  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.
