Modeling the ship white water wake in the midwave infrared

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Abstract
We have modeled the white water wake of a ship as a single layer of bubbles packed on the sea surface within the perimeter of the trailing turbulent wake. The size of the bubbles is considered greater than the midwave infrared wavelengths such that the optical geometrical approximation remains valid. The upper half bubble hemisphere is meshed into facets, and we calculate the probability density function of their slopes and constrain that distribution by the geometrical limits imposed by the position of the receiver through the shadowing of facets by other bubbles and of facets that are facing away from the receiver. For the facets that are visible, we compute the midwave infrared emitted and reflected radiance for the white water wake for atmospheric, solar, and sea conditions that prevailed during a ship wake measurement trial using a homegrown simulation code, the Sea Surface Radiance Simulator. The range of slopes that are visible to the receiver for the white water wake greatly exceeds those that are present in the turbulent wake and in the sea background. Consequently, the variability in the white water wake radiance is substantial. As a function of the downstream distance astern of the ship, we have ad hoc assumed that the white water wake fraction decays linearly or proportionally to the turbulent intensity in the wake. Comparing to measurements, we find an agreement in trend behavior of the midwave radiance contrast of the white water wake with downstream distance for a white water wake fraction that decays proportionally to the square of the turbulence intensity.

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