On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence

The one- and three-dimensional spectral equations for a field of isotropic temperature fluctuations in an isotropic turbulence are derived from the correlation equation. Then, except for the degenerate case of simple conductive decay, stationary fluctuation fields are postulated. Largely by dimensional reasoning and some simple postulates, forms of the temperature fluctuation power spectrum for particular wave number ranges are deduced and are compared with the results of previous analyses giving corresponding segments of the velocity spectrum. Finally, the relative ``effective cut-off'' wave numbers of the two spectra are compared in terms of the fluid Prandtl number.