  We consider stochastic inviscid dyadic models with energy-preserving noise.
It is shown that the models admit weak solutions which are unique in law. Under
a certain scaling limit of the noise, the stochastic models converge weakly to
a deterministic viscous dyadic model, for which we provide explicit convergence
rates in terms of the parameters of noise. A central limit theorem underlying
such scaling limit is also established. In case that the stochastic dyadic
model is viscous, we show the phenomenon of dissipation enhancement for
suitably chosen noise.

Probability