Surface switching of rotating fluid in a cylinder

Suzuki, Toshiyuki; Iima, Makoto; Hayase, Yumino

doi:10.1063/1.2359740

Cited by 37 publications

(80 citation statements)

References 15 publications

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“…In the present paper, we consider more particularly the case (H/R = 0.94), which corresponds to the experimental studies by [8]. In that experiment, only elliptical patterns (m = 2) have been observed.…”

Section: Potential Rotationmentioning

confidence: 99%

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Waves and instabilities in rotating free surface flows

Mougel

Fabre

Lacaze

2014

Mechanics & Industry

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:The stability properties of the rotating free surface flow in a cylindrical container is studied using a global stability approach, considering succesively three models. For the case of solid body rotation (Newton's bucket), all eigenmodes are found to be stable, and are classified into three families : gravity waves, singular inertial modes, and Rossby waves. For the case of a potential flow, an instability is found. The mechanism is explained as a resonance between gravity waves and centrifugal waves, and is thought to be at the origin of the "rotating polygon instability" observed in experiments where the flow is driven by rotation of the bottom plate (see [9]). Finally, we give some preliminary results concerning a third model : the Rankine vortex.

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Section: Potential Rotationmentioning

confidence: 99%

“…For high enough rotation rates, a symmetry breaking is observed, leading to the formation of polygonal patterns rotating at a constant angular velocity on the free surface. This phenomenon, first observed in [10], has been revisited in [5] , [8], [1].…”

Section: Introductionmentioning

confidence: 99%

Waves and instabilities in rotating free surface flows

Mougel

Fabre

Lacaze

2014

Mechanics & Industry

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“…4, since this could be caused by subcritical bifurcations. Indeed, a considerable hysteresis is observed experimentally [2,5].…”

mentioning

confidence: 98%

“…[3,4] that, due to the secondary flows created by boundaries, the surface flow should be close to that of a potential vortex. It is also known that viscosity plays a minor role [2] and that indeed the flow is quite turbulent [5]. The bulk flow is thus not known in detail, and, due to the singularity near the corner C, where the rotating bottom plate meets the stationary sides, it must be quite complex.…”

mentioning

confidence: 99%

Rotating Polygon Instability of a Swirling Free Surface Flow

et al. 2013

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“…In fact, switching transitions are observed in similar but smaller systems, where the flow irregularly switches between a weakly deformed, rotationally symmetric state and a strongly deformed state with two corners. Here, the free surface touches the bottom, and this transition is linked with a transition to turbulence (Suzuki, Iima & Hayase 2006;Tasaka & Iima 2009). Thus the strong mixing present in the turbulent flow seems to be necessary for the formation of surface polygons.…”

Section: Introductionmentioning

confidence: 99%

Polygon formation and surface flow on a rotating fluid surface

et al. 2011

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We present a study of polygons forming on the free surface of a water flow confined to a stationary cylinder and driven by a rotating bottom plate as described by Jansson et al. (Phys. Rev. Lett., vol. 96, 2006, 174502). In particular, we study the case of a triangular structure, either completely 'wet' or with a 'dry' centre. For the dry structures, we present measurements of the surface shapes and the process of formation. We show experimental evidence that the formation can take place as a two-stage process: first the system approaches an almost stable rotationally symmetric state and from there the symmetry breaking proceeds like a low-dimensional linear instability. We show that the circular state and the unstable manifold connecting it with the polygon solution are universal in the sense that very different initial conditions lead to the same circular state and unstable manifold. For a wet triangle, we measure the surface flows by particle image velocimetry (PIV) and show that there are three vortices present, but that the strength of these vortices is far too weak to account for the rotation velocity of the polygon. We show that partial blocking of the surface flow destroys the polygons and re-establishes the rotational symmetry. For the rotationally symmetric state our theoretical analysis of the surface flow shows that it consists of two distinct regions: an inner, rigidly rotating centre and an outer annulus, where the surface flow is that of a point vortex with a weak secondary flow. This prediction is consistent with the experimentally determined surface flow.

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Surface switching of rotating fluid in a cylinder

Cited by 37 publications

References 15 publications

Waves and instabilities in rotating free surface flows

Waves and instabilities in rotating free surface flows

Rotating Polygon Instability of a Swirling Free Surface Flow

Polygon formation and surface flow on a rotating fluid surface

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