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Phys. Fluids 8, 487 (1996); http://dx.doi.org/10.1063/1.868802 (9 pages)
Stability of periodic arrays of vortices
(Received 14 June 1995; accepted 11 October 1995)
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Add to FacebookThe stability of periodic arrays of Mallier–Maslowe or Kelvin–Stuart vortices is discussed. We derive with the energy‐Casimir stability method the nonlinear stability of this solution in the inviscid case as a function of the solution parameters and of the domain size. We exhibit the maximum size of the domain for which the vortex street is stable. By adapting a numerical time‐stepping code, we calculate the linear stability of the Mallier–Maslowe solution in the presence of viscosity and compensating forcing. Finally, the results are discussed and compared to a recent experiment in fluids performed by Tabeling et al. [Europhy. Lett. 3, 459 (1987)]. Electromagnetically driven counter‐rotating vortices are unstable above a critical electric current, and give way to co‐rotating vortices. The importance of the friction at the bottom of the experimental apparatus is also discussed. © 1996 American Institute of Physics.
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