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Research Papers: Offshore Technology

Reconstruction of Extreme Events Through Numerical Simulations

[+] Author and Article Information
Alexey Slunyaev

Institute of Applied Physics,
Nizhny Novgorod, Russia
N. Novgorod State Technical University,
Nizhny Novgorod, Russia
e-mail: slunyaev@hydro.appl.sci-nnov.ru

Efim Pelinovsky

Institute of Applied Physics,
Nizhny Novgorod, Russia
N. Novgorod State Technical University,
Nizhny Novgorod, Russia
National Research University – Higher
School of Economics,
Nizhny Novgorod, Russia
e-mail: pelinovsky@hydro.appl.sci-nnov.ru

C. Guedes Soares

Centre for Marine Technology and Engineering,
(CENTEC), Technical University of Lisbon,
Instituto Superior Tecnico,
1049-001 Lisboa, Portugal
e-mail: guedess@mar.ist.utl.pt

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 5, 2012; final manuscript received July 15, 2013; published online November 12, 2013. Assoc. Editor: Elzbieta Maria Bitner-Gregersen.

J. Offshore Mech. Arct. Eng 136(1), 011302 (Nov 12, 2013) (10 pages) Paper No: OMAE-12-1057; doi: 10.1115/1.4025545 History: Received June 05, 2012; Revised July 15, 2013

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 extreme event reconstruction is robust. In particular, the verification of approximate approaches versus the fully nonlinear numerical simulation is performed. The reconstructed rogue wave is generally less steep than the measured one. Possible reasons for this discrepancy are suggested.

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Topics: Waves , Time series
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Figures

Grahic Jump Location
Fig. 1

Comparison of a Stokes wave (k0H/2 = 0.3) reconstructed within different frameworks: the wave profile and the corresponding Fourier spectrum (a) and (b), and the surface velocity potential and its Fourier spectrum (c) and (d)

Grahic Jump Location
Fig. 2

Reconstruction of a solitary nonlinear wave group (steepness k0H/2 = 0.3) within different frameworks: the wave profile (a), vertical fluid velocity at the water surface (b), Fourier spectrum of the surface elevation (c)

Grahic Jump Location
Fig. 3

Test of the reconstruction procedures for time series. The input time series is the NLS solitary group (peak frequency 1 rad/s, steepness k0H/2 = 0.3, with bound waves of three orders). Panel (a): the target time series and reconstructed envelopes. Panels (b) and (c): Fourier spectra in semilogarithmic scales for the surface displacement and surface velocity potential.

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Fig. 4

Different wave envelope approaches applied to the time series NA199711200151 from the North Alwyn platform: original and reconstructed surface elevation (a), wave envelopes (b), Fourier spectrum of the surface elevation (c), vertical (d), and horizontal (e) fluid velocities at the water surface

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Fig. 5

Explanation diagram for the upstream x-evolution and forward t-evolution

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Fig. 6

Verification of the combined use of the spatial and temporal versions the Dysthe equations. The thick red line is the initial condition, the thin black line is the recovered time series: a train of solitary waves (a), and the time series from the North Alwyn platform (b)–(i), see record codes above the figures.

Grahic Jump Location
Fig. 7

A reconstruction of the wave record NA199711200151. The in situ recorded wave (“record”), the high-frequency filtered time-series (“frequency cut-off”), simulations of the Dysthe equation and the strongly nonlinear HOSM (M = 6) simulation. The whole time series is given in panel (a), and the rogue wave event is shown in a larger scale in panel (b).

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