A simple approximation for the drift rates of rotating polygons on a free fluid surface

We report on laboratory experiments investigating the dynamics of a free fluid surface in a cylindrical tank with a rotating bottom plate. The shear instability in the system creates polygonal structures, which propagate around the domain, along the fixed vertical sidewalls. We analyze the wavelengt...

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Bibliographic Details
Published inThe European physical journal. ST, Special topics Vol. 232; no. 4; pp. 453 - 459
Main Authors Kadlecsik, Ádám, Szeidemann, Ákos, Vincze, Miklós
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023
Springer Nature B.V
Subjects
Approximation
Atomic
Classical and Continuum Physics
Condensed Matter Physics
Cylindrical tanks
Drift rate
Empirical analysis
Gravity waves
IMA10 - Interfacial Fluid Dynamics and Processes
Kelvin-Helmholtz instability
Materials Science
Measurement Science and Instrumentation
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Polygons
Regular Article
Rotation
Wave propagation
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Summary:We report on laboratory experiments investigating the dynamics of a free fluid surface in a cylindrical tank with a rotating bottom plate. The shear instability in the system creates polygonal structures, which propagate around the domain, along the fixed vertical sidewalls. We analyze the wavelengths and drift rates of these patterns, which are known from previous literature to be created by a complex interplay between centrifugal effects and gravity wave propagation in this unique geometry. We find that with an empirical correction factor, the drift rates of the polygonal vortices can be approximated fairly well by a surprisingly simple formula derived from the dispersion relation of linear gravity waves using easily observable parameters.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjs/s11734-023-00787-8