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Core mechanisms of drag enhancement on bodies settling in a stratified fluid

Published online by Cambridge University Press:  22 July 2019

Jie Zhang Open the ORCID record for Jie Zhang [Opens in a new window] ,
Matthieu J. Mercier Open the ORCID record for Matthieu J. Mercier [Opens in a new window]  and
Jacques Magnaudet Open the ORCID record for Jacques Magnaudet [Opens in a new window]
Jie Zhang
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Shaanxi 710049, China Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
Matthieu J. Mercier
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
Jacques Magnaudet*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

Stratification due to salt or heat gradients greatly affects the distribution of inert particles and living organisms in the ocean and the lower atmosphere. Laboratory studies considering the settling of a sphere in a linearly stratified fluid confirmed that stratification may dramatically enhance the drag on the body, but failed to identify the generic physical mechanism responsible for this increase. We present a rigorous splitting scheme of the various contributions to the drag on a settling body, which allows them to be properly disentangled whatever the relative magnitude of inertial, viscous, diffusive and buoyancy effects. We apply this splitting procedure to data obtained via direct numerical simulation of the flow past a settling sphere over a range of parameters covering a variety of situations of laboratory and geophysical interest. Contrary to widespread belief, we show that, in the parameter range covered by the simulations, the drag enhancement is generally not primarily due to the extra buoyancy force resulting from the dragging of light fluid by the body, but rather to the specific structure of the vorticity field set in by buoyancy effects. Simulations also reveal how the different buoyancy-induced contributions to the drag vary with the flow parameters. To unravel the origin of these variations, we analyse the different possible leading-order balances in the governing equations. Thanks to this procedure, we identify several distinct regimes which differ by the relative magnitude of length scales associated with stratification, viscosity and diffusivity. We derive the scaling laws of the buoyancy-induced drag contributions in each of these regimes. Considering tangible examples, we show how these scaling laws combined with numerical results may be used to obtain reliable predictions beyond the range of parameters covered by the simulations.

JFM classification

Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Stratified flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 622 - 656
Copyright
© 2019 Cambridge University Press 

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