Extreme waves are studied in numerical simulations of the so-called Draupner seas that resemble the wave situation near the observation area of the Draupner wave, an iconic example of a freak, rogue wave. Recent new meteorological insights describe these seas as a substantial wind-generated wave system accompanied by two low-frequency lobes. With the significant wave height \(H_\mathrm{s}=\) 12 m above a depth of 70 m and the wide directional spreading over 120\(^\circ \) as design information, results are presented of simulations of phase resolved waves. Quantitative data are derived from 8000 waves over an area of 15 km\(^2\). Very high waves with crest heights exceeding 1.5 \(H_\mathrm{s}\) occur in average in 20 min timespan over an area of 0.8 km\(^2\). Details will be given for an isolated freak wave and a sequence of 3 freak crest heights in a group of 2 high waves. In Part 2, van Groesen and Wijaya (J Ocean Eng Mar Energy, 2017), it will be shown that 60 s before their appearance freak waves can be predicted from radar images on board of a ship that scans the surrounding area over a distance of 2 km.

In Part 1, Van Groesen et al. (J Ocean Eng Mar Energy, 2017), a numerical study of extreme waves in so-called Draupner seas showed that extreme crest heights of 18 m, one-and-a-half times the significant wave height, occur in a time span of 20 min on average in every area less than 1 km\(^2\). Such extreme, steep waves are dangerous for ships and offshore structures. In this Part 2, we demonstrate that using synthetic images of an X-band radar such high waves can be predicted around 60 s before their actual appearance. It will be shown that a recent dynamic average and evolution scenario (DAES) that has demonstrated to lead to good reconstruction of the sea from distorted shadowed radar images of synthetic seas with moderate wave heights can also be applied to the high seas using nonlinear evolution codes. Taking at one instant a reconstructed sea state to calculate the nonlinear sea in future times leads to a qualitatively good prediction that can warn ships of freak waves before their appearance.

This paper shows simulations of high waves over different bathymetries to collect statistical information, particularly kurtosis and crest exceedance, that quantifies the occurrence of exceptionally extreme waves. This knowledge is especially pertinent for the design and operation of marine structures, safe ship trafficking, and mooring strategies for ships near the coast. Taking advantage of the flexibility to perform numerical simulations with HAWASSI software, with the aim of investigating the physical and statistical properties for these cases, this paper investigates the change in wave statistics related to changes in depth, breaking and differences between long- and short-crested waves. Three different types of bathymetry are considered: run-up to the coast with slope 1/20, waves over a shoal, and deep open-water waves. Simulations show good agreement in the examined cases compared with the available experimental data and simulations. Then predictive simulations for cases with a higher significant wave height illustrate the changes that may occur during storm events.

This paper investigates the wind wave deformations above two isolated shallow seamounts using a phase-resolved wave model simulation using the HAWASSI-AB software. The first seamount is located some 8 km from the south coast of Jawa, Indonesia, near Glagah, with its top area about 2 m from the water level, while the second is the Socotra Rock, in the East China Sea, which has a top 4.6 m under the sea surface. The simulations found that isolated shallow bathymetry may generate a crossing sea region endangering ships. In both domains, short-crested wave simulations of second order show strong refraction and diffraction effects when waves run towards and downstream of the top of the seamount. Waves near the summit embrace the seamount and form a focal area with larger waves downstream. After crossing the Socotra Rock, the interaction waves lead to a crossing sea in the deep water. On the other hand, having passed the Glagah, waves further downstream are partly absent over a substantial stretch of the coast. For both cases, the phase-resolved wave simulation results determine detailed wind wave conditions and wave spectra over the whole area, compensating for a lack of experimental data.