Inertial drag on a sphere settling in a stratified fluid

Abstract

We compute the drag force on a sphere settling slowly in a quiescent, linearly stratified fluid. Stratification can significantly enhance the drag experienced by the settling particle. The magnitude of this effect depends on whether fluid-density transport around the settling particle is due to diffusion, to advection by the disturbance flow caused by the particle, or due to both. It therefore matters how efficiently the fluid disturbance is convected away from the particle by fluid-inertial terms. When these terms dominate, the Oseen drag force must be recovered. We compute by perturbation theory how the Oseen drag is modified by diffusion and stratification. Our results are in good agreement with recent direct-numerical simulation studies of the problem at small Reynolds numbers and large (but not too large) Froude numbers.

arXiv comment10 pages, 1 figure

References in corpus (5)

• Preferential sampling and small-scale clustering of gyrotactic microswimmers in turbulence
• Time-dependent lift and drag on a rigid body in a viscous steady linear flow
• The history force on a small particle in a linearly stratified fluid
• Clustering of vertically constrained passive particles in homogeneous, isotropic turbulence
• Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number

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