Abstract
Inviscid flow with a free surface over a flexible boundary is considered. The dispersion relation is obtained, and the conditions for linear instability are investigated. The linear dispersion relation is then used to show that the conditions for nonlinear three-wave resonance are often met. In some circumstances, the resonance may be of the “explosive” sort, involving waves of opposite energy sign; but the most common resonant configurations are non-explosive ones. Next, the wave-amplitude evolution equations for three-wave resonance are derived, firstly by a “direct” approach, and then via a variational (averaged Lagrangian) method. Results are in agreement with those of Case and Chin for capillary-gravity waves, and Craik and Adam, for three-layer fluid flow, on taking the appropriate limits. We also consider a nonlinear model for the flexible boundary.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
