As far as I understand, in general, turbulence describes the process of transfer of energy from a large scale, at which a system is perturbed, to a small scale, where dissipation happens. At intermediate scales, universal and scale invariant behaviour is observed. This is called turbulence.
In the context of turbulence, one often comes across the term "weak" and "strong" turbulence. Both lead to energy cascades, but the difference between the two seems to involve the time scales on which turbulence happens. While weak turbulence is an asymptotical phenomenon, strong turbulence occurs within a finite time span.
Can somebody explain the difference in more detail and correct me if my statements above are wrong? Do the energy cascades, that are found in both cases, agree? Which models (purely mathematical or experimental) show the two types of behaviour?