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 Re_θ=R Re_λ and the Schmidt number Sc=ν/D (where R=τ_θ/τ_e is the scalar/kinetic energy time scale ratio and Re_λ=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.