Direction Symmetry of Wave Field Modulation by Tidal Current and its Consequences for Extreme Nonlinear Waves

Theoretical studies on the modulation of unidimensional regular waves over a flat bottom due to a current typically assign an asymmetry between the effects of opposing/following streams on the evolution of major sea variables, such as significant wave height. The significant wave height is expected to monotonically increase with opposing streams and to decrease with following streams. To some extent, observations on data sets containing a few thousand of waves or over a continuous series of about a day confirm this prediction. Here we show that in very broad-banded seas with high directional spread, the asymptotic behavior of sea variables over large data sets is highly non-trivial and does not follow the theoretical predictions, especially at high values of the ratio between tidal stream and group velocity. Furthermore, we analyze the anomalous statistics originating from both forward and opposing non-stationary currents. Despite the sea states being dominantly broad-banded and featuring a large directional spread, we found that anomalous statistics are of the same order of magnitude of those observed in unidirectional laboratory experiments and symmetrical in regard to the orientation of the tidal current.