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

Research paper by S. V. Filatov, M. Yu. Brazhnikov; A. A. Levchenko; A. M. Lihter

Indexed on: 09 Nov '16Published on: 01 Sep '16Published in: Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques



Abstract

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 .AbstractThe 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 .f p pf b bf b bAβff b bf d df d df b b