Modulation instability of waves in the presence of current

The model of wave's resonances in the presence of the variable current is presented. In spite of numerous numbers of papers devoting to the analysis of the wave and wave-current interactions phenomena, some of extremely strong effects like wave's overpass the adverse current blocking barrier observed in experiments are still waiting for its clear theoretical description. Our analysis shows that the Benjamin-Feir instability of Stokes waves can be strongly modified by the following or adverse horizontal subsurface current. Three wave's resonance system in a no uniform media gives rise to the modulation instability with some special properties. Interaction with countercurrent accelerates the growing of side band modes on a much shorter space scales. On the other side, wave instability on the following current is sharply depressed. The dissipation due to wave breaking gives the asymmetry of side bands modes and frequency downshifting. We theoretically describe the explosion instability of waves on the adverse blocking current and corresponding frequency downshifting. Waves can be blocked only partly and overpass the opposite current barrier at the lower side band resonance frequency.