Various phenomena on a water vortex in a cylindrical tank over a rotating bottom

Abstract

Flows in a cylindrical tank over a rotating bottom are investigated by laboratory experiments. Despite the axisymmetry of the experimental setup, various anisotropic phenomena are observed. The slow rotation of the bottom disk induces a circular flow according to the axisymmetric environment, but polygonal vortices form under faster rotation. Between these two vortex flow states, the flow undergoes a transition with clear hysteresis during which the elliptical shape assumed under faster rotation is retained when the rotation is subsequently slowed to rates that previously supported axisymmetric flow. Sloshing is also observed; here, a calm circular flow state alternates with an oscillation of the water surface along the sidewall of the container. A phase diagram showing the phenomena observed under different combinations of the initial water depth at rest and the rotation rate of the bottom disk is developed following thorough experimental testing over a wide range of parameter values. The features of the dependences of the range for each phenomenon to occur on these parameters are also elucidated.

On the instabilities of a potential vortex with a free surface

“…The Tophøj model has recently been shown by Iima & Tasaka (2016) to be relevant for the rotating bottom experiment in terms of frequencies and mode structure predictions, which confirms that the potential model captures the essence of the instability leading also to the switching phenomenon. In the case of sloshing, as reported by Iga et al (2014), the free surface also breaks axial symmetry intermittently, but the non-symmetric state has strong deformations close to the outer wall in contrast with the rotating polygons where free-surface deformations are located close to the vortex centre. An explanation of the sloshing phenomenon is proposed by using an extension of the Tophøj model to the Rankine vortex.…”

“…The flow in those cases cannot be modelled by a simple potential flow and the azimuthal velocity is believed to approach a Rankine like profile (Bergmann et al 2011) containing a central core in solid body rotation. This model has been first considered by Vatistas, Wang & Lin (1994) and the extension of the Tophøj model to the case of a Rankine vortex is provided in and gives an interpretation of the mechanisms of the sloshing phenomena (Iga et al 2014) in terms of wave interactions. However, the central core in solid body rotation corresponds to a Newton's bucket flow which has been analysed in Mougel, Fabre & Lacaze (2015), where it was shown that inertial waves and Rossby waves play an important role.…”

Dynamics of flow structures and surface shapes in the surface switching of rotating fluid

“…It has been shown that, when the rotation speed is sufficiently high so that the scale of the surface deformation is comparable to the size of the container, the surface shapes are characterised by polygonal horizontal cross sections (rotating polygons; Vatistas (1990); Jansson et al (2006); Vatistas et al (2008); Bergmann et al (2011);Ait Abderrahmane et al (2011); Tophøj et al (2013); Iga et al (2014); Bach et al (2014)). The rotating polygons have been observed when the gap between the rotating bottom disk and the sidewall (the disk-rim gap) is either small ( Jansson et al (2006); Tophøj et al (2013); Bach et al (2014)) or relatively large ( Vatistas (1990); Vatistas et al (2008); Ait Abderrahmane et al (2011); Iga et al (2014)).…”

“…The rotating polygons have been observed when the gap between the rotating bottom disk and the sidewall (the disk-rim gap) is either small ( Jansson et al (2006); Tophøj et al (2013); Bach et al (2014)) or relatively large ( Vatistas (1990); Vatistas et al (2008); Ait Abderrahmane et al (2011); Iga et al (2014)). They have also been observed even if the cylinder wall rotates (Bach et al (2014)).…”

“…whether turbulent or laminar (Jansson et al (2006)). The relationship between the flow parameters and the axisymmetric surface shape was discussed by Iga et al (2014) and Bach et al (2014). To the best knowledge of the authors, previous numerical simulations of rotating flows with free surfaces were limited to cases of axisymmetry (Kahouadji & Witkowski (2014)) and small free surface deviations (Bouffanoais & Jacono (2009)).…”