Skip to main content

Advertisement

SpringerLink
Log in

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

  • Published:
Natural Hazards Aims and scope Submit manuscript

Abstract

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solution of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The spatiotemporal 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 k p h ≥ 1.2. The lifetimes of rogue events may reach up to 30–60 wave periods depending on the water depth. The maximum observed wave has a height of about three 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Bitner-Gregersen EM, Fernandez L, Lefevre JM, Monbaliu J, Toffoli A (2014) The North Sea Andrea storm and numerical simulations. Nat Hazards Earth Syst Sci 14:1407–1415

    Article  Google Scholar 

  • Chalikov D (2005) Statistical properties of nonlinear one-dimensional wave fields. Nonlin Proc Geophys 12:671–689

    Article  Google Scholar 

  • Chalikov D (2009) Freak waves: their occurrence and probability. Phys Fluids 21:076602

    Article  Google Scholar 

  • Christou M, Ewans K (2014) Field measurements of rogue water waves. J Phys Oceanogr 44:2317–2335

    Article  Google Scholar 

  • de Pinho UF, Liu PC, Ribeiro CEP (2004) Freak waves at campos Basin, Brazil. Geofizika 21:53–67

    Google Scholar 

  • Dias F, Brennan J, Leon SP, Clancy C, Dudley J (2015) Local analysis of wave fields produced from hindcasted rogue wave sea states. Proceedings of OMAE2015-41458

  • Didenkulova I (2011) Shapes of freak waves in the coastal zone of the Baltic Sea (Tallinn Bay). Boreal Environ Res 16:138–148

    Google Scholar 

  • Didenkulova I, Anderson C (2010) Freak waves of different types in the coastal zone of the Baltic Sea. Nat Hazards Earth Syst Sci 10:2021–2029

    Article  Google Scholar 

  • Didenkulova I, Rodin A (2012) Statistics of shallow water rogue waves in Baltic Sea conditions: the case of Tallinn Bay. In: IEEE/OES Baltic 2012 international symposium proceedings: IEEE, Klaipeda, Lithuania, pp 1–6, 8–11 May 2012

  • Didenkulova II, Slunyaev AV, Pelinovsky EN, Kharif Ch (2006) Freak waves in 2005. Natural Hazards Earth Syst Sci 6:1007–1015. doi:10.5194/nhess-6-1007-2006

    Article  Google Scholar 

  • Didenkulova II, Nikolkina IF, Pelinovsky EN (2013) Rogue waves in the basin of intermediate depth and the possibility of their formation due to the modulational instability. JETP Lett 97:194–198

    Article  Google Scholar 

  • Dommermuth D (2000) The initialization of nonlinear waves using an adjustment scheme. Wave Motion 32:307–317

    Article  Google Scholar 

  • Doong DJ, Tsai CH, Chen YC, Peng JP, Huang CJ (2015) Statistical analysis on the long-term observations of typhoon waves in the Taiwan sea. J Mar Sci Technol 23:893–900

    Google Scholar 

  • Ducrozet G, Bonnefoy F, Le Touze D, Ferrant P (2007) 3-D HOS simulations of extreme waves in open seas. Nat Hazards Earth Syst Sci 7:109–122

    Article  Google Scholar 

  • Dysthe KB, Trulsen K, Krogstad HE, Socquet-Juglard H (2003) Evolution of a narrow-band spectrum of random surface gravity waves. J Fluid Mech 478:1–10

    Article  Google Scholar 

  • Dysthe K, Krogstad HE, Müller P (2008) Oceanic rogue waves. Annu Rev Fluid Mech 40:287–310

    Article  Google Scholar 

  • Fernandez L, Onorato M, Monbaliu J, Toffoli A (2014) Modulational instability and wave amplification in finite water depth. Nat Hazards Earth Syst Sci 14:705–711

    Article  Google Scholar 

  • Fernandez L, Onorato M, Monbaliu J, Toffoli A (2016) Occurrence of extreme waves in finite water depth. In: Pelinovsky E, Kharif C (eds) Extreme ocean waves. Springer, Switzerland. doi:10.1007/978-3-319-21575-4

    Google Scholar 

  • Gemmrich J, Garrett C (2010) Unexpected waves: intermediate depth simulations and comparison with observations. Ocean Eng 37:262–267

    Article  Google Scholar 

  • Janssen PAEM (2003) Nonlinear four-wave interactions and freak waves. J Phys Oceanogr 33:863–884

    Article  Google Scholar 

  • Kharif C, Pelinovsky E (2003) Physical mechanisms of the rogue wave phenomenon. Eur J Mech/B Fluids 22:603–634

    Article  Google Scholar 

  • Kharif C, Pelinovsky E, Slunyaev A (2009) Rogue waves in the Ocean. Springer, Berlin

    Google Scholar 

  • Kokorina A, Pelinovsky E (2002) The applicability of the Korteweg-de Vries equation for description of the statistics of freak waves. J Korean Soc Coast Ocean Eng 14:308–318

    Google Scholar 

  • Lavrenov I (1998) The wave energy concentration at the Agulhas Current of South Africa. Nat Hazards 17:117–127

    Article  Google Scholar 

  • Mai S, Wihelmi J, Barjenbruch U (2010) Wave height distributions in shallow waters. In: Proceedings of the 32nd international conference on coastal engineering (ICCE), Shanghai, China

  • Mallory JK (1974) Abnormal waves on the South East coast of South Africa. Intl Hydrogr Rev 51:99–129

    Google Scholar 

  • Massel SR (1996) Ocean surface waves: their physics and prediction. World Scientifc Publ, Singapore

    Google Scholar 

  • Mori N, Liu PC, Yasuda T (2002) Analysis of freak wave measurements in the Sea of Japan. Ocean Eng 29:1399–1414

    Article  Google Scholar 

  • Nikolkina I, Didenkulova I (2012) Catalogue of rogue waves reported in media in 2006–2010. Nat Hazards 61:989–1006

    Article  Google Scholar 

  • Onorato M, Osborne AR, Serio M, Bertone S (2001) Freak waves in random oceanic sea states. Phys Rev Lett 86:5831–5834

    Article  Google Scholar 

  • Onorato M, Osborne AR, Serio M (2002) Extreme wave events in directional, random oceanic sea states. Phys Fluids 14:L25–L28

    Article  Google Scholar 

  • Onorato M, Waseda T, Toffoli A, Cavaleri L, Gramstad O, Janssen PA, Kinoshita T, Monbaliu J, Mori N, Osborne AR, Serio M, Stansberg CT, Tamura H, Trulsen K (2009) Statistical properties of directional ocean waves: the role of the modulational instability in the formation of extreme events. Phys Rev Lett 102:114502

    Article  Google Scholar 

  • Pelinovsky E, Sergeeva A (2006) Numerical modeling of the KdV random wave field. Eur J Mech B/Fluid 25:425–434

    Article  Google Scholar 

  • Sergeeva A, Slunyaev A (2013) Rogue waves, rogue events and extreme wave kinematics in spatio-temporal fields of simulated sea states. Nat Hazards Earth Syst Sci 13:1759–1771. doi:10.5194/nhess-13-1759-2013

    Article  Google Scholar 

  • Sergeeva A, Pelinovsky E, Talipova T (2011) Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework. Nat Hazards Earth Syst Sci 11:323–330

    Article  Google Scholar 

  • Sergeeva A, Slunyaev A, Pelinovsky E, Talipova T, Doong D-J (2014) Numerical modeling of rogue waves in coastal waters. Nat Hazards Earth Syst Sci 14:861–870. doi:10.5194/nhess-14-861-2014

    Article  Google Scholar 

  • Shemer L, Sergeeva A, Slunyaev A (2010) Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random field evolution: experimental validation. Phys Fluids 22:016601

    Article  Google Scholar 

  • Slunyaev A (2010) Freak wave events and the wave phase coherence. Eur Phys J Special Topics 185:67–80

    Article  Google Scholar 

  • Slunyaev AV, Sergeeva AV (2011) Stochastic simulation of unidirectional intense waves in deep water applied to rogue waves. JETP Lett 94:779–786. doi:10.1134/S0021364011220103

    Article  Google Scholar 

  • Slunyaev AV, Shrira VI (2013) On the highest non-breaking wave in a group: fully nonlinear water wave breathers vs weakly nonlinear theory. J Fluids Mech 735:203–248. doi:10.1017/jfm.2013.498

    Article  Google Scholar 

  • Slunyaev A, Didenkulova I, Pelinovsky E (2011) Rogue waters. Contemp Phys 52:571–590

    Article  Google Scholar 

  • Slunyaev A, Sergeeva A, Pelinovsky E (2015) Wave amplification in the framework of forced nonlinear Schrödinger equation: the rogue wave context. Phys D 303:18–27. doi:10.1016/j.physd.2015.03.004

    Article  Google Scholar 

  • Socquet-Juglard H, Dysthe KB, Trulsen K, Krogstad HE, Liu J (2005) Probability distributions of surface gravity waves during spectral changes. J Fluids Mech 542:195–216

    Article  Google Scholar 

  • Toffoli A, Onorato M, Babanin AV, Bitner-Gregersen E, Osborne AR, Monbaliu J (2007) Second-order theory and setup in surface gravity waves: a comparison with experimental data. J Phys Oceanogr 37:2726–2739

    Article  Google Scholar 

  • Trulsen K, Zeng H, Gramstad O (2012) Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys Fluids 24:097101. doi:10.1063/1.4748346

    Article  Google Scholar 

  • Viotti C, Dias F (2014) Extreme waves induced by strong depth transitions: fully nonlinear results. Phys Fluids 26:051705. doi:10.1063/1.4880659

    Article  Google Scholar 

  • West BJ, Brueckner KA, Janda RS, Milder DM, Milton RL (1987) A new numerical method for surface hydrodynamics. J Geophys Res 92:11803–11824

    Article  Google Scholar 

  • Xiao W, Liu Yu, Wu G, Yue DKP (2013) Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution. J Fluids Mech 720:357–392

    Article  Google Scholar 

  • Zeng H, Trulsen K (2012) Evolution of skewness and kurtosis of weakly nonlinear unidirectional waves over a sloping bottom. Nat Hazards Earth Syst Sci 12:631–638

    Article  Google Scholar 

Download references

Acknowledgments

The numerical simulation within the fully nonlinear framework was supported by RFBR Grants 15-35-20563 and 16-55-52019; Volkswagen Foundation (for ASl and ASe). The comparative study of the time series processing and the space series processing is performed within the RSF Grant No 16-17-00041.

Author information

Authors and Affiliations

  1. Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia

    A. Slunyaev, A. Sergeeva & I. Didenkulova

  2. Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia

    A. Slunyaev, A. Sergeeva & I. Didenkulova

  3. Marine Systems Institute at Tallinn University of Technology, Tallinn, Estonia

    I. Didenkulova

Authors
  1. A. Slunyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Sergeeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Didenkulova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Slunyaev.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Slunyaev, A., Sergeeva, A. & Didenkulova, I. Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth. Nat Hazards 84 (Suppl 2), 549–565 (2016). https://doi.org/10.1007/s11069-016-2430-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11069-016-2430-x

Keywords

Search

Navigation