Abstract
A viscous boundary‐layer flow, first proposed by Lock as a model for the initiation of water waves by wind, is studied. A stability analysis of the flow indicates that the linear instability present is relatively weak. However, under certain conditions, the system can support coalescing normal modes, and thus, direct resonance between such modes is possible. A nonlinear perturbative analysis at direct resonance is performed, and the equation governing the slow temporal evolution of a finite‐amplitude oscillatory disturbance is derived. The appropriate evolution equation is of second order in time. The nonlinear effects are of crucial importance in the development of a resonant disturbance. Comparison of the theoretical predictions with experiments suggests that direct resonance may play a significant role in explaining the observed large initial growth rates of gravity water waves of wavelength longer than about 12 cm.
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.
