  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.
