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Global time evolution of an axisymmetric vortex ring at low Reynolds numbers
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10.1063/1.2925682
/content/aip/journal/pof2/20/5/10.1063/1.2925682
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/5/10.1063/1.2925682
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Dependence on the Reynolds number of temporal evolution of the traveling speed at small times. The upper thick solid line is Saffman’s formula (30). The solid line is the large-Reynolds-number asymptotics (46) and the lower thin solid line is the present result (45) for early-time behavior at low Reynolds numbers. The dashed lines are the values read off from the graph of numerical simulations conducted by Stanaway et al. (Ref. 19) from above.

Image of FIG. 2.
FIG. 2.

Temporal variation of the traveling speed (43) of the vortex ring. The left dashed line is the small-time asymptotics (45) and the right dashed line is the large-time asymptotics (48).

Image of FIG. 3.
FIG. 3.

The distance traversed by vortex ring (50) as a function of time. The left dashed line is the small-time asymptotics (51) and the right dashed line is the large-time asymptotics (52). The upper horizontal line designates the upper bound on traveling distance (53).

Image of FIG. 4.
FIG. 4.

Comparison of the traveling speed with Saffman’s matured-stage formula. The solid line is calculated from Eq. (43). The dashed lines draw Eq. (56) with and given by Eq. (59) (above) and with and (below).

Image of FIG. 5.
FIG. 5.

Comparison of vorticity distribution (24) (dashed lines) with Gaussian approximation (62) (solid lines) at and 0.222.

Image of FIG. 6.
FIG. 6.

Comparison of radial vorticity profile (24) with the experimental result (Ref. 34), at , for a vortex ring created from a piston-nozzle system. Here, is the diameter of the orifice and is the velocity of discharged jet. The measurement was made at the cross section of distance from the orifice and at the estimated time .

Image of FIG. 7.
FIG. 7.

Comparison of axial vorticity profile (24) with the experimental result (Ref. 34) at .

Image of FIG. 8.
FIG. 8.

The normalized energy as a function of time. The solid line corresponds to definition (67) and the dashed line to , the right-hand side of Eq. (68).

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/content/aip/journal/pof2/20/5/10.1063/1.2925682
2008-05-30
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Global time evolution of an axisymmetric vortex ring at low Reynolds numbers
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/5/10.1063/1.2925682
10.1063/1.2925682
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