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Unstable jets generated by a sphere descending in a very strongly stratified fluid

Published online by Cambridge University Press:  20 March 2019

Shinsaku Akiyama ,
Yusuke Waki ,
Shinya Okino Open the ORCID record for Shinya Okino [Opens in a new window]  and
Hideshi Hanazaki Open the ORCID record for Hideshi Hanazaki [Opens in a new window]
Shinsaku Akiyama
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto Daigaku-Katsura 4, Nishikyo-ku, Kyoto 615-8540, Japan
Yusuke Waki
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto Daigaku-Katsura 4, Nishikyo-ku, Kyoto 615-8540, Japan
Shinya Okino*
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 very strongly stratified fluid ($Fr\lesssim 0.2$) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification ($Fr\gtrsim 0.2$), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number $Fr$ that satisfies $Fr/Re<1.57\times 10^{-3}$. The Froude number $Fr$ here is in the range of $0.0157<Fr<0.157$ or lower, while the Reynolds number $Re$ is in the range of $10\lesssim Re\lesssim 100$ for which the homogeneous fluid shows steady and axisymmetric flows. Since the radius of the jet can be estimated by the primitive length scale of the stratified fluid, i.e. $l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$ or $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=\sqrt{Fr/2Re}$, this predicts that the jet becomes unstable when it becomes thinner than approximately $l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=0.028$, where $N^{\ast }$ is the Brunt–Väisälä frequency, $a^{\ast }$ the radius of the sphere and $\unicode[STIX]{x1D708}^{\ast }$ the kinematic viscosity of the fluid. The instability begins when the boundary-layer thickness becomes thin, and the disturbances generated by shear instabilities would be transferred into the jet. When the flow is marginally unstable, two unstable states, i.e. a meandering jet and a turbulent jet, can appear. The meandering jet is thin with a high vertical velocity, while the turbulent jet is broad with a much smaller velocity. The meandering jet may persist for a long time, or develop into a turbulent jet in a short time. When the instability is sufficiently strong, only the turbulent jet could be observed.

JFM classification

Geophysical and Geological Flows: Internal waves Wakes/Jets: Jets Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 26 - 44
Copyright
© 2019 Cambridge University Press 

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