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the relaxation rate with increasing
u
*
/
c
(e.g., Keller and Wright 1975,
Hughes 1978, Plant 1982). Based on the relaxation theory, in a non-
resonant system (comprised of the modulating current field, the modulated
wave component, and the associated wind generation and breaking dissipa-
tion) the spectral density fluctuation (thus the contrast of radar backscatter)
is larger if the relaxation rate is slower (longer wavelength, lower wind
speed, or faster convection of the modulating current field). The modulus
of relaxation can be expressed as (Hwang and Shemdin 1990)
s
r
M
(2)
2
n
2
E
/
:
1
c
/
C
r
n
g
n
where :
n
and
C
n
are the
n
-th harmonic of the characteristic angular fre-
quency and the phase velocity of the modulating current field,
r
the ratio of
the group velocity,
c
g
, and the phase velocity,
c
, of the modulated short
wave component,
s
the slope of the wave number spectrum in the vicinity
of the modulated short wave component, and E
r
the relaxation rate, which
is approximately proportional to the growth rate, E, of the modulated short
waves. Hwang (1999) presented an analysis of laboratory measurements of
the hydrodynamic modulation of capillary-gravity waves. The result show-
ed that the theoretical predictions were in excellent agreement with the up-
per bound of the experimental data. This is a logical conclusion because in
a wind-generated wave system, growth and decay of short waves are con-
tinuous processes. The interaction time or interaction distance between a
particular modulated wave number component and the modulating long
waves is variable. Therefore, the measurements represent modulation re-
sults at different stages of interaction. Hwang and Shemdin (1990) illus-
trated with numerical computations that the modulus of hydrodynamic
modulation increases monotonically with interaction duration or inter-
action distance.
Although the ratio of
B
III
(
k
)/
B
I
(
k
) presented in the last section is not the
same as the modulus of hydrodynamic modulation, one expects that the
two quantities to be proportional. The increasing trend of hydrodynamic
modulation of short CG waves has important implications in radar remote
sensing. The results suggest that high contrast of sea return can be obtained
from radars of shorter wavelengths, making implementation on spacecraft
or aircraft much easier to accommodate. It is noted that similarly sur-
prising results have been reported for much longer Bragg waves of L- and
X-band radars (about 25 and 3 cm wavelengths). These results suggest that
the hydrodynamic properties of short surface waves (decimetre to millime-
tre scales) are very different from those of longer gravity waves (greater
than ~10 m) that have been studied extensively. For example, one of the
