Advective balance in pipe-formed vortex rings

Shariff, Karim; Krueger, Paul S.

doi:10.1017/jfm.2017.814

Cited by 2 publications

(2 citation statements)

References 32 publications

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“…The interfaces of large vorticity voids in isotropic turbulence might be similar. The asymmetric solutions are also reminiscent of the edge layer at the boundary of a laminar vortex ring [18]. Vorticity diffusing across the dividing streamline is subject to a strain induced by the fact that the ring is moving as a whole.…”

Section: Discussionmentioning

confidence: 96%

Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

Shariff,

Elsinga

2021

Preprint

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Viscous vortex layers subject to a more general uniform strain are considered. They include Townsend's steady solution for plane strain (corresponding to a parameter a = 1) in which all the strain in the plane of the layer goes toward vorticity stretching, as well as Migdal's recent steady asymmetric solution for axisymmetric strain (a = 1/2) in which half of the strain goes into vorticity stretching. In addition to considering asymmetric, symmetric and antisymmetric steady solutions ∀a ≥ 0, it is shown that for a < 1, i.e., anything less than the Townsend case, the vorticity inherently decays in time: only boundary conditions that maintain a supply of vorticity at one or both ends lead to a non-zero steady state. For the super-Townsend case a > 1, steady states have a sheath of opposite sign vorticity. Comparison is made with homogeneous-isotropic turbulence in which case the average vorticity in the strain eigenframe is layer-like, has wings of opposite vorticity, and the strain configuration is found to be super-Townsend. Only zero-integral perturbations of the a > 1 steady solutions are stable; otherwise, the solution grows. Finally, the appendix shows that the average flow in the strain eigenframe is (apart from an extra term) the Reynolds-averaged Navier-Stokes equation. MOTIVATION AND SUMMARY OF RESULTSVortex configurations subjected to a spatially uniform strain can be used to model local regions of more complicated flows where the strain represents the local potential velocity induced by other vortex structures, typically of larger scale than the region being considered. For example, Burgers' [1] axisymmetrically strained tubular vortex is a good model for the high intensity structures of homogeneous isotropic turbulence [2]. Other examples include Townsend's Gaussian vortex layer subject to plane-strain [3], and the celebrated Lundgren spiral which produces Kolmogorov's k −5/3 energy spectrum [4][5][6][7]. While we do not consider the instability of strained layers to wavy perturbations, we mention in passing that Townsend's layer is unstable to the formation of concentrated tubular structures [8,9]. This suggests a similar fate for other solutions presented below.Recently, Migdal [10] presented a steady asymmetric vortex layer solution for the case of axisymmetric strain (a = 1/2 below). In this solution the vorticity decays algebraically on one side of the layer and as a Gaussian on the other. It was the desire to interpret this solution

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Section: Discussionmentioning

confidence: 96%

Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

Shariff,

Elsinga

2021

Preprint

Self Cite

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“…The asymmetric solutions are also reminiscent of the edge layer at the boundary of a laminar vortex ring. 18 Vorticity diffusing across the dividing streamline is subject to a strain induced by the fact that the ring is moving as a whole. The edge layer imposes a Robin-type boundary condition on the vorticity, which is similar to Newton's law of convective cooling at the boundary of a conducting solid.…”

Section: Connecting To Turbulencementioning

confidence: 99%

Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

Shariff

Elsinga

2021

Physics of Fluids

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Viscous vortex layers subject to a more general uniform strain are considered. They include Townsend's steady solution for plane strain (corresponding to a parameter a ¼ 1), in which all the strain in the plane of the layer goes toward vorticity stretching, as well as Migdal's recent steady asymmetric solution for axisymmetric strain (a ¼ 1/2), in which half of the strain goes into vorticity stretching. In addition to considering asymmetric, symmetric, and antisymmetric steady solutions 8a ! 0, it is shown that for a < 1, i.e., anything less than the Townsend case, the vorticity inherently decays in time: only boundary conditions that maintain a supply of vorticity at one or both ends lead to a non-zero steady state. For the super-Townsend case a > 1, steady states have a sheath of opposite sign vorticity. Comparison is made with homogeneous-isotropic turbulence, in which case the average vorticity in the strain eigenframe is layer-like, has wings of opposite vorticity, and the strain configuration is found to be super-Townsend. Only zero-integral perturbations of the a > 1 steady solutions are stable; otherwise, the solution grows. Finally, the appendix shows that the average flow in the strain eigenframe is (apart from an extra term) the Reynolds-averaged Navier-Stokes equation.

show abstract

Advective balance in pipe-formed vortex rings

Cited by 2 publications

References 32 publications

Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

Viscous vortex layers subject to more general strain and comparison to isotropic turbulence

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