Based on an experiment and simulations, we report that an energy cascade in surface capillary waves can be bi-directional, that is, can simultaneously flow towards large and small wavelength scales from the pumping scales. The bi-directional energy cascade provides an effective global coupling mechanism between the scales. We show that formation of the bi-directional cascade leads to creation of large-scale, large-amplitude waves on the fluid surface.

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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.