On internal nonlinear resonant interaction of capillary-gravitational waves on the flat surface of a viscous liquid

Mechanisms behind internal nonlinear resonant interaction of periodic capillary-gravitational waves on the uniformly charged flat surface of an infinitely deep viscous conducting liquid are considered. A mathematical procedure modifying the well-known method of many scales is proposed for constructing an asymptotically valid solution near the resonance. It is shown that the internal nonlinear resonant interaction results in effective energy transfer from long waves to shorter ones. An increase in the viscosity of the liquid diminishes the rate of energy transfer between resonantly interacting waves.