Wall-bounded turbulence exhibits patterns that persist in time and space: coherent
structures. These are important for transport processes and form a conceptual framework for …

Recent remarkable progress in computing power and numerical analysis is enabling us to
fill a gap in the dynamical systems approach to turbulence. A significant advance in this …

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

These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school
in Les Houches. Their aim is to provide a self-contained graduate-student level introduction …

Addition of a small amount of very large polymer molecules or micelle-forming surfactants to
a liquid can dramatically reduce the energy dissipation it exhibits in the turbulent flow …

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 …

We track the secondary bifurcations of coherent states in plane Couette flow and show that
they undergo a periodic doubling cascade that ends with a crisis bifurcation. We introduce a …

Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer
mechanisms sustaining wall turbulence can be ascribed to linear processes. The different …

We derive low-dimensional, data-driven models for transitions among exact coherent states
in one of the most studied canonical shear flows, the plane Couette flow. These one-or two …

We show that turbulent dynamics that arise in simulations of the three-dimensional Navier-
Stokes equations in a triply periodic domain under sinusoidal forcing can be described as …