Since the seminal studies by Osborne Reynolds in the nineteenth century, pipe flow has
served as a primary prototype for investigating the transition to turbulence in wall-bounded …

Spatial localization is a common feature of physical systems, occurring in both conservative
and dissipative systems. This article reviews the theoretical foundations of our …

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 …

Transition from laminar to turbulent flow drastically changes the mixing, transport, and drag
properties of fluids, yet when and how turbulence emerges is elusive even for simple flow …

The route to turbulence in pipe flow is a complex, nonlinear, spatiotemporal process for
which an increasingly clear understanding has emerged in recent years. This paper …

Turbulence is one of the most frequently encountered non-equilibrium phenomena in
nature, yet characterizing the transition that gives rise to turbulence in basic shear flows has …

Over a century of research into the origin of turbulence in wall-bounded shear flows has
resulted in a puzzling picture in which turbulence appears in a variety of different states …

A chimera state is a rich and fascinating class of self-organized solutions developed in high-
dimensional networks. Necessary features of the network for the emergence of such …

Directed percolation (DP) has recently emerged as a possible solution to the century old
puzzle surrounding the transition to turbulence. Multiple model studies reported DP …

We examine the onset of turbulence in Waleffe flow–the planar shear flow between stress-
free boundaries driven by a sinusoidal body force. By truncating the wall-normal …