Extreme Rogue Waves

Extreme rogue waves are a phenomenon that occurs when a large wave is generated by a nonlinear process, such as ocean currents. The resulting waves are much larger than a wave that is predicted by linear wave dynamics. This article explores how nonlinearity and dispersion act to generate rogue waves. It also discusses the use of time series analysis to provide a warning to coastal regions about rogue waves.

Asymmetric cross-sectional profile in main wave direction

Rogue waves can be an unexpected and damaging phenomenon. These waves are typically three times faster than regular waves. However, they are rarely observed. They can form in various sea currents, such as the Gulf Stream and Agulhas currents. They can also damage offshore platforms, such as drilling rigs and drilling platforms. It is important to understand the mechanism of rogue waves. Several theories have been proposed to explain their dynamics. Some of them attribute importance to third-order nonlinear effects. Others attribute importance to second-order narrow band models. A more comprehensive study will help determine the most convincing theories. The rogue wave profile is generally asymmetric about the z m parameter. This asymmetry is manifested as an increasing slope of the wave. In addition, the asymmetry is greater for a falling face than for a rising face. For example, a rogue wave profile has a steeper front crest than a back crest. In addition, the z m of a rogue wave is higher than that of a regular wave. This difference indicates the ratio of the heights of the crest and the trough. Generally, the trough behind the crest is deeper than the preceding trough. Rogue waves have been measured in the Draupner platform in the North Sea. This record showed a crest-to-trough height of 2.15H s. A study was conducted to study the asymmetric cross-sectional profile in the main wave direction of extreme rogue waves. Five space-time (ST) records were collected. The ST records were collected by three different stereo wave imaging systems. The wave data were processed using a high order spectral method. Using the method, the asymmetric cross-sectional profiles were calculated for a range of wave intensities and conditions. By comparison, the simulated wave profiles were matched well with the experimental results. Moreover, the study identified frequency-phase focusing as a rogue wave trend. In addition, the study identified the presence of two large crossing wave systems. One of them may be caused by directional focusing, while the other is a result of the dissipation effects of the rogue wave.

Nonlinear action of dispersion and nonlinearity for the coherent build-up of giant waves

The nonlinear action of dispersion and nonlinearity on the coherent build-up of giant waves in the ocean is a fascinating subject. As the waves expand and become undulatory, they require a strong nonlinear interaction for their continued existence. This is known as the Benjamin-Feir instability process. Several experiments have been carried out to examine the effect of such nonlinearity on the formation of dispersive shockwaves. These have been used on small and intermediate hydrodynamic scales. However, these experiments have been limited in the range of nonlocality that they can observe. It is therefore essential to perform simulations using a thermal medium that allows for a tunable degree of nonlocality. In this context, graphene is being investigated for its potential. During numerical simulations of a two-dimensional NLSE model, we found that the self-organized regime, which manifests as the giant shock singularity, is characterized by a dramatic non-homogeneous redistribution of spatial fluctuations. Aside from the obvious self-stepening, a remarkable spectral broadening occurs near the annular boundary. The reconstructed wave field showed that the coherent wave group is indeed present. The envelope of the wave group resembles a directional soliton, which is known to be unstable in transverse perturbation. Similarly, the oblique envelope soliton shows excellent agreement with the structure of the ocean. However, the reconstructed wave field is not yet large enough to capture the full evolution of the wave group. Therefore, SWEAD, an extension of the technique of stereo imaging, was employed to extend the wave field to a domain of around 900 times larger than the image domain. Moreover, we observed a significant coherence enhancement in the internal part of the beam. In addition, the reconstructed wave field demonstrated the existence of a coherent directional wave group. Overall, this result implies that coherent DSWs exist in the ocean. Nevertheless, the nonlinear effects are still apparent in the long term evolution of the system. This suggests that resonant four-wave interactions are still active. However, a major constraint in identifying the coherent envelope was domain limitations. We also performed a series of numerical simulations to investigate the effect of nonlinearity on the wave group.

Larger waves than predicted by linear wave dynamics

One of the biggest challenges faced by wave physicists is understanding how large waves form. As a result, there has been a tremendous amount of research into extreme waves over the past two decades. This includes a wide range of topics, including wave celerity, nonlinear interactions, and the effects of wind. However, there are still many questions that need to be answered. For instance, what causes the nonlinear focusing of wave energy? A number of nonlinear mechanisms contribute to the growth of large waves. Wind-wave interaction is the dominant mechanism. It enhances both the crests and troughs of waves symmetrically. The strength of this interaction increases with increasing wind speed. In addition to wind-wave interaction, nonlinear focusing may also be involved. Previous studies have identified significant deviations from Gaussian form. These deviations indicate modulational instability. They suggest that the occurrence of extreme waves is possible. To determine the effects of nonlinear focusing on large-scale waves, experiments on monochromatic wave trains were performed. Although the sideband energy of the waves remained unchanged, the wave crests and troughs of these waves were intensified. Compared to their linear counterparts, these waves have much larger amplitude. Another interesting aspect of the study was its comparison of long crested waves with the Tayfun and Forristall distributions. Both of these distributions are widely used to predict wave heights. But there is little agreement on their accuracy. Several recent studies have focused on the importance of directional spreading for the prediction of extreme waves. A paper by Latheef and Swan (2013) highlighted this. Similarly, a study by Socquet-Juglard et al. (2005) investigated the influence of spectral evolution on probability distributions. Their results show that the probability of the occurrence of very large waves increases with wind speed. While these findings demonstrate that the effects of wind on nonlinear wave dynamics are complex and varied, they do not demonstrate an obvious relationship between the wave breaking and wave growth. When wind speeds reach a certain level, wave breaking occurs, but this does not affect the statistics of wave growth.

Time series analysis for rogue wave warnings

Rogue wave warnings can be critical to offshore operators. Large waves are capable of overwhelming ocean-going vessels and can cause massive damage and loss. However, these events are rare. The occurrence of rogue waves is dependent on a variety of parameters. Using time series data, the relationship between sea state characteristics and rogue wave occurrence can be investigated. A machine learning tool can be used to extract patterns from a large dataset and find novel links. This method can provide a low computational cost predictor of rogue wave events. In order to study the met-ocean context of rogue wave observations, a dataset was assembled containing time series of surface currents, vessel traffic, wind, and wave data. These time series are then analysed using spectral and time-series techniques. Results showed a power law relationship between rogue wave occurrence and the mean parameters of the sea states. The spectral bandwidth parameters of rogue seas display significantly different probabilities compared to normal seas. The peakedness parameter Qp appears to be slightly higher for extreme rogue samples. Non-rogue samples appear to cluster around medium bandwidth and directional spreading. The data set was used to calculate the peak period, mean significant wave height, and Benjamin-Feir index. These metrics were then plotted against a frequency spectrum. The results show a pronounced directional spreading. This is not a characteristic of a favorable regime for modulational instability. In addition to the time-series data, the ERA5 reanalysis dataset was used to study the met-ocean context. The dataset is based on ECMWF’s IFS Cycle 41r2 and provides complete reanalysis from 1979 to present. It also offers horizontal resolution of 40 km for the ocean component. The dataset is an order of magnitude larger than previous studies. This is important for the analysis of rare events. There are 80 spatially separate time series allowing for an examination of rogue wave occurrence as a function of sea state characteristics. The use of a low computational cost predictor of a rogue wave event is most valuable for offshore operators. However, to be useful, the predictor must be region specific. If you like what you read, check out our other science articles here.