High waves in Draupner seas—Part 1: numerical simulations and characterization of the seas

Abstract

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 s = 12 m above a depth of 70 m and the wide directional spreading over 120 • 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 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.

Laboratory recreation of the Draupner wave and the role of breaking in crossing seas

“…It has also been shown that for certain angles, crossing seas may also enhance the occurrence of modulational instability (Onorato, Osborne & Serio 2006;Toffoli et al 2011b;Cavaleri et al 2012). For the Draupner wave in a water depth d = 70 m and with a zero-crossing period T z = 12.5 s, the non-dimensional water depth kd = 1.6 (k is the wavenumber) is probably not sufficiently above the limit of 1.36 for modulational stability to have played an important role (Cavaleri et al 2016) Beyond its overall wave height of h = 25.6 m (height abnormality index h/H s = 2.13, where H s is the significant wave height, defined as four times the standard deviation of the surface elevation) and crest height of a = 18.5 m (crest abnormality index a/H s = 1.55), the Draupner wave is exceptional in a number of other ways (see Janssen 2015;Cavaleri et al 2016;van Groesen, Turnip & Kurnia 2017, for a discussion of its likelihood). First, the wave group itself was accompanied by what is most probably a set-up of the wave-averaged free surface, whereas a set-down is expected in the absence of crossing (Walker et al 2004).…”

Spectral AB Simulations for Coastal and Ocean Engineering Applications

“…The a posteriori simulation of generated waves can, for instance, be used to take the Fig. 5 The 2D spectrum as shown in [8] based on [16] Fig. 6 Plot of the sea state at time 2048.7 s looking from south (bottom) to north over the whole observation area.…”

“…To compensate for outflow in the simulation domain, in Sect. 3.3 we use data-assimilated influx, for which repeatedly known field data in a subdomain (instead of from a line) are merged with waves from an ongoing simulation in the complementary remaining domain [8].…”

“…In [8] we simulated such seas in a large area, using data-assimilated influx of linear waves along a circular arc, and investigated details in a much smaller rectangular area of 15 km 2 where nonlinear effects, including four-wave interaction, have This sea has H s 12.1 m and T p 15 s, and the largest crest height in the simulation of 200 waves for this sea was found to be a freak wave of 20 m crest height, more than 1.6 H s . From statistical results [8], the probability of such a crest height in this sea is as high as 1.85 × 10 −9 /m 2 per period, i.e. can be expected on an area of 1 km 2 almost once every 2 h. An impression of the sea elevation at the time of the freak event is shown in a neighbourhood of the freak wave in Fig.…”