For infrared and optical wavelengths, refractive turbulence is characterized mainly by the temperature structure constant, CT2. Traditionally, CT2 is found through analysis of temperature spectra, by identifying a region where the spectra exhibits a –5/3 slope on a log-log plot. Analysis of the temperature structure function, DTT, as opposed to spectra, can facilitate the determination of CT2 because the curves tend to be smoother, so that regions of constant slope are more easily identified.
Calculation of CT2, as well as CU2, CV2 and CW2 , from structure functions were carried out for data acquired in Australia in 1998 and 1999 as well as data from flights in Japan in 1999. Results for level flight segments were compared with corresponding analysis of spectra. The structure function approach was also used to calculate CT2 for 100 second intervals during level flight, climb and descent segments providing time and altitude variations that displayed significant variations in CT2 . For two days during the 1998 Australia campaign, these results were converted to Cn2 , refractive index structure function, and compared with balloon Thermosonde data obtained at the same time as the flights.
For much of the data analyzed, the temperature structure functions also exhibited a distinct change in slope from 2/3 to 2/5, the expected behavior for a buoyancy subrange as predicted by Bolgiano. Such a region is generally not identifiable in the spectra. In some cases of weaker turbulence, the region of 2/5 slope is more dominant than the inertial subrange, extending over a greater range of scales. The buoyancy subrange scaling that leads to the 2/5 scaling predicts that a temperature structure function for such a region would be given by (CT2)B=DTT/r2/5=Cc4/5 (g/T)-2/5 (where c is the temperature dissipation). Analysis of data that exhibited a 2/5 slope indicated that this correlation was well obeyed over several orders of magnitude, and provided an estimate for the constant C.