Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-03T08:51:50.694Z Has data issue: false hasContentIssue false
  • English
  • Français

Evolution of water wave groups with wind action

Published online by Cambridge University Press:  25 August 2022

Montri Maleewong Open the ORCID record for Montri Maleewong [Opens in a new window]  and
Roger Grimshaw
Montri Maleewong*
Affiliation:
Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
Roger Grimshaw
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A modified fully nonlinear model of an air–water system in deep water is presented in which the effect of wind in the air is simply represented by a direct link between the air–water interface pressure and the interface slope. The water system is a fully nonlinear Euler model of incompressible and irrotational fluid flow. Our main aim is to establish and compare with a reduced model represented by a forced nonlinear Schrödinger (FNLS) equation that describes wave groups in a weakly nonlinear asymptotic limit. Wave groups are described by the soliton and breather solutions generated by four cases of initial conditions in the relevant parameter regime. Numerical simulations of wave group formation in both models are compared, both with and without wind forcing. The FNLS model gives a good prediction to the modified fully nonlinear model when the wavenumber and wave frequency of the initial carrier waves are close to unity in dimensionless units based on typical carrier wavenumber and wave frequency. Wind forcing induces an exponential growth rate in the maximum amplitude wave. When the wave steepness becomes high in the fully nonlinear model some wave breaking is observed, but the FNLS model continues to predict large waves without breaking and there is then agreement only in the initial stage for the relevant initial conditions and parameter value ranges.

JFM classification

Waves/Free-surface Flows: Wind-wave interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A35
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Belcher, S.E. & Hunt, J.C.R. 1998 Turbulent flow over hills and waves. Annu. Rev. Fluid Mech. 30, 507–538.CrossRefGoogle Scholar
Benney, D.J. & Newell, A.C. 1967 The propagation of nonlinear wave envelopes. J. Maths Phys. 46, 133–139.CrossRefGoogle Scholar
Brunetti, M., Marchiando, N., Berti, N. & Kasparian, J. 2014 Nonlinear fast growth of water waves under wind forcing. Phys. Lett. A 378, 1025–1030.CrossRefGoogle Scholar
Cavaleri, L., et al. 2007 Wave modelling: the state of the art. Prog. Oceanogr. 75, 603–674.CrossRefGoogle Scholar
Chabchoub, A. & Grimshaw, R. 2016 The hydrodynamic nonlinear Schödinger equation: space and time. Fluids 1, 23–32.CrossRefGoogle Scholar
Cooker, M.J., Peregrine, D.H., Vidal, C. & Dold, J.W. 1990 The interaction between a solitary wave and a submerged semi-circular cylinder. J. Fluid Mech. 215, 1–22.CrossRefGoogle Scholar
Dommermuth, D. 2000 The initialization of nonlinear waves using an adjustment scheme. Wave Motion 32, 307–317.CrossRefGoogle Scholar
Grimshaw, R. 2007 Envelope solitary waves. In Solitary Waves in Fluids: Advances in Fluid Mechanics (ed. R. Grimshaw), vol. 45, pp. 159–179. WIT Press.CrossRefGoogle Scholar
Grimshaw, R. 2018 Generation of wave groups. In IUTAM Symposium Wind Waves (ed. R. Grimshaw, J. Hunt, & E. Johnson), Elsevier IUTAM Procedia Series, vol. 26, pp. 92–101. Elsevier.CrossRefGoogle Scholar
Grimshaw, R. 2019 a Generation of wave groups by shear layer instability. Fluids 4, 39.CrossRefGoogle Scholar
Grimshaw, R. 2019 b Two-dimensional modulation instability of wind waves. J. Ocean Engng Marine Energy 5, 413–417.CrossRefGoogle Scholar
Grimshaw, R., Hunt, J. & Johnson, E. 2018 IUTAM Symposium Wind Waves, 2017. Elsevier IUTAM Procedia Series, vol. 26. Elsevier.CrossRefGoogle Scholar
Grimshaw, R. & Maleewong, M. 2013 Stability of steady gravity waves generated by a moving localised pressure disturbance in water of finite depth. Phys. Fluids 25, 076605.CrossRefGoogle Scholar
Grimshaw, R., Maleewong, M. & Asavanant, J. 2009 Stability of gravity-capillary waves generated by a moving pressure disturbance in water of finite depth. Phys. Fluids 21, 082101.CrossRefGoogle Scholar
Grimshaw, R. & Tovbis, A. 2013 Rogue waves: analytical predictions. Proc. R. Soc. 469, 20130094.CrossRefGoogle Scholar
Hao, X., Cao, T., Yang, Z., Li, T. & Shen, L. 2018 Simulation-based study of wind-wave interaction. In IUTAM Symposium Wind Waves (ed. R. Grimshaw, J. Hunt, & E. Johnson), Elsevier IUTAM Procedia Series, vol. 26, pp. 162–173. Elsevier.CrossRefGoogle Scholar
Hasimoto, H. & Ono, H. 1972 Nonlinear modulation of gravity waves. J. Phys. Soc. Japan 33, 805–811.CrossRefGoogle Scholar
Janssen, P. 2004 The Interaction of Ocean Waves and Wind. Cambridge University Press.CrossRefGoogle Scholar
Jeffreys, H. 1925 On the formation of water waves by wind. Proc. R. Soc. A 107, 189–206.Google Scholar
Kharif, C., Kraenkel, R.A., Manna, M.A. & Thomas, R. 2010 The modulational instability in deep water under the action of wind and dissipation. J. Fluid Mech. 664, 138–149.CrossRefGoogle Scholar
Kharif, C., Pelinovsky, E. & Slunyaev, A. 2009 Rogue Waves in the Ocean. Advances in Geophysical and Environmental Mechanics and Mathematics, vol. 14. Springer.Google Scholar
Leblanc, S. 2007 Amplification of nonlinear surface waves by wind. Phys. Fluids 19, 101705.CrossRefGoogle Scholar
Maleewong, M. & Grimshaw, R. 2022 Amplification of wave groups in the forced nonlinear Schrödinger equation. Fluids 7, 233.CrossRefGoogle Scholar
Miles, J.W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185–204.CrossRefGoogle Scholar
Montalvo, P., Kraenkel, R., Manna, M.A. & Kharif, C. 2013 Wind-wave amplification mechanisms: possible models for steep wave events in finite depth. Nat. Hazards Earth Syst. Sci. 13, 2805–2813.CrossRefGoogle Scholar
Onorato, M. & Proment, D. 2012 Approximate rogue wave solutions of the forced and damped nonlinear Schrödinger equation for water waves. Phys. Lett. A 376, 3057–3059.CrossRefGoogle Scholar
Osborne, A.R. 2010 Nonlinear Ocean Waves and the Inverse Scattering Transform. Elsevier.Google Scholar
Peregrine, D.H. 1983 Water waves, nonlinear Schrödinger equations, and their solutions. J. Austral. Math. Soc. Ser. B 25, 16–43.CrossRefGoogle Scholar
Phillips, O.M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445.CrossRefGoogle Scholar
Phillips, O.M. 1981 Wave interactions - the evolution of an idea. J. Fluid Mech. 106, 215–227.CrossRefGoogle Scholar
Sajjadi, S.G., Drullion, F. & Hunt, J.C.R. 2018 Computational turbulent shear flows over growing and non-growing wave groups. In IUTAM Symposium Wind Waves (ed. R. Grimshaw, J. Hunt, & E. Johnson), Elsevier IUTAM Procedia Series, vol. 26, pp. 145–152. Elsevier.CrossRefGoogle Scholar
Sajjadi, S.G., Hunt, J.C.R. & Drullion, F. 2014 Asymptotic multi-layer analysis of wind over unsteady monochromatic surface waves. J. Engng Maths 84, 73–85.CrossRefGoogle Scholar
Slunyaev, A., Clauss, G.F., Klein, M. & Onorato, M. 2013 Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105.CrossRefGoogle Scholar
Slunyaev, A., Sergeeva, A. & Pelinovsky, E. 2015 Wave amplification in the framework of forced nonlinear Schrödinger equation: the rogue wave context. Phys. D 301, 18–27.CrossRefGoogle Scholar
Sullivan, P.P., Banner, M.L., Morison, R. & Peirson, W.L. 2018 Impacts of wave age on turbulent flow and drag of steep waves. In IUTAM Symposium Wind Waves (ed. R. Grimshaw, J. Hunt, & E. Johnson), Elsevier IUTAM Procedia Series, vol. 26, pp. 184–193. Elsevier.CrossRefGoogle Scholar
Toffoli, A., Gramstad, O., Trulsen, K., Monbalius, J., Bitner-Grerersen, E. & Onorato, M. 2010 Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations. J. Fluid Mech. 664, 313–336.CrossRefGoogle Scholar
Toffoli, A., Proment, D., Salman, H., Monbaliu, J., Frascoli, F., Dafilis, M., Stramignoni, E., Forza, R., Manfrin, M. & Onorato, M. 2017 Wind generated rogue waves in an annular wave flume. Phys. Rev. Lett. 118, 144503.CrossRefGoogle Scholar
Touboul, J., Kharif, C., Pelinovsky, E. & Giovanangeli, J.-P. 2008 On the interaction of wind and steep gravity wave groups using Miles’ and Jeffreys’ mechanisms. Nonlinear Proc. Geophys. 15, 1023–1031.CrossRefGoogle Scholar
Wang, J., Yan, S. & Ma, Q. 2018 Deterministic numerical modelling of three-dimensional rogue waves on large scale with presence of wind. In IUTAM Symposium Wind Waves (ed. R. Grimshaw, J. Hunt, & E. Johnson), Elsevier IUTAM Procedia Series, vol. 26, pp. 214–226. Elsevier.CrossRefGoogle Scholar
Zakharov, V.E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190–194.CrossRefGoogle Scholar
Zakharov, V. 2018 Analytic theory of a wind-driven sea. In IUTAM Symposium Wind Waves (ed. R. Grimshaw, J. Hunt, & E. Johnson), Elsevier IUTAM Procedia Series, vol. 26, pp. 43–58. Elsevier.CrossRefGoogle Scholar
Zakharov, V., Badulin, S., Hwang, P. & Caulliez, G. 2015 Universality of sea wave growth and its physical roots. J. Fluid Mech 780, 503–535.CrossRefGoogle Scholar
Zakharov, V., Resio, D. & Pushkarev, A. 2017 Balanced source terms for wave generation within the Hasselmann equation. Nonlinear Proc. Geophys. 24, 581–597.CrossRefGoogle Scholar