Scaling of optically thick plume signatures

Scaling laws for spectrally resolved infrared source signature from an aircraft or missile exhaust plume in the optically thick carbon dioxide emission region are developed. Using model problems based on approximate flow fields and simplified radiative transport solutions, unusual scaling possibilities are uncovered. According to the results, the signatures from a small plume and a large one can be made to correspond albeit at different wavelengths. Monochromatically, at certain points in the spectrum the emission decreases with increasing size while at other points it increases with increasing size. Under certain conditions, the emission over a broad band follows the usual size scaling that is expected from an optically thick uniform property emitter, i.e. emission proportional to area. The plume is a non-uniform source having a distribution of temperature and species concentrations. In optically thin portions of the spectrum, almost all the radiation emitted escapes the plume with only a small fraction being self absorbed by plume gases. The difficulty in scaling carbon dioxide emission is due to the fact that the bulk of the radiation that arises in the hotter inner regions of the plume is absorbed by the cooler outer layers of the plume