M. Gonzalez

Kinematic properties of passive scalar gradient predicted by a stochastic Lagrangian model

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 (2006)] 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.

Analysis of passive scalar gradient alignment in a simplified three-dimensional case

Numerical simulations as well as recent experiments in turbulent three-dimensional flow show a trend of the gradient of a passive scalar to align with the compressional axis of the strain tensor. In two-dimensional flow, however, it has been proved that the most probable orientation of the scalar gradient can be different from the compressional direction. An idealized situation is used to address this question in the three-dimensional case and to suggest a possible way to reexamine the scalar gradient alignment in three-dimensional flow. This kind of analysis can be applied to the material line alignment as well.

On the alignment dynamics of a passive scalar gradient in a two-dimensional flow

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 Benard-von Karman 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 (1999)] 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.

Nonstationary aspects of passive scalar gradient behaviour

The dynamics of a passive scalar gradient experiencing fluctuating velocity gradient through the Lagrangian variations of strain persistence is studied. To this end, a systematic, numerical analysis based on the equation for the orientation of the gradient of a nondiffusive scalar in two-dimensional flow is performed. When the gradient responds weakly its orientation properties are determined by the mean value of strain persistence. Statistical alignment of the scalar gradient with the direction defined by the opposed actions of strain and rotation, by contrast, requires the gradient to keep up with strain persistence fluctuations. These results have been obtained for both strain- and effective-rotation-dominated regimes and are supported by relevant experimental data. Consequences of the unsteady behaviour of the scalar gradient on mixing properties are also analysed.

Effect of variable mass density on the kinematics of scalar gradient

Analysis of the equations for the orientation and norm of the gradient of a passive scalar shows that the kinematics of the scalar gradient may be deeply altered by non-solenoidal effects felt through the velocity gradient. While these effects are explicitly expressed in the equation for the gradient norm, the orientation equations are unaltered as compared to the incompressible case. In two-dimensional flows the behavior of the scalar gradient is governed by both the strain persistence parameter, r, and the ratio, δ/σ, of velocity divergence to the norm of the deviatoric part of the strain tensor. In particular, in the dilatational case, while large dilatation (δ/σu2009>u20091) unconditionally lessens the scalar gradient, moderate dilatation (0 <δ/σu2009<u20091) needs effective rotation (ru2009≠u20090) to drive the scalar gradient to decrease. In three-dimensional flows the analytic study needs the assumption that vorticity is aligned with a strain principal axis and leads to a more complex picture based on the strain persisten...

Analysis of scalar dissipation in terms of vorticity geometry in isotropic turbulence

The mechanisms promoting scalar dissipation through scalar gradient production are scrutinised in terms of vorticity alignment with respect to strain principal axes. For that purpose, a stochastic Lagrangian model for the velocity gradient tensor and the scalar gradient vector is used. The model results show that the major part of scalar dissipation occurs for stretched vorticity, namely when the vorticity vector aligns with the extensional and intermediate strain eigenvectors. More specifically, it appears that the mean scalar dissipation is well represented by the sample defined by alignment with the extensional strain, while the most intense scalar dissipation is promoted by the set of events for which vorticity aligns with the intermediate strain. This difference is explained by rather subtle mechanisms involving the statistics of both the strain intensities and the scalar gradient alignment resulting from these special alignments of vorticity. The analysis, allowing for the local flow structure, conf...