Abstract
Resonant interaction of wave trains on the sea surface has been recognized as a fundamental mode of energy interchange between waves of different lengths, directions and frequencies. To predict the development of the entire sea-wave spectrum, it is further necessary to understand the mutual influence of short and long waves. Such understanding is also useful for interpreting remote sensing data by microwave radar. In the high frequency end of the spectrum, corresponding to microwaves in the X-band, resonance of three trains of short gravity—capillary McGoldrick waves has been examined by McGoldrick (1965), Simmons (1969), Meiss and Watson (1978) and others. It is natural to ask how this resonance behavior might change in the presence of a much longer wave. Our purpose here is to study the evolution of three resonating gravity—capillary waves propagating in different directions on a long gravity wave. This topic has been considered in the closely related paper Trulsen and Mei (1995) which we subsequently refer to as TM
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Banerjee, P. P. and Korpel, A. (1982), Subharmonic generation by resonant three-wave interaction of deep-water capillary wavesPhys. Fluids 25, 1938 – 1943.
Chen, B. and Saffman, P. G. (1979), Steady gravity-capillary waves in deep water — I. Weakly nonlinear wavesStud. Appl. Math 60, 183 – 210.
Grimshaw, R. (1988), The modulation of short gravity waves by long waves or currentsJ. Austral. Math. Soc. Ser. B 29, 410 – 429.
Henderson, D. M. and Hammack, J. L. (1987), Experiments on ripple instabilities. Part 1. Resonant TriadsJ. Fluid Mech 184, 15 – 41.
McGoldrick, L. F. (1965), Resonant interactions among capillary-gravity wavesJ. Fluid Mech 21, 305 – 331.
McGoldrick, L. F. (1970), An experiment on second-order capillary gravity resonant wave interactionsJ. Fluid Mech 40, 251 – 271.
Ma, Y.-C. (1982), Weakly nonlinear steady gravity-capillary wavesPhys. Fluids 25, 945 – 948.
Meiss, J. D. and Watson; K. M. (1978), Discussion of some weakly nonlinear systems in continuum mechanics. InTopics in Nonlinear Dynamics (Ed. S. Jorna)46, 296–323. American Institute of Physics.
Naciri, M. and Mei, C. C. (1992), Evolution of a short surface wave on a very long surface wave of finite amplitudeJ. Fluid Mech 235, 415 – 452.
Perlin, M., Henderson, D. M. and Hammack, J. L. (1990), Experiments on ripple instabilities. Part 2. Selective amplification of resonant triadsJ. Fluid Mech 219, 51 – 80.
Reeder, J. and Shinbrot, M. (1981), On Wilton ripples, I: Formal derivation of the phenomenonWave Motion 3, 115 – 135.
Simmons, W. F. (1969), A variational method for weak resonant wave interactionsProc. R. Soc. Lond A 309, 551 – 575.
Trulsen, K. and Mei, C. C. (1995), Modulation of three resonating gravity-capillary waves by a long gravity waveJ. Fluid Mech 290, 345 – 376.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Trulsen, K., Mei, C.C. (1996). A Resonating Triad of Gravity—Capillary Waves on a Long Gravity Wave. In: Grue, J., Gjevik, B., Weber, J.E. (eds) Waves and Nonlinear Processes in Hydrodynamics. Fluid Mechanics and Its Applications, vol 34. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0253-4_14
Download citation
DOI: https://doi.org/10.1007/978-94-009-0253-4_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6597-9
Online ISBN: 978-94-009-0253-4
eBook Packages: Springer Book Archive