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

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  • 1 NOAA/ERL Wave Propagation Laboratory, Boulder, CO 80303
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Abstract

Structure parameters for the temperature (Cθ2) and humidity (Cq2) spectra and for the temperature-humidity cospectrum (Cθq) that I have measured and additional values of Cθq/(Cθ2Cq2)1/2 reported in the literature yield an estimate of the ratio of Kolmogorov constants βθq/(βθβq)1/2 via the temperature-humidity covariance budget. Here βθ, βq and βθq are the Kolmogorov constants for the temperature and humidity spectra and the temperature-humidity cospectrum, respectively. The data suggest that βθq/(βθβq)1/2 = 0.80 ± 0.16; consequently, since βθ = βq0.40 ± 0.02, βθq = 0.32 ± 0.08. Considering the uncertainties involved, however, I cannot reject the hypothesis βθ = βqθq. With the dissipation rate (Nn) derived from the refractive index variance budget, and with this apparent equality of βθ, βq, and βθq, the refractive index spectrum (Φn) has the Kolmogorov-Corrsin form Φn(k) = βnNnε−1/3k−5/3 in an inertial-convective subrange, with the Kolmogorov constant βn also roughly 0.40.

Abstract

Structure parameters for the temperature (Cθ2) and humidity (Cq2) spectra and for the temperature-humidity cospectrum (Cθq) that I have measured and additional values of Cθq/(Cθ2Cq2)1/2 reported in the literature yield an estimate of the ratio of Kolmogorov constants βθq/(βθβq)1/2 via the temperature-humidity covariance budget. Here βθ, βq and βθq are the Kolmogorov constants for the temperature and humidity spectra and the temperature-humidity cospectrum, respectively. The data suggest that βθq/(βθβq)1/2 = 0.80 ± 0.16; consequently, since βθ = βq0.40 ± 0.02, βθq = 0.32 ± 0.08. Considering the uncertainties involved, however, I cannot reject the hypothesis βθ = βqθq. With the dissipation rate (Nn) derived from the refractive index variance budget, and with this apparent equality of βθ, βq, and βθq, the refractive index spectrum (Φn) has the Kolmogorov-Corrsin form Φn(k) = βnNnε−1/3k−5/3 in an inertial-convective subrange, with the Kolmogorov constant βn also roughly 0.40.

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