  A method for deriving provably stable low-dimensional Galerkin models of
post-transient incompressible flows is introduced. The proposed approach
involves an iterative procedure for expansion modes that satisfy Lyapunov
stability in the neighborhood of a fixed point. The approach is demonstrated
using two prototypical flow configurations: a two-dimensional mixing layer, and
two-dimensional flow inside a lid-driven cavity. This new methodology can be a
building block in an effort to develop more accurate and more robust
low-dimensional models of incompressible flows.
