Formation of a vortex around a sink: A kind of phase transition in a nonequilibrium open system

Kawakubo, Tatsuyuki; Tsuchiya, Y.; Sugaya, Michihiro; Matsumura, Kazuaki

doi:10.1016/0375-9601(78)90759-4

Cited by 23 publications

(15 citation statements)

References 2 publications

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“…This has however been observed in some other axisymmetric flows (Kawakubo et al 1978 andShingubara et al 1988, in flow around a sink; Torrance 1979, in a hot plume in a stratified environment; and Bojarevics & Shcherbinin 1983, in an axisymmetric meridional flow due to an electric current source).…”

Section: Generation Of Helicity In Initially Helicity-free Flowsmentioning

confidence: 92%

Helicity in Laminar and Turbulent Flow

Moffatt¹,

Tsinober²

1992

Annu. Rev. Fluid Mech.

445

166

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Section: Generation Of Helicity In Initially Helicity-free Flowsmentioning

confidence: 92%

Helicity in Laminar and Turbulent Flow

Moffatt¹,

Tsinober²

1992

Annu. Rev. Fluid Mech.

445

166

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“…In the following we focus on the time-independent bathtub vortex in a rotating container. We shall not discuss the central vortex in source-sink flows in non-rotating systems as investigated experimentally by Kawakubo et al (1978) or the effect of the background rotation of the Earth on the direction of rotation of the bathtub vortex (Shapiro 1962;Trefethen et al 1965).…”

Section: Introductionmentioning

confidence: 99%

The bathtub vortex in a rotating container

et al. 2006

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We study the time-independent free-surface flow which forms when a fluid drains out of a container, a so-called bathtub vortex. We focus on the bathtub vortex in a rotating container and describe the free-surface shape and the complex flow structure using photographs of the free surface, flow visualizations, and velocity measurements. We find that the velocity field in the bulk of the fluid agrees with predictions from linear Ekman theory for the boundary layer at the bottom, and we discuss the limitations of linear Ekman theory for the source-sink flow in the experiment. We introduce a radial expansion approximation of the central vortex core and reduce the model to a single first-order equation. We solve the equation numerically and find that the axial velocity depends linearly on height whereas the azimuthal velocity is almost independent of height. We discuss the model of the bathtub vortex introduced by Lundgren (J. Fluid Mech. vol. 155, 1985, p. 381) and compare it with our experiment. We find that the measured velocities and surface profiles are described well by the model when Ekman upflow and surface tension effects are included.

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“…In spite of the wide spread attention, a true closed form solution of how a vortex forms has not yet presented itself in the literature. This is likely owed to the fact that a number of formation details remain unresolved, as noted by others (Pedley 1969, Kawakubo et al 1978, De Siervi et al 1982, Ramamurthi and Tharakan 1995, Shtern and Hussain 1999. What is decidedly scarcer in the literature is just why a vortex forms.…”

Section: Introductionmentioning

confidence: 84%

The hydraulic vortex - an autocatakinetic system

Carriveau

2006

International Journal of General Systems

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Experiments were performed to provide a phenomenological explanation of how a hydraulic (water) vortex forms. Experimental observation and results gathered from this work also provided a possible explanation as to why such a vortex forms. The data and interpretations presented are intended to support the classification of the hydraulic vortex as a self-organizing, autocatakinetic system; establishing the hydraulic vortex as a member of a broader class of general systems. Two apparatuses were constructed to study hydraulic vortex formation. Each apparatus was also modeled using a commercial computational program. Results have shown that the formation and persistence of a hydraulic vortex rapidly minimizes potentials generated by a circulation source and sink. Other self-organizing characteristics of the flow were revealed including, the arrival of global order in the flow from local interactions, and the bolstering of the vortical system robustness through an interactive feedback stretching force. Finally, the process of vortex formation and persistence were shown to fit well into generalized autocatakinetic systems presented by others.

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Formation of a vortex around a sink: A kind of phase transition in a nonequilibrium open system

Cited by 23 publications

References 2 publications

Helicity in Laminar and Turbulent Flow

Helicity in Laminar and Turbulent Flow

The bathtub vortex in a rotating container

The hydraulic vortex - an autocatakinetic system

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