Wave-particle interaction in the Faraday waves

Abstract

Abstract: Wave motion in disordered Faraday waves is analysed in terms of oscillons or quasi-particles. The motion of these oscillons is measured using particle tracking tools and it is compared with the motion of fluid particles on the water surface. Both the real floating particles and the oscillons, representing the collective fluid motion, show Brownian-type dispersion exhibiting ballistic and diffusive mean squared displacement at short and long times, respectively. While the floating particles motion has been previously explained in the context of two-dimensional turbulence driven by Faraday waves, no theoretical description exists for the random walk type motion of oscillons. It is found that the r.m.s velocity $$\left\langle {\tilde u_{osc} } \right\rangle _{rms}$$ of oscillons is directly related to the turbulent r.m.s. velocity $$\left\langle {\tilde u_{rms} } \right\rangle$$ of the fluid particles in a broad range of vertical accelerations. The measured $$\left\langle {\tilde u_{osc} } \right\rangle _{rms}$$ accurately explains the broadening of the frequency spectra of the surface elevation observed in disordered Faraday waves. These results suggest that 2D turbulence is the driving force behind both the randomization of the oscillons motion and the resulting broadening of the wave frequency spectra. The coupling between wave motion and hydrodynamic turbulence demonstrated here offers new perspectives for predicting complex fluid transport from the knowledge of wave field spectra and vice versa.