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 …

Pipe flow is a prominent example among the shear flows that undergo transition to
turbulence without mediation by a linear instability of the laminar profile. Experiments on …

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

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 basic problems of transition in both incompressible and compressible boundary layers
are reviewed. Flow structures in low-speed transitional and developed turbulent boundary …

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 …

Transition to turbulence in pipe flow is one of the most fundamental and longest-standing
problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow …

The current state of knowledge about the structure of wall-bounded turbulent flows is
reviewed, with emphasis on the layers near the wall in which shear is dominant, and …

We consider long-time simulations of two-dimensional turbulence body forced by with the
purpose of extracting simple invariant sets or 'exact recurrent flows' embedded in this …

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 …