Journal ArticleDOI
Non-axisymmetric vortices in two-dimensional flows
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In this article, the structure of the non-axisymmetric correction generated by an external rotating multipolar strain field to a vortex with a Gaussian vorticity profile is first studied.Abstract:
Slightly non-axisymmetric vortices are analysed by asymptotic methods in the context of incompressible large-Reynolds-number two-dimensional flows. The structure of the non-axisymmetric correction generated by an external rotating multipolar strain field to a vortex with a Gaussian vorticity profile is first studied. It is shown that when the angular frequency w of the external field is in the range of the angular velocity of the vortex, the non-axisymmetric correction exhibits a critical-point singularity which requires the introduction of viscosity or nonlinearity to be smoothed. The nature of the critical layer, which depends on the parameter h = 1/(Re e3/2), where e is the amplitude of the non-axisymmetric correction and Re the Reynolds number based on the circulation of the vortex, is found to govern the entire structure of the correction. Numerous properties are analysed as w and h vary for a multipolar strain field of order n = 2, 3, 4 and 5. In the second part of the paper, the problem of the existence of a non-axisymmetric correction which can survive without external field due to the presence of a nonlinear critical layer is addressed. For a family of vorticity profiles ranging from Gaussian to top-hat, such a correction is shown to exist for particular values of the angular frequency. The resulting non-axisymmetric vortices are analysed in detail and compared to recent computations by Rossi, Lingevitch & Bernoff (1997) and Dritschel (1998) of non-axisymmetric vortices. The results are also discussed in the context of electron columns where similar non-axisymmetric structures were observed (Driscoll & Fine 1990).read more
Citations
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Viscous interactions of two co-rotating vortices before merging
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References
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Stretched vortices - the sinews of turbulence; large-Reynolds-number asymptotics
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A New Class of Nonlinear Waves in Parallel Flows
D. J. Benney,R. F. Bergeron +1 more
TL;DR: In this article, a nonlinear theory is developed which gives rise to a class of disturbances not found in the classical viscous theory, and it is suggested that the modes found from such an analysis may be of importance in the breakdown of laminar flow due to free stream disturbances.