Orientation instability of settling spheroids in a linearly density stratified fluid

TL;DR

This study investigates how shape anisotropy affects the orientation and stability of settling spheroids in stratified fluids through numerical simulations, revealing new reorientation behaviors and instability mechanisms.

Contribution

It provides novel insights into the reorientation instabilities of oblate and prolate spheroids in stratified fluids, highlighting the roles of buoyancy and hydrodynamic torques.

Findings

Spheroids reorient to edge-wise and partially edge-wise orientations in stratified fluids.

Reorientation instabilities occur when settling velocity drops below a threshold.

Stratification enhances drag and influences torque balance on spheroids.

Abstract

Much work has been done to understand the settling dynamics of spherical particles in a homogeneous and a stratified fluid. However, the effects of shape anisotropy on the settling dynamics of a particle in a stratified fluid are not completely understood. To this end, we perform numerical simulations for settling oblate and prolate spheroids in a stratified fluid. We present the results for the Reynolds number, $Re$, in the range $80-250$ and the Richardson number, $Ri$, in the range $0-10$. We find that both the oblate and prolate spheroids reorient to the edge-wise and partially edge-wise orientations, respectively, as they settle in a stratified fluid completely different from the steady-state broad-side on orientation observed in a homogeneous fluid. We observe that reorientation instabilities emerge when the velocity magnitude of the spheroids fall below a particular threshold. We also report the enhancement of the drag on the particle from stratification. The torque due to buoyancy effects tries to orient the spheroid in an edge-wise orientation while the hydrodynamic torque tries to orient it to a broad-side on orientation. Below the velocity threshold, the buoyancy torque dominates; resulting in the onset of reorientation instability. Finally, the asymmetry in the distribution of the baroclinic vorticity generation term around the spheroids explains the onset of the reorientation instability.