Wake instability past a sphere settling in a strongly stratified flow

TL;DR

This study uses detailed simulations to explore wake instabilities behind a sphere in strongly stratified fluids, revealing complex dynamics, instability modes, and the influence of key flow parameters.

Contribution

It provides new insights into the physical mechanisms and stability regimes of wake instabilities in stratified flows through comprehensive numerical analysis.

Findings

Identification of varicose and sinuous instability modes.

Development of a phase map of instability regimes.

Elucidation of the interplay between vorticity, vortex tilting, and density transport.

Abstract

The wake of a body moving across the isopycnals of a strongly stratified fluid is characterized by the presence of an intense jet which, under certain circumstances, may become unstable. To get insight into the phenomenology of this instability and the underlying mechanisms, we conduct fully-resolved three-dimensional time-dependent simulations of the flow past a rigid sphere settling steadily through a linearly stratified fluid over a wide range of flow parameters which include the case of salt-stratified water. Results reveal a rich dynamics characterized by distinct wake symmetries, vortical structures and transverse force signatures. Simulations evidence the existence of varicose and sinuous instability modes that arise from distinct physical mechanisms. Thanks to several metrics, we build a phase map delineating the bounds of each instability regime as a function of the three control parameters of the problem, namely the Froude, Reynolds and Prandtl numbers. We show that the instability mechanism results from a subtle interplay between baroclinic vorticity generation, vortex tilting and radial transport of the mean density gradient within the jet.