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Resonant interactions of rotational water waves in the equatorial f-plane approximation
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Martin, Calin I.
We investigate here the resonance phenomenon in periodic unidirectional water waves in flows of constant vorticity governed by the equatorial f-plane approximation. The relevance of such water waves displaying a one dimensional wave vector is also underlined in the paper—in the context of equatorial capillary-gravity water waves—and serves as the basis for the resonance analysis which is carried out by means of dispersion relations for equatorial water waves that were quite recently derived [see the work of Constantin, Differ. Integr. Equations 26(3-4), 237–252 (2013) and Martin, Nonlinear Anal.: Theory, Methods Appl. 96, 1–17 (2014)]. We show that, while gravity water waves do not exhibit three-wave resonance, the four-wave resonance occurs irrespective of the vorticity.
Resonance phenomenon , Equatorial f-plane approximation
Basu, B. and Martin, C. I. (2018) ‘Resonant interactions of rotational water waves in the equatorial f-plane approximation’, Journal of Mathematical Physics, 59(10), 103101 (10pp). doi:10.1063/1.5027027
© 2018, the Authors. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Basu, B. and Martin, C. I. (2018) ‘Resonant interactions of rotational water waves in the equatorial f-plane approximation’, Journal of Mathematical Physics, 59(10), 103101 (10pp). doi:10.1063/1.5027027 and may be found at https://aip.scitation.org/doi/10.1063/1.5027027.