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 …

In his landmark paper of 1883, Reynolds addressed the question of why the fluid motion
along a pipe changes from a laminar to a turbulent state at modest flow rates. His …

Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity
increases, and the onset of turbulence radically changes transport efficiency and mixing …

The aim of this Book is to give an overview, based on the results of nearly three decades of
intensive research, of transient chaos. One belief that motivates us to write this book is that …

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 …

The breakup of drops and bubbles in turbulent fluids is a key mechanism in many
environmental and engineering processes. Even in the well-studied dilute case, quantitative …

Turbulence is the major cause of friction losses in transport processes and it is responsible
for a drastic drag increase in flows over bounding surfaces. While much effort is invested into …

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 …

The chaotic dynamics of low-dimensional systems, such as Lorenz or Rössler flows, is
guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is …

Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium.
Models are presented in two variables, turbulence intensity and mean shear, that evolve …