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 this paper we apply dynamical systems analyses and computational tools to fluid transport
in empirically measured vortex ring flows. Measurements of quasisteadily propagating …

Accurate numerical simulations of vortex rings impinging on flat boundaries revealed the
same features observed in experiments. The results for the impact with a free-slip wall …

The behaviour and inherent beauty of vortex rings have fascinated researchers for a long
time. In nature, vortex rings are found to occur in various shapes and sizes. Perhaps the …

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 …

The nonlinear, three-dimensional Euler equations can be reduced to a simple linear
equation when the flow has helical symmetry and when the flow consists of a rigidly rotating …

In the early 1970s, Maxworthy [J. Fluid. Mech. 51, 15 (1972)] and Oshima et al.[J. Phys. Soc.
Jpn. 38, 1159 (1975)] attempted to produce leapfrogging between two coaxial vortex rings at …

A recent theoretical study [Borisov, Kilin, and Mamaev,“The dynamics of vortex rings:
Leapfrogging, choreographies and the stability problem,” Regular Chaotic Dyn. 18, 33 …

Regularized point-vortex simulations are presented for vortex sheet motion in planar and
axisymmetric flow. The sheet forms a vortex pair in the planar case and a vortex ring in the …

We describe the application of tools from dynamical systems to define and quantify the
unsteady fluid transport that occurs during fluid–structure interactions and in unsteady …