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In this study we discuss the shapes and statistics of the rogue (freak) wavesemerging due to wave-current interactions. With this purpose, we use a simplegoverning equation which is a nonlinear Schrodinger equation (NLSE) extended byR. Smith (1976). This extended NLSE accounts for the effects of currentgradient on the nonlinear dynamics of the ocean surface near blocking point.Using a split-step scheme we show that the extended NLSE of Smith is unstableagainst random chaotic perturbation in the current profile. Therefore themonochromatic wave field with unit amplitude turns into a chaotic sea statewith many peaks. By comparing the numerical and analytical results, we showthat rogue waves due to perturbations in the current profile are in the form ofrational rogue wave solutions of the NLSE. We also discuss the effects ofmagnitude of the chaotic current profile perturbations on the statistics of therogue wave generation at the ocean surface. The extension term in Smith'sextended NLSE causes phase shifts and it does not change the total energy levelof the wave field. Using the methodology adopted in this work, the dynamics ofrogue wave occurrence on the ocean surface due to blocking effect of currentscan be studied. This enhances the safety of the offshore operations and oceantravel.

Shapes and Statistics of the Rogue Waves Generated by Chaotic Ocean Current