Shear effects on passive scalar spectra

Abstract

The effects of a large-scale shear on the energy spectrum of a passively advected scalar field are investigated. The shear is superimposed on a turbulent isotropic flow, yielding an Obukhov–Corrsin $k^{-5/3}$ scalar spectrum at small scales. Shear effects appear at large scales, where a different, anisotropic behaviour is observed. The scalar spectrum is shown to behave as $k^{-4/3}$ for a shear fixed in intensity and direction. For other types of shear characteristics, the slope is generally intermediate between the $-5/3$ Obukhov–Corrsin and the $-1$ Batchelor values. The physical mechanisms at the origin of this behaviour are illustrated in terms of the motion of Lagrangian particles. They provide an explanation for the scalar spectra that are shallow and dependent on the experimental conditions in shear flows at moderate Reynolds numbers.