  Turbulence in a system of nonlinearly interacting waves is referred to as
wave turbulence. It has been known since seminal work by Kolmogorov, that
turbulent dynamics is controlled by a directional energy flux through the
wavelength scales. We demonstrate that an energy cascade in wave turbulence can
be bi-directional, that is, can simultaneously flow towards large and small
wavelength scales from the pumping scales at which it is injected. This
observation is in sharp contrast to existing experiments and wave turbulence
theory where the energy flux only flows in one direction. We demonstrate that
the bi-directional energy cascade changes the energy budget in the system and
leads to formation of large-scale, large-amplitude waves similar to oceanic
rogue waves. To study surface wave turbulence, we took advantage of capillary
waves on a free, weakly charged surface of superfluid helium He-II at
temperature 1.7K. Although He-II demonstrates non-classical thermomechanical
effects and quantized vorticity, waves on its surface are identical to those on
a classical Newtonian fluid with extremely low viscosity. The possibility of
directly driving a charged surface by an oscillating electric field and the low
viscosity of He-II have allowed us to isolate the surface dynamics and study
nonlinear surface waves in a range of frequencies much wider than in
experiments with classical fluids.
