Joint statistics of the scalar gradient and the velocity gradient in turbulence using linear diffusion models

Abstract

A model for the evolution of scalar gradients in turbulence is proposed. The molecular diffusion is approximated by a linear estimation, while the straining term is closed taking advantage of a previous model for velocity gradients [J. Martín, C. Dopazo, and L. Valiño, >Dynamics of velocity gradient invariants in turbulence: Restricted Euler and linear diffusion models,> Phys. Fluids 10, 2012 (1998)]. The joint statistics of the scalar gradients and velocity gradients obtained from this model are studied. In particular, the alignment of the scalar gradient with the principal strain axis, and the correlations between the strain rate and the scalar dissipation rate are investigated. The results show reasonably good agreement with data from direct numerical simulation, which indicates that this simple model captures the essential geometrical properties of the scalar-gradient/ velocity-gradient coupling in turbulent flows. © 2005 American Institute of Physics.