Dynamical ensemble equivalence between hydrodynamic dissipative equati
ons and suitable time-reversible dynamical systems has been investigat
ed in a class of dynamical systems for turbulence. The reversible dyna
mics is obtained from the original dissipative equations by imposing a
global constraint. We find that, by increasing the input energy, the
system changes from an equilibrium state to a non-equilibrium stationa
ry state in which an energy cascade, with the same statistical propert
ies of the original system, is clearly detected.