  A robust energy transfer mechanism is found in nonlinear wave systems, which
favours transfers towards modes interacting via non-resonant triads, applicable
in meteorology, nonlinear optics and plasma wave turbulence. Transfer
efficiency is maximal when the frequency mismatch of the non-resonant triad
balances the system's nonlinear frequency: at intermediate levels of
oscillation amplitudes an instability is triggered that explores unstable
manifolds of periodic orbits, so turbulent cascades are most efficient at
intermediate nonlinearity. Numerical simulations confirm analytical
predictions.
