We examine the transport properties of a particular two-dimensional, inviscid incompressible
flow using dynamical systems techniques. The velocity field is time periodic and consists of …

In the present paper, we describe the fascinating 150-year history of vortex dynamics, which
started from the classical work by H. Helmholtz (1858). This work contains not only the …

The interaction of two identical circular viscous vortex rings starting in a side-by-side
configuration is investigated by solving the Navier–Stokes equation using a spectral method …

We consider passive tracer advection in a model of a large planar basin of fluid with two
sinks opened alternately. In spite of the incompressibility of the fluid, the phase space of the …

To understand the topology and dynamics of coherent structures (CS), the interactions of CS
with fine-scale turbulence, and the effects of CS on entrainment, mixing and combustion …

The reconnection of two antiparallel viscous vortices is simulated in a periodic domain.
Reynolds numbers based on circulation divided by viscosity range from 1600 to 3200 …

Invariant manifolds can serve as a geometric template for the study of chaotic advection. In
particular, global stable and unstable manifolds of invariant hyperbolic or normally …

We introduce the concept of fractal boundaries in open hydrodynamical flows based on two
gedanken experiments carried out with passive tracer particles colored differently. It is …

We review and generalize recent results on advection of particles in open time-periodic
hydrodynamical flows. First, the problem of passive advection is considered, and its fractal …

The advection problem of passive tracer particles in the time-periodic velocity field of
leapfrogging vortex pairs is investigated in the context of chaotic scattering. We numerically …