The lid-driven cavity is an important fluid mechanical system serving as a benchmark for
testing numerical methods and for studying fundamental aspects of incompressible flows in …

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

In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness
to the transition to turbulence, is of critical importance for both academic and industrial …

This book describes the research that has been done on the problems of Benard convection-
as well as its modern offspring, the Rayleigh-Benard problem-and Taylor vortices. Benard …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

Fundamental aspects of spectral methods are introduced. Recent developments in spectral
methods are reviewed with an emphasis on collocation techniques. Their applications to …

The global linear stability of the flat-plate boundary-layer flow to three-dimensional
disturbances is studied by means of an optimization technique. We consider both the …

The bifurcation diagram for the Eckhaus instability is presented, based on the Ginzburg-
Landau equation in a finite domain with either free-slip or periodic boundary conditions. The …

We report on axisymmetric numerical simulations of rapidly rotating spherical shells in which
the axial rotation rate of the outer shell is modulated in time. This allows us to model …

Axisymmetric spherical Couette flow between two concentric differentially rotating spheres is
computed numerically as an initial-value problem. The time-independent spherical Couette …