Editing Vortex ring (section)

===Formation process===

The formation of vortex rings has fascinated the scientific community for more than a century, starting with [[William Barton Rogers]]<ref>{{cite journal |last1= Rogers|first1= W. B. |date=1858 |title=On the formation of rotating rings by air and liquids under certain conditions of discharge |url=https://www.biodiversitylibrary.org/item/113539#page/255/mode/1up |journal=Am. J. Sci. Arts |volume=26 |pages=246–258 |access-date=2021-08-09}}</ref> who made sounding observations of the formation process of air vortex rings in air, air rings in liquids, and liquid rings in liquids. In particular, [[William Barton Rogers]] made use of the simple experimental method of letting a drop of liquid fall on a free liquid surface; a falling colored drop of liquid, such as milk or dyed water, will inevitably form a vortex ring at the interface due to the [[surface tension]].

A method proposed by [[G. I. Taylor]]<ref>{{cite journal |last1=Taylor|first1= G. I. |date=1953 |title=Formation of a vortex ring by giving an impulse to a circular disk and then dissolving it away |url=https://www.biodiversitylibrary.org/item/113539#page/255/mode/1up |journal=J. Appl. Phys. |volume=24 |issue=1 |pages=104 |doi=10.1063/1.1721114 |bibcode= 1953JAP....24..104T |access-date=2021-08-09}}</ref> to generate a vortex ring is to impulsively start a disk from rest. The flow separates to form a cylindrical vortex sheet and by artificially dissolving the disk, one is left with an isolated vortex ring. This is the case when someone is stirring their cup of coffee with a spoon and observing the propagation of a half-vortex in the cup.

In a laboratory, vortex rings are formed by impulsively discharging fluid through a sharp-edged nozzle or orifice. The impulsive motion of the piston/cylinder system is either triggered by an electric actuator or by a pressurized vessel connected to a control valve. For a nozzle geometry, and at first approximation, the exhaust speed is uniform and equal to the piston speed. This is referred as a parallel starting jet. It is possible to have a conical nozzle in which the streamlines at the exhaust are directed toward the centerline. This is referred as a converging starting jet. The orifice geometry which consists in an [[orifice plate]] covering the straight tube exhaust, can be considered as an infinitely converging nozzle but the vortex formation differs considerably from the converging nozzle, principally due to the absence of boundary layer in the thickness of the orifice plate throughout the formation process. The fast moving fluid ('''A''') is therefore discharged into a quiescent fluid ('''B'''). The [[Shear (fluid)|shear]] imposed at the interface between the two fluids slows down the outer layer of the fluid ('''A''') relatively to the centerline fluid. In order to satisfy the [[Kutta condition]], the flow is forced to detach, curl and roll-up in the form of a vortex sheet.<ref name="didden1979">{{cite journal |last1=Didden |first1=N. |date=1979 |title=On the formation of vortex rings: rolling-up and production of circulation |url=https://link.springer.com/article/10.1007/BF01597484 |journal=  Zeitschrift für Angewandte Mathematik und Physik |volume=30 |issue=1 |pages=101–116 |doi=10.1007/BF01597484 |bibcode=1979ZaMP...30..101D |s2cid=120056371 |access-date=2021-08-09|url-access=subscription }}</ref> Later, the vortex sheet detaches from the feeding jet and propagates freely downstream due to its self-induced kinematics. This is the process commonly observed when a smoker forms [[smoke rings]] from their mouth, and how [[vortex ring toy]]s work.

Secondary effects are likely to modify the formation process of vortex rings.<ref name="didden1979"/> Firstly, at the very first instants, the velocity profile at the exhaust exhibits extrema near the edge causing a large vorticity flux into the vortex ring. Secondly, as the ring grows in size at the edge of the exhaust, negative vorticity is generated on the outer wall of the generator which considerably reduces the circulation accumulated by the primary ring. Thirdly, as the boundary layer inside the pipe, or nozzle, thickens, the velocity profile approaches the one of a [[Poiseuille flow]] and the centerline velocity at the exhaust is measured to be larger than the prescribed piston speed. Last but not least, in the event the piston-generated vortex ring is pushed through the exhaust, it may interact or even merge with the primary vortex, hence modifying its characteristic, such as circulation, and potentially forcing the transition of the vortex ring to turbulence.

Vortex ring structures are easily observable in nature. For instance, a [[mushroom cloud]] formed by a nuclear explosion or volcanic eruption, has a vortex ring-like structure. Vortex rings are also seen in many different biological flows; blood is discharged into the left ventricle of the human heart in the form of a vortex ring<ref name="gharib2006">{{Cite journal |last1=Gharib |first1=M. |last2=Rambod |first2=E. |last3=Kheradvar |first3=A. |last4=Sahn |first4=D. J. |last5=Dabiri |first5=J. O.|date=2006 |title=Optimal vortex formation as an index of cardiac health |journal=Proceedings of the National Academy of Sciences |volume=103 |issue=16 |pages=6305–6308|doi=10.1073/pnas.0600520103 |pmid=16606852 |pmc=1458873 |bibcode=2006PNAS..103.6305G |issn=0027-8424|doi-access=free}}</ref> and jellyfishes or squids were shown to propel themselves in water by periodically discharging vortex rings in the surrounding.<ref>{{Cite journal|last1=Stewart|first1=W. J.|last2=Bartol|first2=I. K.|last3=Krueger|first3=P. S.|date=2010|title=Hydrodynamic fin function of brief squid, Lolliguncula brevis|journal=J. Exp. Biol.|volume=213|issue=12|pages=2009–2024|doi=10.1242/jeb.039057|pmid=20511514|issn=0022-0949|doi-access=free|bibcode=2010JExpB.213.2009S }}</ref> Finally, for more industrial applications, the [[synthetic jet]] which consists in periodically-formed vortex rings, was proved to be an appealing technology for flow control, heat and mass transfer and thrust generation<ref>{{cite journal |last1=Glezer |first1=A. |last2= Amitay|first2=M. |date=2002 |title=Synthetic jets |url=https://www.annualreviews.org/doi/abs/10.1146/annurev.fluid.34.090501.094913 |journal=Annu. Rev. Fluid Mech. |volume=34 |issue=1 |pages=503–529 |doi=10.1146/annurev.fluid.34.090501.094913 |bibcode=2002AnRFM..34..503G |access-date=2021-08-09|url-access=subscription }}</ref>