On the Kolmogorov Constants for the Temperature-Humidity Cospectrum and the Refractive Index Spectrum

Abstract

Structure parameters for the temperature (C?2) and humidity (Cq2) spectra and for the temperature-humidity cospectrum (C?q) that I have measured and additional values of C?q/(C?2Cq2)1/2 reported in the literature yield an estimate of the ratio of Kolmogorov constants ??q/(???q)1/2 via the temperature-humidity covariance budget. Here ??, ?q and ??q are the Kolmogorov constants for the temperature and humidity spectra and the temperature-humidity cospectrum, respectively. The data suggest that ??q/(???q)1/2 = 0.80 ± 0.16; consequently, since ?? = ?q0.40 ± 0.02, ??q = 0.32 ± 0.08. Considering the uncertainties involved, however, I cannot reject the hypothesis ?? = ?q =??q. With the dissipation rate (Nn) derived from the refractive index variance budget, and with this apparent equality of ??, ?q, and ??q, the refractive index spectrum (Φn) has the Kolmogorov-Corrsin form Φn(k) = ?nNn??1/3k?5/3 in an inertial-convective subrange, with the Kolmogorov constant ?n also roughly 0.40.