Despite a long and rich history of scientific investigation, fluid turbulence remains one of the
most challenging problems in science and engineering. One of the key outstanding …

The notion of coherent structures in fluid mechanics–distinguishable regions of the flow field
that share common properties and are correlated in space and time–has played a significant …

The understanding of chaotic dynamics in high-dimensional systems that has emerged in
the last decade offers a promising dynamical framework to study turbulence. Here …

A dynamical systems approach to turbulence envisions the flow as a trajectory through a
high-dimensional state space [Hopf, Commun. Appl. Maths 1, 303 (1948)]. The chaotic …

We introduce a Lagrangian definition for the boundaries of coherent structures in two-
dimensional turbulence. The boundaries are defined as material lines that are linearly stable …

The dynamical theory of moderate Reynolds number turbulence triangulates the infinite-
dimensional Navier–Stokes state space by sets of exact solutions (equilibria, relative …

Our direct numerical simulations show that a coherent structure (scrC) in an initially fine-
scale homogeneous, isotropic turbulent field breeds secondary structures in its vicinity …

Although the equations governing fluid flow are well known, there are no analytical
expressions that describe the complexity of turbulent motion. A recent proposition is that in …

This article discusses the description of wall-bounded turbulence as a deterministic high-
dimensional dynamical system of interacting coherent structures, defined as eddies with …

Turbulent flows in nature and technology possess a range of scales. The largest scales carry
the memory of the physical system in which a flow is embedded. One challenge is to unravel …