Rogue waves, rogue events and extreme wave kinematics in spatio-temporal fields of simulated sea states

A Sergeeva,A Slunyaev

doi:10.5194/nhess-13-1759-2013

Abstract

Abstract. An approach to the extensive study of rogue wave occurrence in numerical simulations is presented. As a result of numerical simulations of the unidirectional wave evolution, spatio-temporal fields of wave data of the size 20 min × 10 km are obtained with high resolution in time and space and are used for statistical analysis with the focus on extreme waves. Having the exhaustive information on the wave evolution enables us to capture the detailed picture of individual rogue waves; to detect intermittent rogue wave events, which last for a significantly longer time, and hence, to depict the portrait of a rogue wave. Due to the benefit of having full-wave data, the question of relation between extreme wave kinematics and extremely high waves is discussed in the statistical sense.

Highlights

1 Introduction tool for studying stochastDicawtaaveSyevsotleutmions. Such experiments have been performed by many authors
Though main physical mechanisms which can cause these waves seem to be formulated, realistic sea waves represent a quite complex object for investigation, so that the very vital problems: what rogue waves look like, how long they live and how probable they are to occur have not been answered with certainty so 2003; 2005, J2a0n0s9se;nG, 2ra0m03s;taSdocaqnGudeteT-Jrouuglsslecanrid,ee2nt0at0li7.f,;ic2A00n5n;enCkhoavlikaonvd, Shrira, 2009; aMnd oladboeraltoDryeevxpeelroimpemntsebny tOnorato et al, 2005, 2009; Mori et al, 2007; and many others), including the authors of the present study, see numerical simulations
We introduce the concept of a rogue event, which incorporates shorter-living extreme waves, which overpass the formal height criterion on a rogue wave with brief interruptions

Summary

Numerical model

The primitive equations of potential hydrodynamics for the surface displacement η(x, t) and the surface velocity potential (x, t) = φ(x, t, z = η) have the form. Equation (3) is the Laplace equation for the velocity potential φ(x, z, t), Eqs. (1)–(4) are integrated by means of a high-order spectral method (HOSM), see The HOSM is not a fully-nonlinear, but a strongly nonlinear algorithm, which resolves the wave-wave interactions up to the predetermined order M (for M = 3 the HOSM approach has the same accuracy as the Zakharov equation (Zakharov, 1968)). The case M = 6 was shown to correspond to a nearly fully nonlinear case, see the discussion in (Clamond et al, 2006)

Initial conditions and preparation of the sea state

Analysis of the spatio-temporal surface elevations

Pictures of rogue waves and rogue events

Findings

Conclusions