  In this study we discuss the shapes and statistics of the rogue (freak) waves
emerging due to wave-current interactions. With this purpose, we use a simple
governing equation which is a nonlinear Schrodinger equation (NLSE) extended by
R. Smith (1976). This extended NLSE accounts for the effects of current
gradient 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 unstable
against random chaotic perturbation in the current profile. Therefore the
monochromatic wave field with unit amplitude turns into a chaotic sea state
with many peaks. By comparing the numerical and analytical results, we show
that rogue waves due to perturbations in the current profile are in the form of
rational rogue wave solutions of the NLSE. We also discuss the effects of
magnitude of the chaotic current profile perturbations on the statistics of the
rogue wave generation at the ocean surface. The extension term in Smith's
extended NLSE causes phase shifts and it does not change the total energy level
of the wave field. Using the methodology adopted in this work, the dynamics of
rogue wave occurrence on the ocean surface due to blocking effect of currents
can be studied. This enhances the safety of the offshore operations and ocean
travel.
