Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

Abstract

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasiequilibrium states characterized by JONSWAP spectra. The spatio-temporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases (k p h > 0.8, where k p is the peak wavenumber, and h is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths. The lifetimes of rogue events may reach up to 30-60 wave periods depending on the water depth. The maximum observed wave has height of about 3 significant wave heights. A few randomly chosen in-situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.

A statistical analysis of rogue waves in the southern North Sea

“…For rogue waves of moderate relative wave heights and wave steepness, numerical studies indicate no fundamental differences between rogue wave frequencies when upcrossing or downcrossing approaches were taken (e.g., Sergeeva and Slunyaev, 2013). However, for extreme rogue waves whose heights exceed 8σ in very steep wave conditions, numerical simulations suggested differences in frequencies when upcrossing or downcrossing definitions were used (Slunyaev et al, 2016). For in situ measurements, de Pinho et al (2004) reported increased rogue wave frequencies when zero upcrossing approaches were taken.…”

Lifetimes of Rogue Wave Events in Direct Numerical Simulations of Deep-Water Irregular Sea Waves

“…In the experimental condition the set of 2D rogue events could be collected if one follows the evolution of sea waves along a straight line (for example, having an array of wave gauges along the direction of wave propagation). The 2D rogue events were previously analyzed in the strongly nonlinear simulations of strictly collinear waves reported in [Sergeeva & Slunyaev, 2013;Slunyaev et al, 2016;Slunyaev & Kokorina, 2017]. The data from those simulations are used in the present work (see series A0 and E0 in Table 1; they are studied in Sec.…”

“…In this section we analyze the dataset of simulations of irregular strictly planar waves accumulated in our previous works [Sergeeva & Slunyaev, 2013;Slunyaev et al, 2016;Slunyaev & Kokorina, 2017], see series A0 and E0 in Table 1. In this case the procedure of selection of the rogue events is equivalent to collecting 2D rogue wave events as described above.…”

Rogue Wave Asymmetry in the Direct Numerical Simulations of Directional Jonswap Waves

“…The asymmetry between the troughs from the rear and front sides of rogue waves is the particular object of the present study. In our previous simulations of unidirectional waves the typical picture of a rogue waves possesses the trend that most of the rogue waves where characterized by deeper rear troughs (Sergeeva & Slunyaev, 2013;Slunyaev et al, 2016). In the present work we broaden the discussion of the rogue wave frontto-crest asymmetry to the directional case (Slunyaev & Kokorina, 2020).…”