Trapping and instability of directional gravity waves in localized water currents

The influence of localized water currents on the nonlinear dynamics and stability of large amplitude, statistically distributed gravity waves is investigated theoretically and numerically by means of an evolution equation for a Wigner function governing the spectrum of waves. It is shown that water waves propagating in the opposite direction of a localized current channel can be trapped in the channel, which can lead to the amplification of the wave intensity. Under certain conditions the wave intensity can be further localized due to a self-focusing (Benjamin-Feir) instability. The localized amplification of the wave intensity may increase the probability of extreme events in the form of freak waves, which have been observed in connection with ocean currents.