Alignment of tracer gradient vectors in 2D turbulence

This numerical study examines the stirring properties of a 2D flow field with 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 particular the second order in time equation for the tracer gradient norm. If the physical 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 simulations of 2D turbulence, that the tracer gradient vector statistically aligns with one of the eigenvector of a tensor that comes out from the second order 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 emphasizes the important role of the time evolution of the strain rate amplitude which, with the rotation of the strain tensor, significantly contributes to the alignment dynamics. Both effects are related to the anisotropic part of the pressure Hessian, which emphasizes the non-locality of the mechanisms involved. These results are reminiscent of those recently obtained by Nomura and Post [J. Fluid Mech. 377 (1998) 65] for 3D turbulence.