  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,
based on a multi-year dataset, we show that in very broad-banded seas with high
directional spread, the asymptotic behavior of sea variables is highly
non-trivial and does not follow the theoretical predictions, especially at high
values of the ratio between tidal stream and group speed.
