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A note on the resonant interaction between a surface wave and two interfacial waves. (English) Zbl 1063.76524
Summary: Hill & Foda (1998) and Jamali (1998) have presented theoretical and experimental studies of the resonant interaction between a surface wave and two oblique interfacial waves. Despite many similarities between the findings there is one seemingly major difference. Hill & Foda’s (1998) analysis indicated that there are only narrow bands of frequency, density ratio and direction angle within which growth is possible. On the other hand, Jamali (1998) predicted and observed wave growth over wide ranges of frequency and direction angle, and for all the density ratios that he investigated. We show that Hill & Foda’s (1998) second-order representation of the dynamic interfacial boundary condition is missing a term proportional to the time derivative of the square of the velocity shear across the interface. When this missing term is included in the analysis, the resulting predictions are consistent with the laboratory experiments.
MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B55Internal waves