A ship moving through the water generates a broad spectrum of surface
waves, which propagate away from their point of origin on the ship track.
Waves satisfying the Bragg criterion will be concentrated along a pair of
lines separated by a half-angle of approximately
C
a = tan”! y* cos $1, (1)
S
where cq is the group velocity of the Bragg waves, Vs is the ship
speed, and ¢ is the radar look direction with respect to the ship track. A
diagram illustrating these waves is shown in Figure 1, for a more complete
discussion of this model refer to Lyden, et al. (1985a)
L-band (23.5 cm wavelength) SAR images collected under very calm sur-
face (low wind) conditions often show bright lines forming narrow angles
which agree with the angles predicted by the model discussed above.
Examples include the wakes produced by the USNS Quapaw in Dabob Bay,
Washington, during the 1983 Georgia Strait Experiment (Kasischke, et al.,
1983), as well as several other wakes observed under similar conditions
behind various ships during the same experiment. One such example is shown
in Figure 2. This image of the Quapaw was collected on 28 July 1983 during
pass 3 of the DREP 8 mission. This image was remapped from a slant-range
to a ground-range representation and the wake angle was measured using two
procedures. The first was based on a regression analysis of the brightest
points along each arm while the other procedure examined the autocorrela-
tion functions of angularly integrated slices across the wake arms. The
autocorrelation procedure was performed with the center of integration at
the ship's location, and with the center at the intersection of the wake
arms based on the regression method. These wake angle measurements are
presented in Figure 3 along with those predicted by Eq. (1) for first- and
second-order Bragg waves. The predicted wake angles include the effects
of: scanning distortion or relativity effects, Doppler displacement due to
surface motion, and the variation of Bragg wavelength with incidence angle.
Several points can be made regarding the wake angles presented in
Figure 3. The regression analysis placed the intersection of the two wake
arms 320 m forward of the observed ship location. This may indicate that
the waves producing the V-wake arms in the SAR image are not generated at
the ship's centerline but at the edges of the hull. An alternative expla-
nation given by Swanson (1986) is that the wake arms are initially dis-
placed outward due to their interaction with surface currents associated
with ship-generated vortices. In his study, Swanson showed close agreement
between the autocorrelation measurements centered at the ship and predic-
tions by a model which incorporated vortex surface currents. The results
presented in Figure 3 indicate close agreement between the angle predic-
tions for first-order Bragg scattering, the regression measurements, and
the autocorrelation measurements when the center of integration was located
forward of the ship. It is interesting to note that the predicted angles
and those measured by the autocorrelation method with the center forward of
the ship increase with distance behind the ship due to the change of Bragg
wavelength with incidence angle. Several other passes from the Georgia
Strait Experiment were examined with similar results.
An interesting subset of these cases are those for which the SAR look
direction is more nearly parallel to the ship track (i.e., ¢ = 0) as shown
for Ship 2 in Figure 4. In this case, the wake lines are observed to be
nearly parallel but displaced in the SAR along-track direction by an
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