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].