The Effects of Volume Averaging on Spectra Measured with a Lyman-Alpha Hygrometer

Abstract

Because the Lyman-alpha hygrometer averages turbulent fluctuations in humidity over a right circular cylinder, the spectral response of the instrument degrades at higher wavenumbers. This paper contains a derivation of the three-dimensional spectral averaging function and uses this function, with a new model for the scalar spectrum, to numerically evaluate how this spatial averaging affects measured humidity spectra and humidity variance dissipation rates. In general, hygrometer parameters can be chosen that allow spectral measurements to moderately high wavenumbers; but with the size of source and detector tubes currently in use, an accurate measurement of the humidity variance dissipation rate appears impossible.