3 added 313 characters in body
source | link

I currently don't have access to the paper, but this should meet your needs:

Vortex Ring Interactions (by Wakelin-Riley)
http://qjmam.oxfordjournals.org/content/49/2/287.abstract

Here is my interpretation: Consider two rings moving co-axially in the positive x-direction with their rings in the y-planes (ring A in front of ring B). The particles in each circle of the (fattened) ring circulate and force spreading of the air in front of it (see http://en.wikipedia.org/wiki/File:Vortex_ring.gif). Then
1) A's circulations will force B to spread and enlarge (visually look at the vectors in the vicinity of A). Then A moves through and this repeats, because B's circulation will now spread A.
2) Here ring A is moving in positive x-direction and B in negative x-direction. Their respective circulations will stretch each other and slow them down until they meet at rest and fade.

Here are more direct papers:
A Note on the Leapfroggeing Between Coaxial Vortex Rings at Low Reynolds Numbers (by Lim) http://pof.aip.org/resource/1/phfle6/v9/i1/p239_s1
Interaction of Two Vortex Rings Moving along a Common Axis of Symmetry (by Oshima)
http://jpsj.ipap.jp/link?JPSJ/38/1159/

I currently don't have access to the paper, but this should meet your needs:

Vortex Ring Interactions (by Wakelin-Riley)
http://qjmam.oxfordjournals.org/content/49/2/287.abstract

Here is my interpretation: Consider two rings moving co-axially in the positive x-direction with their rings in the y-planes (ring A in front of ring B). The particles in each circle of the (fattened) ring circulate and force spreading of the air in front of it (see http://en.wikipedia.org/wiki/File:Vortex_ring.gif). Then
1) A's circulations will force B to spread and enlarge (visually look at the vectors in the vicinity of A). Then A moves through and this repeats, because B's circulation will now spread A.
2) Here ring A is moving in positive x-direction and B in negative x-direction. Their respective circulations will stretch each other and slow them down until they meet at rest and fade.

I currently don't have access to the paper, but this should meet your needs:

Vortex Ring Interactions (by Wakelin-Riley)
http://qjmam.oxfordjournals.org/content/49/2/287.abstract

Here is my interpretation: Consider two rings moving co-axially in the positive x-direction with their rings in the y-planes (ring A in front of ring B). The particles in each circle of the (fattened) ring circulate and force spreading of the air in front of it (see http://en.wikipedia.org/wiki/File:Vortex_ring.gif). Then
1) A's circulations will force B to spread and enlarge (visually look at the vectors in the vicinity of A). Then A moves through and this repeats, because B's circulation will now spread A.
2) Here ring A is moving in positive x-direction and B in negative x-direction. Their respective circulations will stretch each other and slow them down until they meet at rest and fade.

Here are more direct papers:
A Note on the Leapfroggeing Between Coaxial Vortex Rings at Low Reynolds Numbers (by Lim) http://pof.aip.org/resource/1/phfle6/v9/i1/p239_s1
Interaction of Two Vortex Rings Moving along a Common Axis of Symmetry (by Oshima)
http://jpsj.ipap.jp/link?JPSJ/38/1159/

2 added 797 characters in body
source | link

I currently don't have access to the paper, but this should meet your needs:

Vortex Ring Interactions (by Wakelin-Riley)
http://qjmam.oxfordjournals.org/content/49/2/287.abstract

Here is my interpretation: Consider two rings moving co-axially in the positive x-direction with their rings in the y-planes (ring A in front of ring B). The particles in each circle of the (fattened) ring circulate and force spreading of the air in front of it (see http://en.wikipedia.org/wiki/File:Vortex_ring.gif). Then
1) A's circulations will force B to spread and enlarge (visually look at the vectors in the vicinity of A). Then A moves through and this repeats, because B's circulation will now spread A.
2) Here ring A is moving in positive x-direction and B in negative x-direction. Their respective circulations will stretch each other and slow them down until they meet at rest and fade.

I currently don't have access to the paper, but this should meet your needs:

Vortex Ring Interactions (by Wakelin-Riley)
http://qjmam.oxfordjournals.org/content/49/2/287.abstract

I currently don't have access to the paper, but this should meet your needs:

Vortex Ring Interactions (by Wakelin-Riley)
http://qjmam.oxfordjournals.org/content/49/2/287.abstract

Here is my interpretation: Consider two rings moving co-axially in the positive x-direction with their rings in the y-planes (ring A in front of ring B). The particles in each circle of the (fattened) ring circulate and force spreading of the air in front of it (see http://en.wikipedia.org/wiki/File:Vortex_ring.gif). Then
1) A's circulations will force B to spread and enlarge (visually look at the vectors in the vicinity of A). Then A moves through and this repeats, because B's circulation will now spread A.
2) Here ring A is moving in positive x-direction and B in negative x-direction. Their respective circulations will stretch each other and slow them down until they meet at rest and fade.

1
source | link

I currently don't have access to the paper, but this should meet your needs:

Vortex Ring Interactions (by Wakelin-Riley)
http://qjmam.oxfordjournals.org/content/49/2/287.abstract