Chemistry Reference
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waves increases monotonically with wave number and achieves a maxi-
mum in the range 9-12 rad cm
-1
(wavelengths about 5-7 mm). A nonlinear
mechanism of wave damping for cm-mm-scale waves has been hypo-
thesized, based on the assumption that nonlinearity of dm-cm-scale waves
makes a significant contribution to the spectrum of cm-mm-scale waves.
Short dm-cm-scale gravity waves are characterized, even at low winds,
by rather large slope values, so that nonlinear effects can determine the
wind wave spectrum in the gravity-capillary range. One of the effects is
connected with a non-sinusoidal profile of dm-cm-scale surface waves,
which can be considered as a result of generation of “bound waves” - high-
order harmonics and parasitic capillary ripples (Longuet-Higgins 1992).
The bound waves move with the phase velocities of basic gravity waves,
as experimentally confirmed for cm-scale waves (Yuen and Lake 1982)
and for the parasitic capillary ripples (Ermakov et al.1986), generated by
periodic gravity waves. The phase velocities of cm-mm-scale wind ripples
are determined by free capillary-gravity waves and by bound waves. Mea-
surements of phase velocities of wind ripples in support of this assumption
are scarce and have so far been carried out in a frequency range of about
1.5-10 Hz (wavelengths 40-2.5 cm) using contact methods (Yuen and Lake
1982, Ramamonjarisoa and Giovanangeli 1978), and, also at two wave-
lengths of about 1.5 cm and 0.5 cm using X-band and K
a
-band radar mea-
surements (Gade et al. 1998). No other measurements of phase velocity of
capillary-gravity wind waves (wavelengths smaller than 2-3 cm) have been
reported, at sea or in wave tanks, although these studies are very important
for the development of models of wind waves.
The amplitudes of the high-order harmonics very strongly depend on the
amplitude of the basic waves. For Stokes waves, for example, the ampli-
tude of the n-th harmonic is proportional to the n-th power of the ampli-
tude of the basic wave. Therefore, even weak damping of dm-scale basic
waves due to films can lead to strong nonlinear depression of the bound
waves (“cascade” effect), the latter effect can result in a maximum of the
damping in the mm-scale wavelength range.
This paper presents wave tank optical measurements of phase velocities
of wind waves on clean water surfaces and on water surfaces covered with
organic films and measurements of film-induced water wave damping. The
results confirm the assumption that the wind wave spectrum contains non-
linear cm-mm-scale harmonics bound to the dominant wind waves, giving
a strong contribution to the damping of wind waves due to films.
