  We provide a scenario for a singularity-mediated turbulence based on the
self-focusing non-linear Schr\"odinger equation, for which sufficiently smooth
initial states leads to blow-up in finite time. Here, by adding dissipation,
these singularities are regularized, and the inclusion of an external forcing
results in a chaotic fluctuating state. The strong events appear randomly in
space and time, making the dissipation rate highly fluctuating. The model shows
that: i) dissipation takes place near the singularities only, ii) such intense
events are random in space and time, iii) the mean dissipation rate is almost
constant as the viscosity varies, and iv) the observation of an
Obukhov-Kolmogorov spectrum with a power law dependence together with an
intermittent behavior using structure functions correlations, in close
correspondence with fluid turbulence.
