Here is a talk I first gave at DSPDES in Barcelona in June 2010.
It should be useful in understanding the connection between
convective instability, transient growth, singular value decomposition (SVD).
It also addresses computational issues
and response functions for spiral waves in excitable media.

This is based on work with

Hugh Blackburn
Chris Cantwell
Spencer Sherwin

Irina Biktasheva
Vadim Biktashev
Andy Foulkes

Papers on the subject can be found here.
For fluid dynamics, the basic formalism is described in this paper.
I also recommend these notes by DJ Estep.