Numerical Simulations of Air–Water Flow of a Non-linear Progressive Wave in an Opposing Wind
- 222 Downloads
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.
KeywordsAir–sea interaction Air–water flow Opposing wind Progressive wave
We would like to thank the constructive comments of the reviewers.
- Cohen JE (1997) Theory of turbulent wind over fast and slow waves. PhD thesis, University of Cambridge, CambridgeGoogle Scholar
- Crapper GD (1984) Introduction to water wave Ellis Horwood. Wiley, New York 224 ppGoogle Scholar
- Dean RG, Dalrymple RA (1984) Water Wave Mechanics for Engineers and Scientists. Prentice-Hall Inc., Upper Saddle River 353 ppGoogle Scholar
- Donelan MA (1990) Air–sea interaction. Sea: Ocean Eng Sci 9:239–292Google 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 ppGoogle 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, SingaporeGoogle Scholar
- Hasselmann D, Bosenberg J (1991) Field measurements of wave-induced pressure over wind-sea and swell. J Fluid Mech 230:391–428Google Scholar
- Lamb H (1916) Hydrodynamics. Cambridge University Press, Cambridge 708 ppGoogle Scholar
- Mastenbroek C (1996) Wind wave interaction. PhD thesis, Delft Technical UniversityGoogle Scholar
- Milne-Thomson LM (1994) Theoretical hydrodynamics. Dover Publications Inc, New York 743 ppGoogle 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