An experimental investigation on the initial instability of nonlinear deep-water wave
trains including wind effects is reported. The experiment was conducted at the Ocean
Engineering Laboratory wind-wave facility (50 m long, 4.2 m wide, 2.1 m deep), with
a fully computer-controlled mechanical wave generator to explore the parameter
space: steepness; sideband frequency; wind speed. The estimated growth rates of
the Benjamin–Feir instability from seeded wind-free experiments agreed well with
the theoretical prediction derived from Krasitskii's four-wave reduced equation as
computed here. Wind was added to the same wave system; the growth rates of the
sidebands were reduced for weak, and enhanced for strong wind forcing. Experiments
with naturally selected sidebands, i.e. unseeded, were conducted as well; measurements
showed that wind did not inhibit the growth of sidebands in the case of either two-dimensional or three-dimensional instabilities. A comparison of the results with earlier
work suggests that there are two independent effects of wind: first, the alteration of
the inviscid growth for a given modulational frequency as shown by comparison with
the seeded experiments without wind; second, a change in the natural modulational
frequency appearing in the presence of wind which is a function of the wave age,
as observed in unseeded experiments. Both effects combined will determine whether
the modulational instability is enhanced or suppressed; comparison of experimental
results with theoretical predictions suggests that the effect of wind on the natural
selection of the modulational frequency is the dominant effect. It was shown that
for moderate to old waves, the net effect of wind on the modulational instability is
small. For all the experiments except a few unseeded cases with weak breakers, the
modulation was small and no breaking was observed within the tank.
Stabilization of uni-directional water wave trains over an uneven bottom