Instability of flows and their transition to turbulence are widespreadphenomena in engineering and the natural environment and are important inapplied mathemati... » 

Instability of flows and their transition to turbulence are widespreadphenomena in engineering and the natural environment and are important inapplied mathematics astrophysics biology geophysics meteorologyoceanography and physics as well as engineering. This is a textbook tointroduce these phenomena at a level suitable for a graduate course bymodelling them mathematically and describing numerical simulations andlaboratory experiments. The visualization of instabilities is emphasized withmany figures and in references to more still and moving pictures. The relationof chaos to transition is discussed at length. Many worked examples andexercises for students illustrate the ideas of the text. Readers are assumed tobe fluent in linear algebra advanced calculus elementary theory of ordinarydifferential equations complex variables and the elements of fluid mechanics.The book is aimed at graduate students but will also be very useful forspecialists in other fields. «