Abstract
We show that interaction of two monochromatic waves at the water surface enters a different dynamic regime if their wavenumbers become very close. The study is conducted by means of a fully nonlinear wave model. In the course of evolution of the two waves, downshifting of the initial wave energy and growth of the first mode occur depending on wave steepness and dk/k. Behaviour of these features changes if dk/k < 0.0025: both downshifting and growth rate become independent of dk/k, accompanied by rapid transfer of wave energy to large scales.
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References
Agnon Y, Mei CC (1985) Slow-drift motion of a two-dimensional block in beam seas. J Fluid Mech 151:279–294
Babanin AV, Chalikov D, Young IR, Saveliev I (2010) Numerical and laboratory investigation of breaking of steep two-dimensional waves in deep water. J Fluid Mech 644:433–463
Baldock TE, Huntley DA, Bird PAD, O’Hare T, Bullock GN (2000) Breakpoint generated surf beat induced by bichromatic wave groups. Coast Eng 39:213–242
Chalikov D (2012) On the nonlinear energy transfer in the unidirected adiabatic surface waves. Phys Lett A 376:2795–2798
Chalikov D, Sheinin D (2005) Modelling extreme waves based on equations of potential flow with a free surface. J Comput Phys 210:247–273
Chiang WS, Hsia SC, Hwung HH (2007) Evolution of sidebands in deep-water bichromatic wave trains. J Hydraulic Res 45:67–80
Dyachenko AI, Zakharov VE (2005) Modulational instability of Stokes wave—freak wave. Pis’ma v ZhETF 81:318–322
Galchenko A, Babanin AV, Chalikov CD, Young IR, Hsu TW (2010) Modulational instabilities and breaking strength for deep-water wave groups. J Phys Oceanogr 40:2313–2324
Liebisch TC, Blanshsan E, Donley EA, Kitching J (2012) Atom-number amplification in a magneto-optical trap via stimulated light forces. Phys Rev A 85(013407):4p
Madsen PA, Furhman DR (2006) Third-order theory for bichromatic bi-directional water waves. J Fluid Mech 557:369–397
Osborne AR (2010) Nonlinear ocean waves and the inverse scattering transform, Elsevier, 994p
Trulsen K, Stansberg CT (2001) Spatial evolution of water surface waves: numerical simulation and experiment of bichromatic waves. Proc. ISOPE, Stavanger, pp 71–77
Toffoli A, Onorato M, Babanin AV, Bitner-Gregersen EM, Monbaliu J (2007) Second-order theory and set-up in surface gravity waves: a comparison with experimental data. J Phys Oceanogr 37:2726–2739
Tulin MP, Waseda T (1999) Laboratory observations of wave group evolution, including breaking effects. J Fluid Mech 378:197–232
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Responsible Editor: Oyvind Breivik
This article is part of the Topical Collection on the 13th International Workshop on Wave Hindcasting and Forecasting in Banff, Alberta, Canada October 27 - November 1, 2013
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Babanin, A.V., Babanina, A.V. & Chalikov, D. Interaction of surface waves at very close wavenumbers. Ocean Dynamics 64, 1019–1023 (2014). https://doi.org/10.1007/s10236-014-0727-4
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DOI: https://doi.org/10.1007/s10236-014-0727-4