Unfamiliar Properties оf Surface Waves
Abstract
Numerical 2-D and 3-D models of surface waves allowed to simulate and prove most of the facts studied both experimentally and analytically. In addition, a detailed modelling discovers new regularities beyond the scope of traditional concepts. The results obtained mostly at Saint-Petersburg Branch of Oceanography Institute RAS are listed. The facts, which were never discussed in papers of other authors and never explained are described. These facts are mostly contradict general views. The results are based on accurate numerical models of potential liquid motion with a free surface. Harmonic waves quickly obtain bound modes and, on the average, turn into Stokes waves. The Fourier analysis of exact solutions shows that a real field is rather a superposition of Stokes waves with different amplitudes and phases, than the superposition of linear modes. Wave field is the result of superposition of unstable modes whose amplitudes fluctuate in time under the influence of reversible interactions. Development of extreme waves occurs over the time of the order of one wave period. Such fast evolution cannot be explained by the theory of modulational instability. Calculations of extreme wave probability, using a linear model, provide the results close to the calculations by a non-linear model. This is why the role of the nonlinearity in generation of extreme waves is evidently not very significant. When crest merging occurs, a quick nonlinear wave interaction takes place, which leads to a sharp increase of the resulting wave and further possibility of overturning. A jaggy character of 2-D wave spectrum with high resolution (presence of steady peaks and holes) is a typical result of direct wave modeling. The results of the numerical modeling significantly depend on the minor details of initial conditions. Therefore, the results confirmed statistically should be obtained by ensemble modeling. Such modeling, in particular, does not prove correctness of the Hasselmann’s theory.
About the Author
D. V. Chalikov
Saint-Petersburg Department of the P. P. Shirshov Institute of Oceanology of RAS; Swinburne University of Technology
Russian Federation
Russian Federation
St.-Petersburg
Melbourne
References
1. Stokes G. G. On the theory of oscillatory waves // Trans. Cambridge Philos. Soc. N 8. P. 441—445; Math. Phys. Pap. 1847. N 1. P. 197—229.
2. Crapper G. D. An exact solution for progressive capillary waves of arbitrary amplitude // Journal of Fluid Mech. 1957. V. 96. P. 417—445.
3. Chalikov D., Sheinin D. Numerical modeling of surface waves based on principal equations of potential wave dynamics // Technical Note. 1996. NOAA/NCEP/OMB, 54 p.
4. Chalikov D., Sheinin D. Direct Modeling of One-dimensional Nonlinear Potential Waves. Nonlinear Ocean Waves, ed. W. Perrie // Advances in Fluid Mechanics. 1998. 17. P. 207—258.
5. Sheinin D., Chalikov D. Hydrodynamical modeling of potential surface waves. Problems of hydrometeorology and environment on the eve of XXI century // Proceedings of international theoretical conference, St.-Petersburg, June 24—25, 2001. St.-Petersburg, Hydrometeoizdat. P. 305—337.
6. Chalikov D., Sheinin D. Numerical simulation of surface waves based on equations of potential wave dynamics // Proc. ONR, Ocean Waves Workshop. 1994. Tucson, Arizona
7. Benjamin T. B., Feir J. E. The Disintegration of Wave Trains in Deep Water // J. Fluid. Mech. 1967. V. 27. P. 417—430.
8. Chalikov D. Simulation of Benjamin-Feir instability and its consequences // Physics of Fluid. 2007. V. 19. 016602-15.
9. Chalikov D. Statistical properties of nonlinear one-dimensional wave fields // Nonlinear processes in geophysics. 2005. V. 12. P. 1—19.
10. Hasselmann K. On the non-linear energy transfer in a gravity wave spectrum. Part 1 // J. Fluid Mech. 1962. V. 12. P. 481—500.
11. Чаликов Д. В. Трансформация гармонических волн на глубокой воде // Фундаментальная и прикладная гидрофизика. 2010. Т. 9, № 3. С. 14—21.
12. Chalikov D., Sheinin D. Modeling of Extreme Waves Based on Equations of Potential Flow with a Free Surface // Journ. Comp. Phys. 2005. V. 210. P. 247—273.
13. Babanin A. V., Babanina A., Chalikov D. Interaction of surface waves at very close wavenumbers // Ocean dynamics. 2014. V. 64, N 7. P. 1019—1023.
14. Yuen H. C., Lake B. M. Nonlinear Dynamics of Deep-Water Gravity Waves // Adv. in Appl. Mech. 1982. V. 22. P. 67—229.
15. Chalikov D., Babanin A. V. Three-dimensional periodic fully-nonlinear potential waves. Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013, July, 9—14, 2013, Nantes, France, 8 p. DOI: 978-0-7918-5533-1.
16. Chalikov D., Babanin A. V., Sanina E. Numerical Modeling of Three-Dimensional Fully Nonlinear Potential Periodic Waves // Ocean dynamics. 2014. V. 64, N 10. P. 1469—1486.
17. Chalikov D., Babanin A. V. Simulation of Wave Breaking in One-Dimensional Spectral Environment // Journal Phys. Ocean. 2012. V. 42, N 11. P. 1745—1761.
18. Longuet-Higgins M. S., Tanaka M. On the crest instabilities of steep surface waves // J. Fluid. Mech. 1997. V. 336. P. 51—68.
19. Johannessen T. B., Swan C. A numerical transient water waves. Part 1: A numerical method of computation with comparison to 2-D laboratory data // Appl. Ocean Res. 1997. V. 19. P. 293—308.
20. Johannessen T. B., Swan C. A laboratory study of the focusing of transient and directionally spread surface water waves // Proc. R. Soc. Lond. 1997. A457. P. 971–1006.
21. Johannessen T. B., Swan C. On the nonlinear dynamics of wave groups produced by the focusing of surface-water waves // Proc. R. Soc. Lond. 2003. A459. P. 1021—1052.
22. Brown M. G., Jensen A. Experiments in focusing unidirectional water waves // J. Geophys. Res. 2001. C106. P. 16917—16928.
Review
For citations:
Chalikov D.V. Unfamiliar Properties оf Surface Waves. Fundamental and Applied Hydrophysics. 2016;9(1):8-16. (In Russ.)
Views:
101
Email this article 