The decay of a pair of point vortices in a viscous fluid

Ohring, Samuel; Lugt, Hans J.

doi:10.1063/1.858689

Cited by 3 publications

(8 citation statements)

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“…While a maximum is hard to locate in a vortex method with an arbitrary distribution of vortices, our results agree well with the exact Stokes solution and with the results of Ohring and Lugt. 5 In particular we agree with the conclusion of Ohring and Lugt that the maximum moves away from the symmetry plane at all times. We do note that there is too much noise in our position of the maximum to find an accurate vertical propagation velocity for it.…”

Section: Resultssupporting

confidence: 91%

“…These results agree with those of Ohring and Lugt. 5 They also agree with the results of Buntine and Pullin 4 for a smoothed initial condition. Their results at Reynolds numbers 40 and 160 are indistinguishable, similar to our results at 50 and 100.…”

Section: Resultssupporting

confidence: 88%

“…In general, our numerical results agree with those of Ohring and Lugt, 5 Lo and Ting, 3 and Buntine and Pullin, 4 even though the latter two studies used a smooth initial condition. This provides additional support for the analytical and numerical results of this paper.…”

Section: Vill Conclusionsupporting

confidence: 89%

“…For example, the large time expansion pre( the same drift velocity for the vortex maxima, a predict that seems to be in good agreement with the numerica sults of Ohring and Lugt. 5 However, the average velocity O is not based on a ticular location in the vortex system. Hence there is no son to assume it would show the same asymptotic drif locity.…”

Section: Rmentioning

confidence: 99%

“…5 They applied artificial boundary conditions at distances of 10 times the vortex spacing. The results of this paper will provide a check on the validity of such boundary conditions; our velocity is found from the Biot-Savart law and does not require additional boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Two counter-rotating diffusing vortices

Dommelen

Subramaniam

1995

Physics of Fluids

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The problem of the diffusion of two counter-rotating vortices of equal strength is studied numerically and analytically. Asymptotic expansions are derived for the limiting behavior of the solution for small times, for small Reynolds numbers, and for large times. The results are used to more fully understand the drift and decay of the vortex system. Thus it is shown that different measures for the position of the vortex system used by previous authors may give significantly different values for the drift velocity of the vortices. The expansion for small Reynolds number shows that these differences remain even in the Stokes limit Re-40, in which the vorticity system becomes symmetric about the line connecting the vortex centers. But surprisingly, the large time expansion shows that for large times all drift velocities become identical. Moreover, this universal velocity is different from the average velocity in each half plane although it equals the velocity of the centers of vorticity of those planes. The small time expansion shows that increasing Reynolds number makes the vortices more symmetric. This tends to reduce the differences between the drift velocities. The small time expansion describes the numerical solution well as long as the vortices remain small compared to their spacing. The numerical results show that the Stokes solution describes various flow quantities fairly well for Reynolds numbers up to 600 based on the circulation; however, nonzero Reynolds number reduces the decay of the circulation of the vortices even on a diffusive time scale. C 1995 American Institute of Physics.

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Section: Resultssupporting

confidence: 91%

Section: Resultssupporting

confidence: 88%

Section: Vill Conclusionsupporting

confidence: 89%

Section: Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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