Gravity-capillary waves in layered fluid - M.La Rocca; Sciortino, G.; Boniforti, M. (Нелінійні коливання, 2003)
In this work we analyse stability of a gravity wave generated on the separation surface of two immiscible liquids inside a moving container and perturbed by a capillary wave. Such a phenomenon is experimentally observed when the amplitude and the frequency of the motion imposed to the container attain certain values. Evolution of the system is described by the variational principle. We assume that motion of the system is decomposed into two modes: the gravity mode and the capillary mode. With suitable scaling assumptions it is possible to show that the evolution of the gravity mode is determined by the forcing motion, while the capillary mode is excited by the nonlinear interactions between the capillary and gravity modes. At last, an analytical dispersion relation is obtained for the pulsation of the capillary mode. This relation is a function of several quantities, all depending on the capillary wavenumber and the characteristics of the exciting motion.