Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence?

This paper investigates the dynamics of tracer gradient for a two-dimension al flow. More precisely, the alignment of the tracer gradient vector with t he eigenvectors of the strain-rate tensor is studied theoretically and nume rically. We show that the basic mechanism of the gradient dynamics is the c ompetition between the effects due to strain and an effective rotation due to both the vorticity and to the rotation of the principal axes of the stra in-rate tensor. A nondimensional criterion is derived to partition the flow into different regimes: In the strain dominated regions, the tracer gradie nt vector aligns with a direction different from the strain axes and the gr adient magnitude grows exponentially in time. In the strain-effective rotat ion compensated regions, the tracer gradient vector aligns with the bisecto r of the strain axes and its growth is only algebraic in time. In the effec tive rotation dominated regions, the tracer gradient vector is rotating but is often close to the bisector of the strain axes. A numerical simulation of 2D (two-dimensional) turbulence clearly confirms the theoretical prefere ntial directions in strain and effective rotation dominated regions. Effect ive rotation can be dominated by the rotation rate of the strain axes, and moreover, proves to be larger than strain rate on the periphery of vortices . Taking into account this term allows us to improve significantly the Okub o-Weiss criterion. Our criterion gives the correct behavior of the growth o f the tracer gradient norm for the case of axisymmetric vortices for which the Okubo-Weiss criterion fails. (C) 1999 American Institute of Physics. [S 1070-6631(99)01312-4].