On the nonlinear energy transfer in the unidirected adiabatic surface waves

► An exact numerical model of 1D surface gravity waves was used for long-term simulations of wave field evolution for different wave steepness. ► Unidirected wave field transformation occurs due to reversible and irreversible wave interactions. The last produces the systematic energy shift towards low wave numbers (downshifting). ► The results support the Benjamin-Feir instability theory and contradict to Hasselmannʼs results. ► The Hasselmannʼs theory is unable to predict the development of the unidirected waves and consequently - the waves with a narrow angle spectrum.