Reconstruction of Extreme Events Through Numerical Simulations

Abstract

In this paper, some abnormal or rogue wave events registered in the North Sea by means of the surface elevation measurements are reconstructed with the help of theoretical models for water waves and numerical simulations of wave evolution. Time series of surface elevation, which are measured at a single point, provide incomplete information about the waves. The registered time series are used to restore the wave dynamics under reasonable assumptions. Different frameworks associated with the relation between the surface elevation and the fluid velocity fields are considered, and different numerical models are used to simulate the wave dynamics in time and space. It is shown that for some abnormal or rogue wave records the result of the e.xtreme event reconstruction is robust. In particular, the verification of approximate approaches versus the fully nonlinear numerical simulation is peiformed. The reconstructed rogue wave is generally less steep than the measured one. Possible reasons for this discrepancy are suggested.

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

“…Numerical modeling performed with a higher-order nonlinear Schrödinger equation can provide more information, as shown in the comparison with real data from field experiment collected in the WACSIS JIP (WAve Crest Sensor Intercomparison Study) done in the work of Liu et al (2005), as well as in other studies that dealt with full-scale data (Slunyaev et al, 2005(Slunyaev et al, , 2013.…”

Numerical modeling of rogue waves in coastal waters

“…The rogue wave evolution is reconstructed on the basis of in situ instrumental records of the surface elevation in the manner similar to Trulsen (2001), Slunyaev et al (2005Slunyaev et al ( , 2014, and Slunyaev (2006). The asymptotic equations for surface water waves, which describe wave evolution in space, are solved numerically.…”

“…This procedure assumes that the in situ surface elevation time series η(t) are described by the deep-water Dysthe theory for weakly nonlinear weakly modulated wave trains. This assumption means that the second-and third-order wave corrections and also the large-scale wave-induced flow are taken into account (see details of the approach in Trulsen (2001Trulsen ( , 2006, Slunyaev (2005), and Slunyaev et al (2014)). Similarly, the bound wave harmonics are computed for a given B(t) to produce the surface elevation function η(t).…”

“…As a result, not only can much more detailed wave information in the vicinity of the measurement point be obtained, but also the rogue wave evolution can be recovered. Importantly, application of the weakly nonlinear theory for wave modulations is able to produce reliable results even for very steep modulated waves (Slunyaev et al, 2014). A credible reconstruction of the wave dynamics was possible for about 10 min.…”

“…Under these assumptions the surface wave dynamics can be considered as one-dimensional, for which the boundary value problem becomes in principle treatable. Numerical reconstruction of the evolution of such wave systems on the basis of instrumental records was performed in Trulsen (2001), Divinsky et al (2004), Slunyaev et al (2005Slunyaev et al ( , 2014, and Slunyaev (2006) by means of approximate evolution equations for modulated waves. As a result, not only can much more detailed wave information in the vicinity of the measurement point be obtained, but also the rogue wave evolution can be recovered.…”