional waves. A parameterization of the kurtosis estimated from directional spectra is proposed here; the error of the parameterization is at most 10%. The parameterization is verified against laboratory data, and good agreement is obtained.

Mooring Analysis of a Weathervaning FPSO in Bi-Directional Sea-States

Experimental studies were carried out at the Institute for Ocean Technology, Canada, in collaboration with the University of Western Australia (UWA) to assess the response of a moored 1:60 scaled Floating Production Storage and Offloading (FPSO) model in bi-directional seastates. The seastates comprise of a regular swell approaching in the head sea condition, and a JONSWAP wind sea approaching at various angles. The FPSO was moored in position by four spring-loaded mooring lines attached to an internal turret about which the model could weathervane. Previous papers by the authors have described the unpredictable yaw instability of the FPSO driven by long period swells, which was evidenced in the experiments. This creates difficulties in comparing motions from unidirectional and bi-directional seas, because the headings alter the response. However, the mooring tensions are relatively immune to yaw instabilities and this paper discusses effects of bi-directional seas on the mooring tensions. Numerical simulations are conducted using a time domain analysis software which simulates the motions of floating and moored structures in response to irregular seas. Simulations based on the software when compared with model tests at 45, 60 and 90 deg separation between the sea and swell shows reasonable agreement in terms of mooring tensions. Simulations are then conducted for a range of separation angles, and the effects of bi-directionality are further evaluated. It is found that a linear addition of the individual seastates can produce non-conservative results, which reinforces the fact that bi-directional seastates are important considerations for offshore operations of an FPSO.

The evolution of large ocean waves: the role of local and rapid spectral changes

This paper concerns the formation of large-focused or near-focused waves in both unidirectional and directional sea-states. When the crests of wave components of varying frequency superimpose at one point in space and time, a large, transient, focused wave can occur. These events are believed to be representative of the largest waves arising in a random sea and, as such, are of importance to the design of marine structures. The details of how such waves form also offer an explanation for the formation of the so-called freak or rogue waves in deep water. The physical mechanisms that govern the evolution of focused waves have been investigated by applying both the fully nonlinear wave model of Bateman et al . (Bateman et al . 2001 J. Comput. Phys . 174 , 277–305) and the Zakharov's evolution equation (Zakharov 1968 J. Appl. Mech. Tech. Phys . 9 , 190–194). Aspects of these two wave models are complementary, and their combined use allows the full nonlinearity to be considered and, at the same time, provides insights into the dominant physical processes. In unidirectional seas, it has been shown that the local evolution of the wave spectrum leads to larger maximum crest elevations. In contrast, in directional seas, the maximum crest elevation is well predicted by a second-order theory based on the underlying spectrum, but the shape of the largest wave is not. The differences between the evolution of large waves in unidirectional and directional sea-states have been investigated by analysing the results of Bateman et al . (2001) using a number of spectral analysis techniques. It has been shown that during the formation of a focused wave event, there are significant and rapid changes to the underlying wave spectrum. These changes alter both the amplitude of the wave components and their dispersive properties. Importantly, in unidirectional sea-states, the bandwidth of the spectrum typically increases; whereas, in directional sea-states it decreases. The changes to the wave spectra have been investigated using Zakharov's equation (1968). This has shown that the third-order resonant effects dominate changes to both the amplitude of the wave components and the dispersive properties of the wave group. While this is the case in both unidirectional and directional sea-states, the consequences are very different. By examining these consequences, directional sea-states in which large wave events that are higher and steeper than second-order theory would predict have been identified. This has implications for the types of sea-states in which rogue waves are most likely to occur.

Drift Motions of a Floating Barge in Random Multi-Directional Waves

This paper presents results of a numerical and laboratory investigation into the mooring line forces and slow drift oscillations of large floating structures in multidirectional waves. A procedure for computing the spectral density of the second-order forces in random multi-directional waves based on the concept of a bidirectional, bifrequency quadratic transfer function is presented. Laboratory tests were carried out with a floating barge model, restrained horizontally by soft linear springs. The barge was subjected to random multi-directional waves with different degrees of directional spreading. The influence of wave directionality on the mooring line forces and low frequency motions is investigated by comparing results in unidirectional and multi-directional sea states with an identical frequency spectrum. The results indicate a significant reduction of the mean and standard deviation of the surge response, and an increased sway and yaw response. The mooring line forces were affected by wave directionality in a similar manner as the surge response.