A Kind of Boundary-Layer 'Flutter': The Turbulent History of a Fluid Mechanical Instability

Abstract

The transition from laminar to turbulent flow has been a notorious riddle in fluid dynamics since the nineteenth century. Hydrodynamic instabilities were regarded as a cause for the onset of turbulence, but their theoretical investigation led to paradoxical results. I focus on studies about the instability of laminar boundary-layer flow along a flat plate. The experimental discovery of boundary-layer oscillations (Tollmien-Schlichting waves) in the USA during World War II vindicated a long-disputed theory developed in Germany in the 1920s and 1930s. However, the instability which causes these oscillations marks only the initial phase of the onset of turbulence; higher-order instabilities had to be assumed in order to extend the analysis to the regions of the transition zone where more complex phenomena (such as "turbulent spots") mark the onset of turbulence. There is still no theory to describe these processes in a satisfactory manner. The emphasis on the fundamental character of the problem, however, tends to obscure the practical interests which motivated the study of boundary-layer instabilities throughout its long history. The disputed theories played a role in the quest for "laminar airfoils" and other practical applications. Theory and practice are entangled more intimately than it would appear from the rhetoric about the fundamental character of the "turbulence problem".