Introduction

The research belongs to the wide topic of hydrodynamic instability and transition to turbulence. Knowing how turbulence emerges in a fluid flow is crucial to many engineering applications; when the flow is turbulent, its characteristics vary substantially due to chaotic motions on many different scales. Significant changes to the characteristics of heat exchange, intensity of mixing, combustion, and forces acting on walls can result from such flow transformations. To develop effective methods of controlling the transition it is necessary to understand what scenarios for the transition there may be and what physical reasons affect the change of regimes in the transition process. Also, understanding how turbulence originates is of fundamental importance, since it may shed new light on the turbulence phenomenon itself. The following quotation reflects the essence of the study and is still highly relevant, despite the fact that much progress has been made in pure theory and applications on turbulence since then.

“Although the turbulent motion has been extensively discussed in literature from different points of view, the very essence of this phenomenon is still lacking sufficient clearness. To the author’s opinion, the problem may appear in a new light if the process of initiation of turbulence is examined thoroughly.” (Nobel laureate L. Landau, 1944)

The current project singles out a characteristic stage of the transition – the onset of three-dimensionality – and aims to deepen the understanding of this part of the transition by developing a general-purpose framework for its study and revealing general patterns in 3D transition.

Framework

The framework uses the methods of the theory of hydrodynamic stability, computational fluid dynamics, and high-performance computing, which are specifically adjusted to the problem of transition to 3D. In particular, it includes the tools for

Canonical Problem 1: Flow Around a Circular Cylinder

The geometrical simplicity of this flow has made the problem attractive to a number of theoretical and experimental studies.

Nevertheless, two modes of 3D instability, discovered more than 30 years ago, still lack a commonly accepted physical explanation.

   

The main difficulty is connected to the causality issue: the cyclic perturbation evolution involves complex interactions with the previously formed perturbed regions.

3D flow in the wake is a consequence of both the absolute instability in the vortex formation region and the convective instability in the developed wake. Since the former becomes unstable at higher Reynolds numbers than the latter, non-decaying 3D vortex structures are observed as soon as the formation-region flow becomes unstable.

An explaination for this instability pattern is suggested: 3D small perturbations of a specific spanwise wavelength tend to self-organize so that the flow in each spanwise cross-section corresponds to the initial 2D flow at slightly shifted times (with known spanwise dependence). This mechanism is problem-independent, it explains why even for stable non-stationary 2D flows one can observe local growth of 3D structures and allows one to a priori estimate the spatial structure of 3D perturbations.

For the periodic flow around a cylinder, the time-shifting pattern repeats after each vortex shedding cycle, but in unstable (stable) regimes its intensity grows (decays). To explain this overall flow instability, we track the action of the physical mechanisms affecting the growth of perturbations in fluid particles. The analysis revealed the mechanism for the local amplification and feedback processes, whose balance defines the overall flow instability.

To be continued ...