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Sustaining mechanism of small-scale turbulent eddies in a precessing sphere

Yasufumi Horimoto* and Susumu Goto†

  • Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531 Japan

  • *y_horimoto@fm.me.es.osaka-u.ac.jp
  • †goto@me.es.osaka-u.ac.jp
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Phys. Rev. Fluids 2, 114603 – Published 10 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.114603

Abstract

It has been known for a long time that fully developed turbulence is sustained in a precessing container. The aim of the present study is to reveal the sustaining mechanism of turbulence in a precessing sphere by means of laboratory experiments. We conduct experiments using a Newtonian fluid (water) and viscoelastic fluids (dilute solutions of surfactant, cetyltrimethyl ammonium chloride, and polymers, polyethylene oxide) to understand the sustaining mechanism of turbulence of Newtonian fluids by examining turbulence modifications due to the surfactant and polymer additives. When the Reynolds number based on the spin angular velocity and radius of the sphere is fixed, the most developed turbulence is sustained with the Poincaré number (the precession rate) being about 0.1. The key ingredient of the developed turbulence is a pair of large-scale vortex tubes which robustly exists in the flow. Assuming that these vortex tubes sustain small-scale turbulent eddies through an energy cascading process, we can explain all our experimental observations. Concerning the turbulence modification by the additives, the time-scale criteria by Lumley [J. Polymer Sci.: Macromol. Rev. 7, 263 (1973)] and the refined theory by Tabor and de Gennes [Europhys. Lett. 2, 519 (1986)] explain the experimental result that the pair of large-scale vortex tubes survives even when small-scale turbulent eddies are drastically suppressed by the surfactant additive.

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Phys. Rev. Fluids 2, 114603– Published 10 November, 2017
  • Received 23 March 2017

©2017 American Physical Society

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