  A study of the relationship between Lagrangian statistics and flow topology
in fluid turbulence is presented. The topology is characterized using the Weiss
criterion that provides a simplified tool to partition the flow into
topologically different regions: elliptic (vortex dominated), hyperbolic
(deformation dominated), and intermediate (turbulent background). The flow
corresponds to forced two-dimensional Navier-Stokes turbulence in doubly
periodic and circular bounded domains with non-slip boundary conditions. In the
double periodic domain, the probability density function (pdf) of the Weiss
field exhibits a negative skewness consistent with the fact that in periodic
domains the flow is dominated by coherent vortex structures. On the other hand,
in the circular domain, the elliptic and hyperbolic regions seem to be
statistically similar. We follow a Lagrangian approach and obtain the
statistics by tracking large ensembles of passively advected tracers. The pdfs
of residence time in the topologically different regions are computed using the
Lagrangian Weiss field, i.e., the Weiss field computed along the particles'
trajectories. In elliptic and hyperbolic regions, the pdfs of the residence
time have self-similar algebraic decaying tails. On the other hand, in the
intermediate regions the pdf has exponential decaying tails. The conditional
(with respect to the flow topology) pdfs of the Lagrangian velocity exhibit
Gaussian behavior in the periodic and in the bounded domains. In contrast to
the freely decaying turbulence case, the conditional pdfs of the Lagrangian
acceleration in forced turbulence show a comparable level of intermittency in
the periodic and the bounded domains. The conditional pdfs of the Lagrangian
curvature are characterized, in all cases, by self-similar power law behavior
with a decay exponent of order -2.

Fluid Dynamics;Statistical Mechanics