Diffusion of a ring vortex

Berezovskii, A. A.; Kaplanskii, F. B.

doi:10.1007/bf01050718

Cited by 9 publications

(8 citation statements)

References 7 publications

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“…A similar solution was deduced in the paper by Berezovskii and Kaplanskii (1988), where the problem was solved using the "quasi-self-similar" approach at the limit of small Reynolds numbers. A similar solution was deduced in the paper by Berezovskii and Kaplanskii (1988), where the problem was solved using the "quasi-self-similar" approach at the limit of small Reynolds numbers.…”

Section: Fig 210 Infinitely Thin Vortex Ringsupporting

confidence: 59%

Theory of Concentrated Vortices

2008

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Section: Fig 210 Infinitely Thin Vortex Ringsupporting

confidence: 59%

Theory of Concentrated Vortices

2008

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“…A similar suggestion was made by Rhines & Young (1983) for planar vortices. Berezovski & Kaplanski (1987) obtained a time-dependent Stokes-flow vortex ring solution with a peaked vorticity distribution. This solution has zero thickness at νt = 0 and tends to the selfsimilar solution obtained by Phillips (1956) as νt → ∞.…”

Section: Present Workmentioning

confidence: 99%

Advective balance in pipe-formed vortex rings

Shariff

Krueger

2017

J. Fluid Mech.

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Vorticity distributions in axisymmetric vortex rings produced by a piston-pipe apparatus are numerically studied over a range of Reynolds numbers, $\mathrm{Re}$, and stroke-to-diameter ratios, $L/D$. It is found that a state of advective balance, such that $\zeta \equiv \omega_\phi/r \approx F(\psi, t)$, is achieved within the region (called the vortex ring bubble) enclosed by the dividing streamline. Here $\zeta \equiv\omega_\phi/r$ is the ratio of azimuthal vorticity to cylindrical radius, and $\psi$ is the Stokes streamfunction in the frame of the ring. Some but not all of the $\mathrm{Re}$ dependence in the time evolution of $F(\psi, t)$ can be captured by introducing a scaled time $\tau = \nu t$, where $\nu$ is the kinematic viscosity. When $\nu t/D^2 \gtrsim 0.02$, the shape of $F(\psi)$ is dominated by the linear-in-$\psi$ component, the coefficient of the quadratic term being an order of magnitude smaller. An important feature is that as the dividing streamline ($\psi = 0$) is approached, $F(\psi)$ tends to a non-zero intercept which exhibits an extra $\mathrm{Re}$ dependence. This and other features are explained by a simple toy model consisting of the one-dimensional cylindrical diffusion equation. The key ingredient in the model responsible for the extra $\mathrm{Re}$ dependence is a Robin-type boundary condition, similar to Newton's law of cooling, that accounts for the edge layer at the dividing streamline

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“…For solving equation system (1)- (2) we use the two-scale decomposition method [3]. We set some nondimensional initial values of helical vortex and core radii: a * (t 0 ) = a 0 , * (t 0 ) = 0 , and consider two types of non-dimensional variables -external (marked with *) and internal (marked with line):…”

Section: Epj Web Of Conferencesmentioning

confidence: 99%

“…Speed of motion of a helical vortex [1] as well as a vortex ring motion velocity [3] have a logarithmic dependence on vortex core radius and according to (6), at the initial stage of evolution it have a logarithmic dependence on time. Helical vortex movement is directed along a binormal to the helix.…”

Section: Thermophysical Basis Of Energy Technologiesmentioning

confidence: 99%

On the viscosity influence on a helical vortex flament evolution

Agafontseva

Куйбин

2015

EPJ Web of Conferences

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Abstract. Helical vortices whose parameters have a strong influence on the efficiency of the apparatus is often occur in technical devices using swirling flow (cyclones, separators, etc.). To date the internal structure of such vortices is poorly understood. In [1] a model of helical vortex with uniform vorticity distribution in the core is proposed. Vortices arising in real flow always have a smooth vorticity distribution due to the viscosity action. The problem on steady moving helical vortices with the vortex core of small size in an inviscid fluid was solved in [2]. The non-orthogonal 'helical' coordinate system was introduced that allowed author to reduce the problem to two dimensional one. However, the velocity of the vortex motion was written only in the form of a quadratures computation of which is difficult. This paper presents first attempt for research on the diffusion and dynamics of a viscous helical vortex.In this paper we consider the non-stationary problem of diffusion of helical vortex with a small diameter of core in viscous fluid. The aim is to describe the structure of the vortex and to find the speed of its movement.Consider coordinate system introduced in [2]:Here H ( ) is a helix, unit vectors ( T ( ), N( ), B( )) are directed along the tangent, normal and binormal to the helix (components of some vector in this coordinate system will be shown by use angle brackets < •, •, • >). Jacobian determinant of this system depends only on one coordinate:is the curvature of helical line, a is the helix radius and 2 l -is the helix pitch. Helical symmetry condition [1] written in the Cartesian coordinates looks as follows:

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Diffusion of a ring vortex

Cited by 9 publications

References 7 publications

Theory of Concentrated Vortices

Theory of Concentrated Vortices

Advective balance in pipe-formed vortex rings

On the viscosity influence on a helical vortex flament evolution

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