Modulation Instability of a Gravity Wave and Generation of a Direct Cascade of Vortex Energy on the Surface of Water

Abstract

The development of instability of gravity-capillary waves on the surface of water excited by two perpendicular plungers has been experimentally observed. As a result of a four-wave process, waves with a frequency of 8 Hz scatter in pairs into waves with frequencies of 3.92 and 4.08 Hz, as well as 11.98 and 12.02 Hz. The amplitude of low-frequency waves increases exponentially with a characteristic time of about 90 s which exceeds the time of viscous wave damping almost by an order of magnitude. Along with the main pumping mode, the appeared low-frequency harmonics, propagating on the surface of water at an angle of 15° to each other, form large-scale vortex flows on the surface of water. The wave energy is transferred from the pumping region directly to vortices with a size comparable to the length of a bath wall. In a vortex system, a direct energy cascade with the energy distribution close to E(k) ~ k^–5/3 is formed from the region of low wave vectors.