Skip to main content

Advertisement

SpringerLink
Log in

Numerical Simulations of Air–Water Flow of a Non-linear Progressive Wave in an Opposing Wind

  • Article
  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

We present detailed numerical results for two-dimensional viscous air–water flow of a non-linear progressive water wave when the speed of the opposing wind varies from zero to 1.5 times the wave phase speed. It is revealed that at any speed of the opposing wind there exist two rotating airflows, one anti-clockwise above the wave peak and one clockwise above the wave trough. These rotating airflows form a buffer layer between the main stream of the opposing wind and the wave surface. The thickness of the buffer layer decreases and the strength of rotation increases as the wind speed increases. The profile of the average \(x\)-component of velocity reveals that the water wave behaves as a solid surface producing larger wind stress compared to the following-wind case.

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

Similar content being viewed by others

References

  • Cohen JE (1997) Theory of turbulent wind over fast and slow waves. PhD thesis, University of Cambridge, Cambridge

  • Crapper GD (1984) Introduction to water wave Ellis Horwood. Wiley, New York 224 pp

  • Dean RG, Dalrymple RA (1984) Water Wave Mechanics for Engineers and Scientists. Prentice-Hall Inc., Upper Saddle River 353 pp

  • Donelan MA (1990) Air–sea interaction. Sea: Ocean Eng Sci 9:239–292

    Google Scholar 

  • Donelan MA (1999) Wind-induced growth and attenuation of laboratory waves. In: Sajjadi SG, Thomas NH, Hunt JCR (eds) Wind-over-wave coupling, perspective and prospects. Clarendon Press, Oxford 356 pp

  • Fenton J (1985) A fifth-order Stokes theory for steady waves. Waterw Port Coast Ocean Eng 111(2):216–234

    Article  Google Scholar 

  • Grare L, Peirson WL, Branger H, Walker JW, Giovanangeli JP, Makin V (2013) Growth and dissipation of wind-forced, deep-water waves. J Fluid Mech 722:5–50

    Article  Google Scholar 

  • Harris JA, Fulton I, Street RL (1995) Decay of waves in an adverse wind. In: Proceedings of the sixth Asian congress of fluid mechanics, May 22–26, Singapore

  • Hasselmann D, Bosenberg J (1991) Field measurements of wave-induced pressure over wind-sea and swell. J Fluid Mech 230:391–428

  • Kalvig SM, Manger E, Kverneland R (2013) Structure of air flow separation over wind wave crests method for wave driven wind simulation with CFD. Energy Procedia 35:148–156

    Article  Google Scholar 

  • Lamb H (1916) Hydrodynamics. Cambridge University Press, Cambridge 708 pp

    Google Scholar 

  • Li PY, Xu D, Taylor PA (2000) Numerical modelling of turbulent airflow over water waves. Bound-Layer Meteorol 95:397–425

    Article  Google Scholar 

  • Mastenbroek C (1996) Wind wave interaction. PhD thesis, Delft Technical University

  • Milne-Thomson LM (1994) Theoretical hydrodynamics. Dover Publications Inc, New York 743 pp

  • Mitsuyasu H, Yoshida Y (2005) Air–sea interactions under the existence of opposing swell. J Oceanogr 61:141–154

    Article  Google Scholar 

  • Peirson WL, Garcia AW, Pells SE (2003) Water wave attenuation due to opposing wind. J Fluid Mech 487:345–365

    Article  Google Scholar 

  • Snyder RL, Dobson FW, Elliott JA, Long RB (1981) Array measurements of atmospheric pressure fluctuations above surface gravity waves. J Fluid Mech 102:1–59

    Article  Google Scholar 

  • Sullivan PP, Edson JB, Hristov T, McWilliams JC (2008) Large-Eddy simulations and observations of atmospheric marine boundary layers above non-equilibrium surface waves. Atmos Sci 65:1225–1245

    Article  Google Scholar 

  • Wen X (2012) The analytical expression for the mass flux in the wet/dry areas method. ISRN Applied Mathematics. 2012: Article ID 451693, 15 pages, doi:10.5402/2012/451693

  • Wen X (2013) Wet/dry areas method for interfacial (free surface) flows. J Num Methods Fluids 71(3):316–338

    Article  Google Scholar 

  • Wen X, Mobbs (2014) Numerical simulations of laminar air–water flow of a non-linear progressive wave at low wind speed. Bound-Layer Meteorol 150:381–398

    Article  Google Scholar 

  • Young IR, Sobey RJ (1985) Measurements of the wind-wave energy flux in an opposing wind. J Fluid Mech 151:427–442

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank the constructive comments of the reviewers.

Author information

Authors and Affiliations

  1. Institute for Climate and Atmospheric Science, School of Earth and Environment, Centre for Computational Fluid Dynamics, University of Leeds, Leeds, LS2 9JT, UK

    Xianyun Wen

  2. National Centre for Atmospheric Science, Centre for Computational Fluid Dynamics, University of Leeds, Leeds, LS2 9JT, UK

    Stephen Mobbs

Authors
  1. Xianyun Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen Mobbs
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianyun Wen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wen, X., Mobbs, S. Numerical Simulations of Air–Water Flow of a Non-linear Progressive Wave in an Opposing Wind. Boundary-Layer Meteorol 156, 91–112 (2015). https://doi.org/10.1007/s10546-015-0012-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-015-0012-1

Keywords

Search

Navigation