A modeled equation for the gradient of a passive scalar is derived consistently with the approach of Chevillard and Meneveau for the velocity gradient tensor ͓Phys. Rev. Lett. 97, 174501 ͑2006͔͒ and its predictions are analyzed in three-dimensional, isotropic turbulence. General features of scalar gradient kinematics, namely, production of scalar gradient norm and alignment with respect to strain principal axes and vorticity are rather well described. A strain persistence parameter defined for tight alignment of vorticity with a strain eigenvector is used to bring further insight into geometric properties of the scalar gradient. In particular, the model results lend support to the existence of special alignments of the scalar gradient which are determined by local strain persistence and are different from the directions of strain principal axes as already shown in two-dimensional turbulence.
A Lagrangian study of the statistical properties of the orientation of a passive scalar gradient is performed using experimental data and a simple, numerical analysis. It is shown that, in a low-Reynolds number Bénard-von Kármán street, the temperature gradient downstream of a heated line source does not align with the asymptotic orientation predicted by the Lapeyre et al. model ͓Phys. Fluids 11, 3729 ͑1999͔͒ in the hyperbolic regions. This result is ascribed to fluctuations of strain persistence along Lagrangian trajectories. A numerical analysis of the scalar gradient alignment properties shows that these fluctuations, together with a low level of the rate of strain, may lead to preferential orientations that are different from the theoretical one predicted by an asymptotic model.
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