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

We provide an overview of current techniques and typical applications of numerical
bifurcation analysis in fluid dynamical problems. Many of these problems are characterized …

Pipe flow and many other shear flows show a transition to turbulence at flow rates for which
the laminar profile is stable against infinitesimal perturbations. In this brief review the recent …

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic
interactions by considering a finite number of harmonics in the frequency domain using the …

Several new families of nonlinear three-dimensional travelling wave solutions to the Navier–
Stokes equation, also known as exact coherent states, are computed for Newtonian plane …

In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows
and present recent achievements in the understanding of this problem. The transition is …

We demonstrate the existence of an exact invariant solution to the Navier–Stokes equations
for the asymptotic suction boundary layer. The identified periodic orbit with a very long …

The dynamics on the laminar–turbulent separatrix is investigated numerically for boundary-
layer flows in the subcritical regime. Constant homogeneous suction is applied at the wall …

The spatiotemporal aspects of the transition to turbulence are considered in the case of a
boundary-layer flow developing above a flat plate exposed to free-stream turbulence …

We present an equilibrium solution of plane Couette flow that is exponentially localized in
both the spanwise and streamwise directions. The solution is similar in size and structure to …