  We describe the theory and present numerical evidence for a new type of
nonlinear resonant interaction between gravity waves on the surface of deep
water. The resonance constitutes a generalisation of the usual 'exact'
resonance as we show that exchanges of energy between the waves can be enhanced
when the interaction is three-wave rather than four and the linear frequency
mismatch, or detuning, is non-zero i.e. $\omega_1\pm\omega_2\pm\omega_3 \neq0.$
This is possible because the resonance condition is now a match between the
so-called 'precession frequency' of a given $\textit{triad interaction}$ and an
existent nonlinear frequency in the system. In the limit of weak nonlinearity
this precession frequency is simply due to the linear 'drift' of the triad
phase; therefore, it tends toward the detuning. This means precession resonance
of this type can occur at finite amplitudes, with nonlinear corrections
contributing to the resonance. We report energy transfer efficiencies of up to
40%, depending on the model options. To the authors' knowledge this represents
the first new type of nonlinear resonance in surface gravity waves since the
seminal work of Benjamin & Feir (1967).
