Turbulence in the system of capillary waves on the surface of water

Abstract

The experimental results of studying wave turbulence in a system of capillary waves on the surface of water in a cylindrical vessel are presented. Waves on the surface are excited by vertical vibrations of the water-filled vessel with accelerations below the parametric-instability threshold at a fixed frequency f_p or in the frequency band from 30 to 50 Hz. The deviation of the surface from equilibrium is recorded by a laser beam reflecting from water. It is shown experimentally that the position of the high-frequency boundary of the inertial range f_b of the turbulent cascade is shifted towards high frequencies with an increase in the pump amplitude А and described by the power function f_b ~ A^β with index β equal to 1.2 ± 0.1 for monochromatic pumping and 1.10 ± 0.15 for broadband pumping. The value of the index β for monochromatic pumping is close to the theoretical estimate; for broadband pumping, it is less by a factor of 2.5. In the dissipation region f > f_b, the turbulent distribution is damped exponentially with the characteristic frequency f_d depending on the amplitude and spectral characteristic of the excitation force. It follows from the amplitude dependences that the frequency f_d is proportional to the frequency of the boundary of the inertial range f_b.