In 1883, Reynolds published his classical work on the experimental study of the
stability of shear shows. Since then the issue of the critical Reynolds number at which
laminar flows become unstable has been studied by numerous people, including
Sommerfeld, Heisenberg, C. C. Lin, Orazag, and more recently, Trefethen, Hof,
Barkley, Eckhardt, etc. Despite this great deal of effort, the theoretical question as to
how the critical Reynolds number should be determined still remains open. In this talk,
we present an approach using ideas drawn from statistical physics and large deviation
This is joint work with Xiaoliang Wan and Haijun Yu.