Modeling the turbulent trailing ship wake in the infrared.

The sea surface turbulent trailing wake of a ship, which can be rather easily observed in the infrared by airborne surveillance systems, is a consequence of the difference in roughness and temperature between the wake and the sea background. We have developed a phenomenological model for the infrared radiance of the turbulent wake by assuming that the sea surface roughness is dependent upon the turbulent intensity near the sea surface. Describing the sea surface roughness with a Cox and Munk probability distribution function of slopes, we distinguish on the sea surface between the sea background and the turbulent wake by the variance of sea surface slopes, σCM2=constant and σTW2(x,y)≠constant. The latter dependence is assumed to be inversely proportional to the turbulent intensity of the wake, U(x,y). Given the incident solar, atmospheric, and sky infrared radiances, we calculate the reflected and emitted sea surface radiance from both the wake and the background. We compare the infrared contrast of the wake with infrared image data obtained in an airborne trial. Our predictions and the measurements agree very well in trend over a significant range of observer zenith angles. Our calculations reveal the strong dependence of the wake radiance on the observer zenith angle, allowing for positive and negative contrasts with the background.