Loss of monotonicity and anomalous scaling behavior in the passive scalar gradient

Abstract

PurposeThe purpose of this paper is to discuss some fundamental aspects regarding the anomalies in the passive scalar field advected by forced homogenous and isotropic turbulence, by inspection of the analytical properties of the governing equations and with the aid of direct numerical simulation (DNS) data.Design/methodology/approachResults from a pseudo‐spectral DNS of a unitary‐Schmidt‐ number passive scalar advected by a low Reynolds number flow field, Reλ=50 and 70 (based on the Taylor microscale λ) allow for a preliminary assessment of the developed numerical model.FindingsManipulation of the governing equations for the scalar field (which are monotonic) reveals that the unboundedness of the scalar gradient magnitude is not ruled out by the mathematical properties of the correspondent conservation equation. Classic intermittency effects in the passive scalar field have been reproduced, such as non‐Gaussian behavior of the passive scalar statistics, loss of local isotropy, and multi‐fractal scaling of scalar structure functions. Moreover, Taylor and Richardson theories are, surprisingly, not confirmed only in the dissipation range (small‐scales anomalies).Originality/valueThe authors suggest that the origin of intermittency (qualitatively pictured here as violent burst in spatial gradient quantities) should be sought in the loss of monotonicity of the evolution equation of the scalar gradient.