Formation of low-frequency harmonics on the surface of liquid hydrogen and helium in a turbulent regime

Abstract

The formation of harmonics at frequencies below a monochromatic pump frequency in a system of capillary-gravity waves on surfaces of liquid hydrogen and superfluid helium in a turbulent regime is studied experimentally. By choosing the spectral characteristics of the exciting force and the resolution in the spectrum of the surface oscillations, it is possible to create conditions for low-frequency wave generation by changing the boundaries of the experimental cell. For certain monochromatic pump frequencies, low-frequency harmonics are observed on liquid hydrogen surfaces only in a rectangular cell. Energy transfer to the low-frequency subharmonics, as well as to high-frequency harmonics, is caused by three-wave decay processes. An inverse cascade develops on superfluid helium surfaces in a cylindrical cell as a result of three-wave decay processes, with about 90% of the energy concentrated in the inverse cascade.

Cascades and transitions in turbulent flows

“…These experiments provided means to compare with the theoretical predictions and against numerical simulations [613,626,627]. Finally, we note that evidence for a split energy cascade has been observed in gravito-capilary turbulence [96,97] on the surface of liquid Helium. A recent review of these experimental results can be found in [628].…”

“…Similar behaviour has been attributed to astrophysical flows (like the atmosphere of Venus and Jupiter [88,89], and accretion discs [90]), in plasma flows [91] and in industrial applications (like in tokamak [92]) either due to the thinness of the layer, to fast rotation or to the presence of strong magnetic fields. Split cascades have also been observed in wave systems [93], multi-scale optical turbulence [94], acoustic turbulence [95] and capillary turbulence on the surface of liquid hydrogen and helium [96,97]. In many of these systems, a change from a split to a strict forward cascade has also been detected with a critical transition behaviour.…”

Observation of dynamic maximum in a turbulent cascade on the surface of liquid hydrogen

“…The influence of discreetness on the turbulent distribution in the system of waves on the liquid hydrogen surface was studied before in [10,11].…”

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

“…In a system of gravity waves formation of the both direct and inverse cascades is possible and the wave energy could be directed into both high and low frequency domains. From our experiment and subsequent numerical simulations [5][6][7] it follows that in a finite size cell, where the spectrum of the wave excitations is discrete, one might observe an energy flow from the pumping region towards both high and low frequency domains even for capillary waves. It should be mentioned that in all the numerical simulations the authors preferred to use asymptotic approximations,…”

“…Detailed method of registration of surface elevations is given in [5]. Any variations of the angle between the gliding laser beam and the oscillating surface led to modulation of the power of the reflected beam.…”