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Velocity distribution around a sphere descending in a linearly stratified fluid

Published online by Cambridge University Press:  10 August 2017

Shinya Okino Open the ORCID record for Shinya Okino [Opens in a new window] ,
Shinsaku Akiyama  and
Hideshi Hanazaki
Shinya Okino
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto daigaku-katsura 4, Nishikyo-ku, Kyoto 615-8540, Japan
Shinsaku Akiyama
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto daigaku-katsura 4, Nishikyo-ku, Kyoto 615-8540, Japan
Hideshi Hanazaki*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto daigaku-katsura 4, Nishikyo-ku, Kyoto 615-8540, Japan
*
†Email address for correspondence: [email protected]
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Abstract

The flow around a sphere descending at constant speed in a salt-stratified fluid is observed by particle image velocimetry. A unique characteristic of this flow is the appearance of a thin and high-speed rear jet whose maximum velocity can reach more than five times the sphere velocity. In this study we have investigated how the velocity distributions, especially those in the jet and in the boundary layer of the sphere, vary when the Froude number $Fr(=W^{\ast }/N^{\ast }a^{\ast })$ or the Reynolds number $Re(=W^{\ast }(2a^{\ast })/\unicode[STIX]{x1D708}^{\ast })$ ($W^{\ast }$: vertical velocity of the sphere, $N^{\ast }$: Brunt–Väisälä frequency, $a^{\ast }$: radius of the sphere, $\unicode[STIX]{x1D708}^{\ast }$: kinematic viscosity of the fluid) is changed. The results show that the radius of the jet and the thickness of the boundary layer are comparable, and they decrease for smaller Froude numbers and larger Reynolds numbers. Both of them are estimated at moderate Reynolds numbers by the primitive length scale of the stratified fluid ($l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$), or in non-dimensional form by $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=(Fr/2Re)^{1/2}$. The overall velocity distribution in the lee of the sphere is measured to identify the internal wave patterns and their effect on the velocity variation along the jet. Corresponding numerical simulation results using the axisymmetry assumption are in agreement with the experimental results.

JFM classification

Geophysical and Geological Flows: Internal waves Wakes/Jets: Jets Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 759 - 780
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© 2017 Cambridge University Press 

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