Remote Sensing Applications - Marine Surface Films - page 278

dN dt S S S S 0

(2)

wind nonlin visdis break

has to be taken into account (Hasselmann 1960) as well; here N is the
spectral action density of surface waves. As correctly noted by Gade et al.
(1998) the source term for nonlinear wave/wave interaction ( S nonlin ) is still
poorly known and cannot easily be determined.
Let us analyse the case of August 22 nd under a point of view that the ef-
fect was caused by a modification of the wave field. In suggestion that
dominant wind waves can determine the phenomenon, one of the possible
mechanisms is the «overshoot» effect in the generation of wind waves. In
spill and slick areas short wind waves of cm- and partly dm-wavelengths
are damped strongly and result in the damping of long dominant wind
waves (Phillips 1977). A spill or a slick drifting due to the wind action
leaves behind itself (i.e., at the upwind side) an area where wind waves
start to develop. It is well known that wind waves reach their equilibrium
state not monotonously, so that wind waves at short fetches exhibit higher
amplitudes than in the equilibrium range (the overshoot effect). Character-
istic fetches L at which long wind waves achieve maximum amplitudes are
of the order of 10 3 O corresponding to characteristic times for the dominant
wind waves of the order of W:

(3)

3

W | L C 4 S g 10 O T

gr

where Ois the characteristic dominant wavelength, C gr is the group veloc-
ity, g the gravity acceleration and T the period of the dominant waves. One
can expect that long waves can be amplified at the upwind side of a spill
due to the overshoot effect, if the characteristic drifting time
W

(4)

W | I V | I 0 03

drift spill drift spill

l spill is the characteristic scale of the spill, V drift the drift velocity and W (the
wind speed) is comparable with W. The last condition is satisfied for mod-
erate wind velocities (5-7 m s -1 ) and spill scales of the order of several
kilometres. The wind wave intensification due to the overshoot effect is
about twice that at the equilibrium level; this is comparable with the posi-
tive contrasts observed at the upwind side of spills. Using the numbers
given in the Table 1, W drift and Wcan be determined. If, in our analysis, l spill =
2.6 km, O= 150 m, W = 5-7 m s -1 , T = 10.5 s and g = 9.81 m s -2 , then W drift =
3.4 - 4.8 hr and W| 5.1 hr. Calculations using equations (3) and (4) show
that the characteristic time of the spill drift W drift is comparable or smaller
than the overshoot characteristic time W. For this reason, the overshoot ef-
fect for waves travelling into the area left by the drifting spill is significant