Hydrodynamic Stability and Turbulence (1922–1948)

Abstract

Heisenberg’s long paper (No. 2, p. 31 *), devoted in part to a study of the stability of plane-parallel laminar flows, is, by any standards, an important and fundamental contribution to the subject. In this paper, besides describing the essential steps that must be taken to solve the underlying mathematical problem, Heisenberg devises for the first time the use of “inner” and “outer” approximations with suitable matching conditions for the solution of ordinary differential equations (of order two or higher) with a turning point — a method later to be described by the initials “W.K.B.”. And beneath the mathematical developments, one can discern the operation of a powerful physical insight. Heisenberg himself described later the physical and the mathematical ideas in this early work of his in an address to the International Congress of Mathematicians in 1950 [1]. Perhaps a somewhat more technical account of these ideas may be useful as an introduction to his paper.