This article reviews linear instability analysis of flows over or through complex two-
dimensional (2D) and 3D geometries. In the three decades since it first appeared in the …

▪ Abstract The objective of this review is to critically assess the different approaches
developed in recent years to understand the dynamics of open flows such as mixing layers …

Completely revised text focuses on use of spectral methods to solve boundary value,
eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational …

Results are reported from a highly accurate, global numerical stability analysis of the
periodic wake of a circular cylinder for Reynolds numbers between 140 and 300. The …

Results are reported from a three-dimensional computational stability analysis of flow over a
backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds …

This review article addresses the dynamics and control of low-frequency unsteadiness, as
observed in some aerodynamic applications. It presents a coherent and rigorous linearized …

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

We reveal a new scenario for the transition of solitons to chaos in a mode-locked fiber laser:
the modulated subharmonic route. Its universality is confirmed in two different laser …

A collection of methods is presented to adapt a pre-existing timestep** code to perform
various bifurcation-theoretic tasks. It is shown that the implicit linear step of a time-step** …

While the wake of a circular cylinder and, to a lesser extent, the normal flat plate have been
studied in considerable detail, the wakes of elliptic cylinders have not received similar …