A model for the spectrum of passive scalars in an isotropic turbulence field

Abstract

A simple model is developed for the wavenumber spectrum of the variance of a passive scalar quantity in an isotropic turbulence field. The model can define the spectral distributions at all wavenumbers as an arbitrary function of a scalar Reynolds number Reθ=R Reλ and the Schmidt number Sc=ν/D (where R=τθ/τe is the scalar/kinetic energy time scale ratio and Reλ=u′λ/ν is the turbulence Reynolds number). The model is compared with one-dimensional spectral data over a range of Reynolds numbers and for Sc=0.7, 7, and 700; model and data are shown to be in reasonable agreement.