Numerical stability and three dimensionality of a streamline hyperbolic critical point in wake at low Reynolds number

TL;DR

This study investigates the numerical stability and three-dimensional behavior of hyperbolic saddle critical points in wake flows at low Reynolds numbers, revealing their influence on wake stability and flow divergence.

Contribution

It uncovers novel analytical relationships between hyperbolic critical points, flow divergence, three-dimensionality, and shear-layer interactions in wake flows.

Findings

HSP evolves along shear-layer interfaces and affects pressure gradients.

HSP is associated with positive fluid divergence and 3D flow features.

Formation of stagnant zones around HSP impacts wake stability.

Abstract

In this work the numerical stability of a streamline singular hyperbolic/saddle critical point (HSP) and its relationship with the divergence of pressure force/fluid flux are numerically investigated at low Reynolds numbers. Three canonical configurations at different Reynolds numbers are considered: (a) an isolated circular cylinder; (b) side-by-side circular cylinders and (c) a near-wall circular cylinder. The objective is to investigate the behavior of a HSP subjecting to imbalanced shear-layer interaction and different Reynolds numbers. It is found that a HSP evolves along the shear-layer interfaces and imposes adverse pressure gradients, which potentially deteriorates near-wake stability. The inherent characteristics of a HSP is linked with net positive fluid-fluid divergence and fluid three dimensionality. A vorticity-free stagnant zone is formed around a HSP, which cut the kinetic energy supply of shear layers in wake, project third-dimensional fluid fluxes and develops three-dimensional streamwise braids. These findings are confirmed and explained via the quantification of the fluid-flux divergence, the hydrodynamic responses of cylinder(s) and the secondary enstrophy. The primary focus in this article is to reveal the subtle analytical relationships between HSP, divergence of pressure force/fluid flux, fluid three dimensionality and imbalanced shear-layer interaction. To the knowledge of authors, so far these analytical relationships have not been reported in literature.