Abstract
A theory of viscous evolution and selection of symmetric two-dimensional dipoles is suggested, based on a combination of numerical simulations and an asymptotic analysis, where the slow time scale associated with the vorticity diffusion due to viscosity is incorporated. It is shown that viscosity first brings a dipole to an intermediate asymptotic state, which is independent of the initial conditions, and then slowly takes the dipole away from this state. We demonstrate that, among the variety of possible ideal-fluid dipole solutions, viscosity going to zero selects a unique solution, which is described to high accuracy by the elliptical dipole solution with a separatrix aspect ratio of 1.037.
| Original language | English |
|---|---|
| Pages (from-to) | 492-508 |
| Number of pages | 17 |
| Journal | Journal of Fluid Mechanics |
| Volume | 658 |
| DOIs | |
| State | Published - Sep 2010 |
Bibliographical note
Funding Information:This research was supported by Israel Science Foundation grant 628/06. The authors are indebted to M. Cohen for performing some preliminary simulation, and to J. Juul Rasmussen for sharing his code with which this preliminary simulation was performed. Y. Stepanyants and the three anonymous referees are thanked for their helpful comments.
Funding
This research was supported by Israel Science Foundation grant 628/06. The authors are indebted to M. Cohen for performing some preliminary simulation, and to J. Juul Rasmussen for sharing his code with which this preliminary simulation was performed. Y. Stepanyants and the three anonymous referees are thanked for their helpful comments.
| Funders | Funder number |
|---|---|
| Israel Science Foundation | 628/06 |
Keywords
- vortex dynamics
- vortex flows
- vortex interactions