An approximate equation for the spectrum of a conserved scalar quantity in a turbulent fluid

Abstract

The formula for transfer of -stuff across the θ-spectrum, which was obtained by Batchelor, Howells & Townsend (1959) for wave-numbers at which molecular conduction is important, is extended here to smaller wave-numbers by means of a simplified general picture of the mechanism involved. The interaction of velocity and temperature fields is represented by a combination of eddy conductivity due to the smaller eddies, and a straining action due to the larger eddies, and this leads to an approximate equation for the θ-spectrum, for a fluid of arbitrary Prandtl number, over at least the equilibrium range of wave-numbers.