Stochastic scattering model of anomalous diffusion in arrays of steady vortices

We investigate the occurrence of anomalous transport phenomena associated with tracer particles propagating through arrays of steady vortices. The mechanism responsible for the occurrence of anomalous transport is identified in the particle dynamic, which is characterized by long collision-less trajectories (Lévy flights) interrupted by chaotic interactions with vortices. The process is studied via stochastic molecular models that are able to capture the underlying non-local nature of the transport mechanism. These models, however, are not well suited for problems where computational efficiency is an enabling factor. We show that fractional-order continuum models provide an excellent alternative that is able to capture the non-local nature of anomalous transport processes in turbulent environments. The equivalence between stochastic molecular and fractional continuum models is demonstrated both theoretically and numerically. In particular, the onset and the temporal evolution of heavy-tailed diffused fields are shown to be accurately captured, from a macroscopic perspective, by a fractional diffusion equation. The resulting anomalous transport mechanism, for the selected ranges of density of the vortices, shows a superdiffusive nature.

Subdiffusive and superdiffusive transport in plane steady viscous flows

Deterministic transport of passive tracers in steady laminar plane flows of incompressible viscous fluids through lattices of solid bodies or arrays of steady vortices can be anomalous. Motion along regular patterns of streamlines is often aperiodic: Repeated slow passages near stagnation points and/or solid surfaces serve for eventual decorrelation. Singularities of passage times near the obstacles, dictated by the boundary conditions, affect the character of transport anomalies: Flows past arrays of vortices are subdiffusive whereas tracers advected through lattices of solid obstacles can feature superdiffusion. We calculate the transport characteristics with the help of the simple and computationally efficient model: the special flow.

Axisymmetric propagating vortices in centrifugally stable Taylor–Couette flow

We present numerical as well as experimental results of axisymmetric, axially propagating vortices appearing in counter-rotating Taylor–Couette flow below the centrifugal instability threshold of circular Couette flow without additional externally imposed forces. These propagating vortices are periodically generated by the shear flow near the Ekman cells that are induced by the non-rotating end walls. These axisymmetric vortices propagate into the bulk towards mid-height, where they get annihilated by rotating, non-propagating defects. These propagating structures appear via a supercritical Hopf bifurcation from axisymmetric, steady vortices, which have been discovered recently in centrifugally stable counter-rotating Taylor–Couette flow (Abshagen et al., Phys. Fluids, vol. 22, 2010, 021702). In the nonlinear regime of the Hopf bifurcation, contributions of non-axisymmetric modes also appear.

A Molecular Dynamics Study on Obstructed Flow Around Single and Two Paratactic Circular Cylinders

Obstructed flow around single and two paratactic circular cylinders were investigated with two-dimensional molecular dynamics simulation (MDS) methods in the view of discrete particles. The transient and time-averaged profiles of streamline and density were obtained in order to analyze the characteristics of the wake flow. For single cylinder case, different flow patterns, i.e. Stokes flow, steady vortices flow, periodic vortices-shedding flow with the Ka´rma´n vortex street and supersonic flow, were divided based on Reynolds number (Re), 4<Re<12, 12<Re<20, 20<Re<62 and Re>62 respectively. For two paratactic cylinders case, different flow patterns, namely periodic vortices-shedding flow, periodic vortices-shedding flow with gap-flow, bistable flow and synchronized vortex-shedding flow, were observed with different center-to-center pitch ratios (D*/d*), D*/d* = 1.0, 1.0<D*/d*<1.1, 1.1<D*/d*<1.8 and D*/d*>1.8 respectively. The results show qualitative or quantitative agreement with those obtained from experiments and other MDS and indicate that most macroscopic obstructed flow patterns still exist even in nanoscale.

STEADY VORTICES IN ARTERIAL FLOWS

Many authors describe the movement in veins and arteries applying the Poisseuille flow pattern, according to which all streamlines are parallel to the walls of vessels, and the blood flow rate is proportional to the pressure drop. The presence of vortices may imply two-dimensional stress state in the wall of the vessel. It may be suggest that the additional stress may increase the probability to injure the cells of endothelium. The progressive development of atheroma sedimentation in the vicinity of bifurcations of arteries confirms the hypothesis mentioned above.