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Horizontal diffusive motion of columnar vortices in rotating Rayleigh–Bénard convection

Published online by Cambridge University Press:  21 May 2019

D. Noto Open the ORCID record for D. Noto [Opens in a new window] ,
Y. Tasaka Open the ORCID record for Y. Tasaka [Opens in a new window] ,
T. Yanagisawa  and
Y. Murai
D. Noto
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo, Japan
Y. Tasaka*
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo, Japan
T. Yanagisawa
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo, Japan Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokosuka, Japan
Y. Murai
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo, Japan
*
†Email address for correspondence: [email protected]
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Abstract

In laboratory experiments, horizontal translational motion of columnar vortices formed in rotating Rayleigh–Bénard convection was investigated. Two types of measurements, vertical velocity fields and horizontal temperature fields, were conducted with water as the test fluid. Using particle image velocimetry, the vertical velocity fields determined the parameter range at which the quasi-two-dimensional columnar vortices emerged. Locally, the duration characteristics of the columns, evaluated with their vertical coherence, indicate the minimum time scale of translational motion of the vortices in the horizontal plane. Vortex tracking of the horizontal temperature fields over long observation periods (${>}10^{3}~\text{s}$) was conducted using encapsulated thermochromic liquid crystal visualization. Two cylindrical vessels with different radii showed the emergence of the centrifugal effect in $O({>}10^{2}~\text{s})$ despite the small Froude number ($Fr<0.1$). Further, in the horizontal plane the columnar vortices behaved in a random-walk-like diffusive motion. The statistically calculated mean-squared displacements indicated anomalous diffusive motion of the columns; displacement increasing with time as $t^{\unicode[STIX]{x1D6FE}}$ with $\unicode[STIX]{x1D6FE}\neq 1$. We discuss the causes of this anomaly in both the instantaneous and long-term statistical data gathered from experimental observations over different time scales. The enclosure effect from the repulsion of up-welling and down-welling vortices ensures that vortices diffuse only little, resulting in a sub-diffusive (decelerated) motion $\unicode[STIX]{x1D6FE}<1$ in $O(10^{1}~\text{s})$. With this weak centrifugal contribution, the translational motion of the columns slowly accelerates in the radial direction and thereby yields a super-diffusive (accelerated) motion $\unicode[STIX]{x1D6FE}>1$ in $O(10^{2}~\text{s})$.

JFM classification

Geophysical and Geological Flows: Rotating flows Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , pp. 401 - 426
Copyright
© 2019 Cambridge University Press 

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