In  there is a derivation of the theory of weak turbulence. In contrast to Kolmogorov's turbulence definition, the theory of weak turbulence does not demand that you look at length scales far from those, at which energy is pumped into and out of the system.
When the theory of weak turbulence is related to particles floating on
capillary waves such as in our measurement on the Faraday experiment, you get
the following relation