Wave turbulence on the surface of liquid hydrogen in restricted geometry: The influence of the boundary conditions

Abstract

Formation of low frequency harmonics on turbulent distribution in the system of waves on the surface of liquid hydrogen has been studied in the frequency range 1–100 Hz (capillary-gravity waves). It is shown that the geometry of the experimental cell has a significant influence on the direct cascade of capillary waves generated by monochromatic force as well as on the direction of the wave energy transfer from the range of pumping towards that of dissipation. Besides a direct turbulent cascade, single half-frequency harmonic generation was observed in a cylindrical cell under high pump power. In a square cell we observed not only a half-frequency harmonic but a number of low frequency harmonics below the driving frequency generated by the nonlinear three-wave interaction. In the case of a rectangular cell we observed formation of incommensurate low frequency harmonics caused by the three-wave interaction of capillary waves and generation of a wave mode of ∼1 Hz in the frequency range of gravity waves which could be attributed to the four-wave interaction.