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Eur I Mech H Fluids I

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Eur. .I. Mech. H/Fluids, 18, (I), 67-91, 1999 Interaction between a Stokes wave packet and a solitary wave D. CLAMOND a*, J.P. GERMAIN b ABSTRACT. - This paper is a theoretical and experimental study of the propagation of a short gravity wave packet (modulated Stokes wave) over a solitary wave. The theoretical approach used here relies on a nonlinear WKB-type perturbation method. This method yields a theory of gravity waves that can describe both short and long waves simultaneously. We obtain explicit analytical solutions describing the interaction between the soliton and the short wave packet: phase shifts, variations of wavelengths and of frequencies (Doppler effects). In the experimental part of this work the phase shift experienced by the Stokes wave is measured. The theoretical conclusions are contirmed. Q Elsevier. Paris. 1. Introduction The study of the interaction between waves of short and long wavelengths has many applications in various branches of physics where nonlinear dispersive effects are present. The investigation of the interaction between long and short surface waves has already attracted considerable attention. For infinite depth, the works of Henyey et al. (1988), Zhang and Melville (1990), Naciri and Mei (1992), Naciri and Mei (1993) and Woodruff and Messiter (1994) are noteworthy.

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