Asymptotic properties of wall-induced chaotic mixing in point vortex pairs

Details Asymptotic properties of wall-induced chaotic mixing in point vortex pairs Asymptotic properties of wall-induced chaotic mixing in point vortex pairs

2011-09-12

arxiv.org/abs/1109.2423v2

Physics

Fluid Dynamics

Scientific paper

The purpose of this work is to analyze the flow due to a potential point vortex pair in the vicinity of a symmetry line (or "wall"), in order to understand why the presence of the wall, even far from the vortices, accelerates fluid mixing around the vortex pair. An asymptotic analysis, in the limit of large distances to the wall, allows to approximate the wall effect as a constant translation of the vortex pair parallel to the wall, plus a straining flow which induces a natural blinking vortex mechanism with period half the rotation period. A Melnikov analysis of lagrangian particles, in the frame translating and rotating with the vortices, shows that a homoclinic bifurcation indeed occurs, so that the various separatrices located near the vortex pair (and rotating with it) do not survive when a wall is present. The thickness of the resulting inner stochastic layer is estimated by using the separatrix map method, and is shown to scale like the inverse of the squared distance to the wall. This estimation provides a lower-bound to the numerical thickness measured from either Poincar\'e sections or simulations of lagrangian particles transported by the exact potential velocity field in the laboratory frame. In addition, it is shown that the outer homoclinic cycle, separating the vortices from the external (open) flow, is also perturbed from inside by the rotation of the vortex pair. As a consequence, a stochastic layer is shown to exist also in the vicinity of this cycle, allowing fluid exchange between the vortices and the outer flow. However, the thickness of this outer stochastic zone is observed to be much smaller than the one of the inner stochastic zone near vortices, as soon as the distance to the wall is large enough.

Affiliated with

Also associated with

No associations

Rating

Asymptotic properties of wall-induced chaotic mixing in point vortex pairs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic properties of wall-induced chaotic mixing in point vortex pairs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic properties of wall-induced chaotic mixing in point vortex pairs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-59760