On the anisotropy of the turbulent passive scalar in the presence of a mean scalar gradient

Abstract

AbstractWe investigate the origin of the scalar gradient skewness in isotropic turbulence on which a mean scalar gradient is imposed. The problem of the advection of an anisotropic scalar field is reformulated in terms of the advection of an isotropic vector field. For this field, triadic closure equations are derived. It is shown how the scaling of the scalar gradient skewness depends on the choice of the time scale used for the Lagrangian decorrelation of the vector field. The persistent anisotropy in the small scales for the third-order statistics is shown to be perfectly compatible with Corrsin–Obukhov scaling for second-order quantities, since second- and third-order scalar quantities are governed by a different triad correlation time scale. Whereas the inertial range dynamics of second-order scalar quantities is governed by the Lagrangian velocity correlation time, the third-order quantities remain correlated over a time related to the large-scale dynamics of the scalar field. It is argued that this time is determined by the average time it takes for a fluid particle to travel between ramp-cliff scalar structures.