Alignment of tracer gradient vectors in 2D turbulence

This numerical study examines the stirring properties of a 2D how field wit h a specific focus on the alignment dynamics of tracer gradient vectors. In accordance with the study of Hua and Klein [Physica D 113 (1998) 98], our approach involves the full second order Lagrangian dynamics and in particul ar the second order in time equation for the tracer gradient norm. If the p hysical space is partitioned into strain-dominated regions and "effective" rotation-dominated regions (following a criterion defined by Lapeyre et al. [Phys. Fluids 11 (1999) 3729]), the new result of this study concerns the "effective" rotation-dominated regions: it is found, from numerical simulat ions of 2D turbulence, that the tracer gradient vector statistically aligns with one of the eigenvector of a tensor that comes our from the second ord er equation and is related to the pressure Hessian. The consequence is that , in those regions, the observed exponential growth or decay of the tracer gradient vector can be predicted contrary to previous results which implied zero growth and only a rotation of this vector. This result strongly empha sizes the important role of the time evolution of the strain rate amplitude which, with the rotation of the strain tensor, significantly contributes t o the alignment dynamics. Both effects are related to the anisotropic part of the pressure Hessian, which emphasizes the non-locality of the mechanism s involved. These results are reminiscent of those recently obtained by Nom ura and Post [J. Fluid Mech. 377 (1998) 65] for 3D turbulence. (C) 2000 Els evier Science B.V. All rights reserved.