Chaotic Advection near 3-Vortex Collapse

Details Chaotic Advection near 3-Vortex Collapse Chaotic Advection near 3-Vortex Collapse

2000-06-14

arxiv.org/abs/nlin/0006019v2

Phys. Rev. E, 63, 036224 (2001)

Nonlinear Sciences

Chaotic Dynamics

42 pages, 24 figures

Scientific paper

10.1103/PhysRevE.63.036224

Dynamical and statistical properties of tracer advection are studied in a family of flows produced by three point-vortices of different signs. A collapse of all three vortices to a single point is then possible. Tracer dynamics is analyzed by numerical construction of Poincar\'{e} sections, and is found to be strongly chaotic: advection pattern in the region around the center of vorticity is dominated by a well developed stochastic sea, which grows as the vortex system approaches the collapse; at the same time, the islands of regular motion around vortices, known as vortex cores, shrink. An estimation of the core's radii from the minimum distance of vortex approach to each other is obtained. Tracer transport was found to be anomalous: for all of the three numerically investigated cases, the variance of the tracer distribution grows faster than a linear function of time, corresponding to a super-diffusive regime. The transport exponent varies with time decades, implying the presence of multi-fractal transport features. Yet, its value is never too far from 3/2, indicating some kind of universality. Statistics of Poincar\'{e} recurrences is non-Poissonian: distributions have long power-law tails. The anomalous properties of tracer statistics are the result of the complex structure of the advection phase space, in particular, of strong stickiness on the boundaries between the regions of chaotic and regular motion. The role of the different phase space structures involved in this phenomenon is analyzed. Based on this analysis, a kinetic description is constructed, which takes into account different time and space scalings by using a fractional equation.

Affiliated with

Also associated with

No associations

Rating

Chaotic Advection near 3-Vortex Collapse 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 Chaotic Advection near 3-Vortex Collapse, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Chaotic Advection near 3-Vortex Collapse will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-547659