Transient growth and why we should care about it?

Abstract

The phrases 'transient growth' and 'non-normality' have become common parlance in fluid mechanics nowadays. We present these ideas with a simple two-dimensional system, to enable the reader to look for transient growth, as a trigger for nonlinear behaviour to set in, in a variety of situations probably having nothing to do with fluid mechanics. The article is aimed at undergraduate students of science, engineering, finance, etc., and the material is based completely on the excellent books of Trefethen and Embree, and Schmid and Henningson.