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.