Skip to main content
SpringerLink
Log in

Statistical properties of extreme waves in multidirectional wave fields over complex bathymetry

  • Published:
Ocean Dynamics Aims and scope Submit manuscript

Abstract

In the present study, a fully nonlinear Boussinesq equation model, FUNWAVE 2.0, is employed to simulate the propagation of multidirectional irregular waves over a sloping bottom. The influences of both the principal wave direction and the directional spreading of the wave energy on the statistics of extreme waves are examined. Comparisons of the skewness, the kurtosis, and the probability density function of the surface elevation analyzed based on the measurements of wave fields with various principal wave directions and different directional spreading parameters are conducted. The results show that both the principal wave direction and the directional spreading of the wave field have significant influences on the statistical parameters associated with extreme waves at different relative water depths. It is consequently essential to include the effects of the two directional factors in the context of extreme waves to have an accurate estimation of their probability of occurrence in the nearshore region. Furthermore, the effect of the wave nonlinearity of multidirectional wave fields is also revealed by comparing the simulated results with the theoretical predictions based on the linear and seconder-order nonlinear wave theories.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  • Abroug I, Matar R, Abcha N (2022) Spatial evolution of skewness and kurtosis of unidirectional extreme waves propagating over a sloping beach. J Mar Sci Eng. 10(10):1475

    Google Scholar 

  • Bi CW, Zhao YP, Dong GH et al (2014) Numerical simulation of the interaction between flow and flexible nets. J Fluids Struct. 45:180–201

    Google Scholar 

  • Bitner-Gregersen EM, Toffoli A (2014) Occurrence of rogue sea states and consequences for marine structures. Ocean Dyn 64(10):1457–1468

    Google Scholar 

  • Chawla A, Kirby JT (2000) A source function method for generation of waves on currents in Boussinesq models. Appl Ocean Res 22:75–83

    Google Scholar 

  • Chen Q, Kirby JT, Dalrymplre RA, Shi FY, Thornton EB (2003) Boussinesq modeling of longshore currents. J Geophys Res Ocean. 108:3362

    Google Scholar 

  • Chen HZ, Jiang DH, Tang XC et al (2019) Evolution of irregular wave shape over a fringing reef flat. Ocean Eng 192:106544

    Google Scholar 

  • Cherneva Z, Petrova P, Andreeva N et al (2005) Probability distributions of peaks, troughs and heights of wind waves measured in the Black Sea coastal zone. Coast Eng 52:599–615

    Google Scholar 

  • Donelan MA (2001) A new method for directional wave analysis based on wavelets. Proceedings of the 4th International Symposium on Ocean Wave Measurement and Analysis, American Society of Civil Engineers, San Francisco, pp 310–317

  • Dong GH, Zheng YN, Li YC et al (2008) Experiments on wave transmission coefficients of floating breakwaters. Ocean Eng 35(8–9):931–938

    Google Scholar 

  • Dong GH, Xu TJ, Zhao YP et al (2010) Numerical simulation of hydrodynamic behavior of gravity cage in irregular waves. Aquac Eng 42(2):90–101

    Google Scholar 

  • Ducrozet G, Gouin M (2017) Influence of varying bathymetry in rogue wave occurrence within unidirectional and directional sea-states. J Ocean Eng Mar Energ 3(4):309–324

    Google Scholar 

  • Fedele F (2015) On the kurtosis of deep-water gravity waves. J Fluid Mech 782(7):25–36

    Google Scholar 

  • Fedele F, Brennan J, De León SP et al (2016) Real world ocean rogue waves explained without the modulational instability. Sci Rep 6(1):1–11

    Google Scholar 

  • Fu RL, Ma YX, Dong GH et al (2021) A wavelet-based wave group detector and predictor of extreme events over unidirectional sloping bathymetry. Ocean Eng 229:108936

    Google Scholar 

  • Gallagher EL, Elgar S, Guza RT (1998) Observations of sand bar evolution on a natural beach. J Geophys Res Oceans 103(C2):3203–3215

    Google Scholar 

  • Gao JL, Ma XZ, Zang J et al (2020) Numerical investigation of harbor oscillations induced by focused transient wave groups. Coast Eng 158:103670

    Google Scholar 

  • Gao JL, Ma XZ, Dong GH et al (2021) Investigation on the effects of Bragg reflection on harbor oscillations. Coast Eng 170:103977

    Google Scholar 

  • Gao JL, Chen HZ, Mei LL et al (2021) Statistical analyses of wave height distribution for multidirectional irregular waves over a sloping bottom. China Ocean Eng 35(4):504–517

    Google Scholar 

  • Goda Y (1999) A comparative review on the functional forms of directional wave spectrum. Coast Eng J 41(1):1–20

    Google Scholar 

  • Gramstad O, Zeng H, Trulsen K et al (2013) Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water. Phys Fluids 25(12):122103

    Google Scholar 

  • Janssen PAEM (2003) Nonlinear four-wave interactions and freak waves. J Phys Ocean 33(4):863–884

    Google Scholar 

  • Janssen TT, Herbers THC (2009) Nonlinear wave statistics in a focal zone. J Phys Ocean 39(8):1948–1964

    Google Scholar 

  • Janssen PAEM, Onorato M (2007) The intermediate water depth limit of the Zakharov equation and consequences for wave prediction. J Phys Ocean 37:2389–2400

    Google Scholar 

  • Janssen P, Bidlot JR (2009) On the extension of the freak wave warning system and its verification. European Centre for Medium-Range Weather Forecasts

  • Judge FM, Hunt-Raby AC, Orszaghova J et al (2019) Multi-directional focused wave group interactions with a plane beach. Coast Eng 152:103531

    Google Scholar 

  • Karmpadakis I, Swan C, Christou M (2020) Assessment of wave height distributions using an extensive field database. Coastal Eng 157:103630

    Google Scholar 

  • Kashima H, Mori N (2019) Aftereffect of high-order nonlinearity on extreme wave occurrence from deep to intermediate water. Coast Eng 153:103559

    Google Scholar 

  • Kashima H, Hirayama K, Mori N (2014) Estimation of freak wave occurrence from deep to shallow water regions. Coast Eng Proc 1(34):36

    Google Scholar 

  • Katsardi V, de Lutio L, Swan C (2013) An Experimental Study of large waves in intermediate and shallow water depths. Part1: wave height and crest height statistics. Coast Eng 73:43–57

    Google Scholar 

  • Kirby JT, Long W, Shi F (2003) Funwave 2.0 Fully nonlinear boussinesq wave model on curvilinear coordinates. Center for Applied Coastal Research Department of Civil & Environmental Engineering. University of Delaware

  • Li Y (2021) Three-dimensional surface gravity waves of a broad bandwidth on deep water. J Fluid Mech 926:A34

    Google Scholar 

  • Li YS, Liu SX, Yu YX, Lai GZ (2000) Numerical modelling of multi-directional irregular waves through breakwaters. Appl Math Model 24(8–9):551–574

    Google Scholar 

  • Liu SX, Sun ZB, Li JX (2012) An unstructured FEM model based on Boussinesq equations and its application to the calculation of multidirectional wave run-up in a cylinder group. Appl Math Model 36(9):4146–4164

    Google Scholar 

  • Longuet-Higgins MS (1952) On the statistical distribution of heights of sea waves. J Mar Res 11(3):245–266

    Google Scholar 

  • Longuet-Higgins MS (1963) The effect of non-linearities on statistical distribution in the theory of sea waves. J Fluid Mech 17:459–480

    Google Scholar 

  • Lyu Z, Mori N, Kashima H (2021) Freak wave in high-order weakly nonlinear wave evolution with bottom topography change. Coast Eng 167:103918

    Google Scholar 

  • Ma YX, Chen HZ, Ma XZ, Dong GH (2017) A numerical investigation on nonlinear transformation of obliquely incident random waves on plane sloping bottoms. Coast Eng 130:65–84

    Google Scholar 

  • McAllister ML, van den Bremer TS (2020) Experimental study of the statistical properties of directionally spread ocean waves measured by buoys. J Phys Ocean 50(2):399–414

    Google Scholar 

  • Mori N, Janssen PAEM (2006) On kurtosis and occurrence probability of freak waves. J Phys Ocean 36:1471–1483

    Google Scholar 

  • Mori N, Onorato M, Janssen PAEM et al (2007) On the extreme statistics of long-crested deep water waves: theory and experiments. J Geophys Res 112(C9):C09011

    Google Scholar 

  • Mori N, Onorato M, Janssen PAEM (2011) On the estimation of the kurtosis in directional sea states for freak wave forecasting. J Phys Ocean 41(8):1484–1497

    Google Scholar 

  • Onorato M, Osborne AR, Serio M et al (2001) Freak wave in random oceanic sea states. Phys Rev Lett 86(25):5831–5834

    Google Scholar 

  • Onorato M, Osborne AR, Serio M (2006) Modulation instability in crossing sea states: a possible machanism for the formation of freak waves. Phys Rev Lett 96:014503

    Google Scholar 

  • Onorato M, Waseda T, Toffoli A et al (2009) Statistical properties of directional ocean waves: the role of the modulational instability in the formation of extreme events. Phys Rev Lett 102:11 114502

    Google Scholar 

  • Petrova P, Soares CG (2008) Maximum wave crest and height statistics of irregular and abnormal waves in an offshore basin. Appl Ocean Res 30(2):144–152

    Google Scholar 

  • Shemer L, Sergeeva A (2009) An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield. J Geophys ResOceans 114(C1):C01015

    Google Scholar 

  • Shi FY, Dalrymple RA, Kirby JT et al (2001) A fully nonlinear Boussinesq model in generalized curvilinear coordinates. Coast Eng 42(4):337–358

    Google Scholar 

  • Socquet-Juglard H, Dysthe K, Trulsen K et al (2005) Probability distributions of surface gravity waves during spectral changes. J Fluid Mech 542(1):195–216

    Google Scholar 

  • Toffoli A, Onorato M, Bitner-Gregersen E et al (2008) Surface gravity waves from direct numerical simulations of the Euler equations: a comparison with second order theory. Ocean Eng 35:367–379

    Google Scholar 

  • Toffoli A, Benoit M, Onorato M et al (2009) The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth. Nonlinear Process Geophys 16(1):131–139

    Google Scholar 

  • Trulsen K, Zeng H, Gramstad O (2012) Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys Fluids 24(9):097101

    Google Scholar 

  • Trulsen K, Raustøl A, Jorde S, Rye L (2020) Extreme wave statistics of long-crested irregular waves over a shoal. J Fluid Mech 882:R2

    Google Scholar 

  • Viotti C, Dias F (2014) Extreme waves induced by strong depth transitions: Fully nonlinear results. Phys Fluids 26(5):287–310

    Google Scholar 

  • Wang L, Zhou BZ, Jin P, Li JX, Liu SX, Ducrozet G (2022) Relation between occurrence probability of freak waves and kurtosis/skewness in unidirectional wave trains under single-peak spectra. Ocean Eng 248:110813

    Google Scholar 

  • Waseda T, Kinoshita T, Tamura H (2009) Evolution of a random directional wave and freak wave occurrence. J Phys Ocean 39(3):621–639

    Google Scholar 

  • Waseda T (2006) Impact of directionality on the extreme wave occurrence in a discrete random wave system. Proceedings of 9th International Workshop on Wave Hindcasting and Forecasting, Victoria, Canada

  • Wei G, Kirby JT, Grilli ST, Subramanya R (1995) A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves. J Fluid Mech 294:71–92

    Google Scholar 

  • Xiao W, Liu Y, Wu G et al (2013) Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution. J Fluid Mech 720(1):357–392

    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(3):631–638

    Google Scholar 

  • Zhang J, Benoit M, Kimmoun O, Chabchoub A, Hsu HC (2019) Statistics of extreme waves in coastal waters: large scale experiments and advanced numerical simulations. Fluids 4(2):99

    Google Scholar 

  • Zhang R, Ahammad NA, Raju CSK et al (2022) Quadratic and linear radiation impact on 3D convective hybrid nanofluid flow in a suspension of different temperature of waters: transpiration and fourier fluxes. Int Commun Heat Mass Transf 138:106418

    Google Scholar 

  • Zhang R, Shah NA, El-Zahar ER et al (2023) Numerical analysis of fractional-order emden–fowler equations using modified variational iteration method. Fractals 31(02):2340028

    Google Scholar 

  • Zheng Y, Lin Z, Li Y et al (2020) Fully nonlinear simulations of unidirectional extreme waves provoked by strong depth transitions: The effect of slope. Phys Rev Fluids. 5(6):064804

    Google Scholar 

Download references

Funding

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 42376205 and 51809039) and the Key Research and Development Program of Zhejiang Province (Grant No. 2023C02029).

Author information

Authors and Affiliations

  1. National Engineering Research Center for Marine Aquaculture, Zhejiang Ocean University, Zhoushan, 316000, China

    Lili Mei, Hongzhou Chen, Xu Yang & Fukun Gui

  2. School of Marine Engineering Equipment, Zhejiang Ocean University, Zhoushan, 316000, China

    Hongzhou Chen

Authors
  1. Lili Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongzhou Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fukun Gui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongzhou Chen.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mei, L., Chen, H., Yang, X. et al. Statistical properties of extreme waves in multidirectional wave fields over complex bathymetry. Ocean Dynamics 73, 827–849 (2023). https://doi.org/10.1007/s10236-023-01586-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10236-023-01586-4

Keywords

Search

Navigation