Coherent structures in wall-bounded turbulence

TL;DR

This paper models wall-bounded turbulence as a high-dimensional dynamical system of coherent structures, emphasizing the importance of minimal randomness for understanding flow behavior and control.

Contribution

It introduces a deterministic framework for turbulence based on coherent structures, linking flow statistics to eddy decomposition and classifying large-scale structures.

Findings

Intense eddies satisfy coherence properties

Large structures are shear-driven and span the boundary layer

Dispersive waves and bursts are key coherent structures

Abstract

This article discusses the description of wall-bounded turbulence as a deterministic high-dimensional dynamical system of interacting coherent structures, defined as eddies with enough internal dynamics to behave relatively autonomously from any remaining incoherent part of the flow. The guiding principle is that randomness is not a property, but a methodological choice of what to ignore in the flow, and that a complete understanding of turbulence, including the possibility of control, requires that it be kept to a minimum. After briefly reviewing the underlying low-order statistics of flows at moderate Reynolds numbers, the article examines what two-point statistics imply for the decomposition of the flow into individual eddies. Intense eddies are examined next, including their temporal evolution, and shown to satisfy many of the properties required for coherence. In particular, it is shown that coherent structures larger than the Corrsin scale are a natural consequence of the shear. In wall-bounded turbulence, they can be classified into coherent dispersive waves and transient bursts. The former are found in the viscous layer near the wall and as very-large structures spanning the boundary layer thickness. Although they are shear-driven, these waves have enough internal structure to maintain a uniform advection velocity. Conversely, bursts exist at all scales, are characteristic of the logarithmic layer, and interact almost linearly with the shear. While the waves require a wall to determine their length scale, the bursts are essentially independent from it. The article concludes with a brief review of our present theoretical understanding of turbulent structures, and with a list of open problems and future perspectives.