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Density distribution in the flow past a sphere descending in a salt-stratified fluid

Published online by Cambridge University Press:  29 September 2021

Shinya Okino Open the ORCID record for Shinya Okino [Opens in a new window] ,
Shinsaku Akiyama ,
Koki Takagi  and
Hideshi Hanazaki Open the ORCID record for Hideshi Hanazaki [Opens in a new window]
Shinya Okino
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto daigaku-katsura 4, Nishikyo-ku, Kyoto615-8540, Japan
Shinsaku Akiyama
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto daigaku-katsura 4, Nishikyo-ku, Kyoto615-8540, Japan
Koki Takagi
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto daigaku-katsura 4, Nishikyo-ku, Kyoto615-8540, Japan
Hideshi Hanazaki*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto daigaku-katsura 4, Nishikyo-ku, Kyoto615-8540, Japan
*
†Email address for correspondence: hanazaki.hideshi.5w@kyoto-u.ac.jp
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Abstract

The density distribution around a sphere descending in a salt-stratified fluid is measured by the laser-induced fluorescence (LIF) method. The corresponding velocity distribution is measured by particle image velocimetry (PIV), and numerical simulation is also performed to supplement the observations by LIF and PIV. In steady flow, LIF observes a thin and vertically long structure which corresponds to a buoyant jet. The bell-shaped structure, which appears under strong stratification and moderate Reynolds number (Froude number $Fr \lesssim 3$, Reynolds number $50 \lesssim Re \lesssim 500$), is also identified. The measured density distributions in the salinity boundary layer and in the jet agree with the numerical simulations which use the Schmidt number of the fluorescent dye ($Sc \sim 2000$). The initially unsteady process of the jet formation is also investigated. Under weak stratification, the LIF shows an initial development of an axisymmetric rear vortex as observed in homogeneous fluids. However, as time proceeds and the effect of stratification becomes significant, the vortex shrinks and disappears, while the jet extends vertically upward. Under strong stratification, a thin jet develops without generating a rear vortex, since the effect of stratification becomes significant in a short time before the vortex is generated.

JFM classification

Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Abaid, N., Adalsteinsson, D., Agyapong, A. & McLaughlin, R.M. 2004 An internal splash: levitation of falling spheres in stratified fluids. Phys. Fluids 16 (5), 1567–1580.CrossRefGoogle Scholar
Akiyama, S., Waki, Y., Okino, S. & Hanazaki, H. 2019 Unstable jets generated by a sphere descending in a very strongly stratified fluid. J. Fluid Mech. 867, 26–44.CrossRefGoogle Scholar
Camassa, R., Falcon, C., Lin, J., McLaughlin, R.M. & Parker, R. 2009 Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime. Phys. Fluids 21, 031702.CrossRefGoogle Scholar
Camassa, R., Falcon, C., Lin, J., McLaughlin, R.M. & Mykins, N. 2010 A first-principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number. J. Fluid Mech. 664, 436–465.CrossRefGoogle Scholar
D'Asaro, E.A. 2003 Performance of autonomous Lagrangian floats. J. Atmos. Ocean. Technol. 20, 896–911.2.0.CO;2>CrossRefGoogle Scholar
D'Asaro, E. 2018 Oceanographic floats: principles of operation. In Observing the Oceans in Real Time (Springer Oceanography) (ed. R. Venkatesan, A. Tandon, E. D'Asaro & M.A. Atmanand), pp. 77–98, Springer.CrossRefGoogle Scholar
Doostmohammadi, A., Dabiri, S. & Ardekani, A.M. 2014 A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid. J. Fluid Mech. 750, 5–32.CrossRefGoogle Scholar
Fortuin, J.M.H. 1960 Theory and application of two supplementary methods of constructing density gradient columns. J. Polym. Sci. 44, 505–515.CrossRefGoogle Scholar
Hanazaki, H., Kashimoto, K. & Okamura, T. 2009 a Jets generated by a sphere moving vertically in a stratified fluid. J. Fluid Mech. 638, 173–197.CrossRefGoogle Scholar
Hanazaki, H., Konishi, K. & Okamura, T. 2009 b Schmidt-number effects on the flow past a sphere moving vertically in a stratified diffusive fluid. Phys. Fluids 21, 026602.CrossRefGoogle Scholar
Hanazaki, H., Nakamura, S. & Yoshikawa, H. 2015 Numerical simulation of jets generated by a sphere moving vertically in a stratified fluid. J. Fluid Mech. 765, 424–451.CrossRefGoogle Scholar
Hanson, K.M., Davis, S.K. & Bardeen, C.J. 2007 Two-photon standing-wave fluorescence correlation spectroscopy. Opt. Lett. 32, 2121–2123.CrossRefGoogle ScholarPubMed
Houghton, I.A., Koseff, J.R., Monismith, S.G. & Dabiri, J.O. 2018 Vertically migrating swimmers generate aggregation-scale eddies in a stratified column. Nature 556, 497–500.CrossRefGoogle Scholar
Lee, H., Fouxon, I. & Lee, C. 2019 Sedimentation of a small sphere in stratified fluid. Phys. Rev. Fluids 4, 104101.CrossRefGoogle Scholar
MacIntyre, S., Alldredge, A.L. & Gotschalk, C.C. 1995 Accumulation of marine snow at density discontinuities in the water column. Limnol. Oceanogr. 40 (3), 449–468.CrossRefGoogle Scholar
Mehaddi, R., Candelier, F. & Mehlig, B. 2018 Inertial drag on a sphere settling in a stratified fluid. J. Fluid Mech. 855, 1074–1087.CrossRefGoogle Scholar
Mercier, M.J., Wang, S., Péméja, J., Ern, P. & Ardekani, A.M. 2020 Settling disks in a linearly stratified fluid. J. Fluid Mech. 885, A2.CrossRefGoogle Scholar
Mowbray, D.E. & Rarity, B.S.H. 1967 The internal wave pattern produced by a sphere moving vertically in a density stratified liquid. J. Fluid Mech. 30 (3), 489–495.CrossRefGoogle Scholar
Mrokowska, M.M. 2018 Stratification-induced reorientation of disk settling through ambient density transition. Sci. Rep. 8, 412.CrossRefGoogle ScholarPubMed
Ochoa, J.L. & Van Woert, M.L. 1977 Flow visualization of boundary layer separation in a stratified fluid. Unpublished report. Scripps Institution of Oceanography, 28.Google Scholar
Okino, S., Akiyama, S. & Hanazaki, H. 2017 Velocity distribution around a sphere descending in a linearly stratified fluid. J. Fluid Mech. 826, 759–780.CrossRefGoogle Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Japan 11 (10), 1104–1108.CrossRefGoogle Scholar
Thames, F.C., Thompson, J.F., Mastin, C.W. & Walker, R.L. 1977 Numerical solutions for viscous and potential flow about arbitrary two-dimensional bodies using body-fitted coordinate systems. J. Comput. Phys. 24, 245–273.CrossRefGoogle Scholar
Torres, C.R., Hanazaki, H., Ochoa, J., Castillo, J. & Van Woert, M. 2000 Flow past a sphere moving vertically in a stratified diffusive fluid. J. Fluid Mech. 417, 211–236.CrossRefGoogle Scholar
Troy, C.D. & Koseff, J.R. 2005 The generation and quantitative visualization of breaking internal waves. Exp. Fluids 38, 549–562.CrossRefGoogle Scholar
Yick, K.Y., Torres, C.R., Peacock, T. & Stocker, R. 2009 Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers. J. Fluid Mech. 632, 49–68.CrossRefGoogle Scholar
Zhang, J., Mercier, M.J. & Magnaudet, J. 2019 Core mechanisms of drag enhancement on bodies settling in a stratified fluid. J. Fluid Mech. 875, 622–656.CrossRefGoogle Scholar