Inertial drag on a sphere settling in a stratified fluid

TL;DR

This paper analyzes how stratification and fluid motion affect the drag force on a sphere settling in a stratified fluid, using perturbation theory and comparing with numerical simulations.

Contribution

It provides a theoretical framework for understanding how diffusion and advection influence inertial drag in stratified fluids, extending previous models.

Findings

Stratification can significantly increase drag on settling spheres.

The modified Oseen drag accounts for diffusion and stratification effects.

Results agree with recent numerical simulations at small Reynolds numbers.

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.