us 
  
amount consistent with the Doppler shift due to the phase velocity of the 
Bragg waves. Thus, these wakes appear to be due to Bragg waves travelling 
along the ship track in both directions (i.e., in the same direction as 
the ship and in the opposite direction). 
The apparent agreement between these observations and the wake geometry 
predicted by the simple Bragg model suggests that this model is basically 
correct. There are several puzzling aspects of this explanation, however, 
which are not yet well-understood. First, the "standard" Kelvin theory 
(discussed below) predicts that the short waves involved in this model 
should form linear wavefronts aligned at small angles to the ship track. 
Thus, these wakes should be visible only for look directions approximately 
perpendicular to the ship track, in contradiction to many observations. 
The probable reason for this discrepancy is that the short waves are gener- 
ated with essentially random phases, so that the Kelvin theory does not 
apply. 
The second puzzling aspect of this model is the apparent lifetime of 
the Bragg waves, which exceeds 400 sec for the Dabob Bay wakes. This is 
considerably longer than expected by many investigators. It should be 
noted, however, that this figure is consistent with growth rates obtained 
by Plant (1982), assuming an equivalence between the growth and decay 
rates. When wind speeds are more than about 3 m/s, these wakes do not 
appear, which is consistent with the strong wind speed dependence of the 
growth rates obtained by Plant and others, and also with the decay rates 
due to nonlinear interactions with ambient waves as discussed by Watson in 
JASONs (1984). To investigate the decay of the wake arms, a series of mea- 
surements were performed on the data in Figure 3 of the peak wake arm 
intensity at 500 m intervals extending to 2.5 kilometers aft of the ship. 
These measurements are shown plotted in Figure 5. These data are plotted 
relative to the measurement 500 m aft of the ship which was normalized to 
0 dB. The solid line corresponds to the linear regression of the measure- 
ments. Also plotted as dashed lines are the predicted fall-offs of radar 
backscatter for wind speeds of 0 and 3 m/s based on Watson's decay times. 
The regression of the measurements corresponds very closely to the 2 m/s 
prediction. The wind speed at 10 m height during this pass was 2.8 m/s. 
The decay times were related to a distance aft of the ship by assuming a 
ship speed of 7.5 m/s. These results support the theory that the V-wakes 
features observed in Seasat and aircraft L-band SAR data are the result of 
scattering from Bragg waves generated by the ship which decay in time due 
to viscosity and wind effects. A more complete description of the above 
measurements is given by Lyden (1985b). 
No clearcut examples of narrow V-wakes have been observed at X-band 
(3.2 cm wavelength). Similarly appearing X-band wakes have been noted, but 
these are probably associated with the turbulent wake and are discussed in 
the next section. It is postulated that the type of wake discussed above 
does not occur at X-band either because the lifetime of the X-band Bragg 
waves is too short or these waves are not able to propagate outside of the 
turbulent region because their group velocity is too small. 
The second sub-category of ship-generated surface waves is made up of 
the longer gravity waves which form the classical Kelvin wake. A diagram of 
the Kelvin wake system is shown in Figure 6. This system consists of two 
sets of wavefronts formed by the constructive interference of waves gener- 
ated along the ship track. Waves with wavelengths less than 
415