Instability and Transition

Abstract

Fluid flows can be in an ordered or laminar state, or they can be in a relatively-disordered, chaotic or turbulent state. The theory of hydrodynamic stability, which has a history of some 100 years, is concerned with the evolution between these two separate basic states of laminar flow and turbulent flow. Early theoretical work in the subject, associated with such names as Reynolds, Kelvin, Rayleigh, Orr, Sommerfeld, Prandtl, Taylor, Heisenberg, Tollmien, Schlichting, Squire, Jeffreys, Lin and Meksyn, was concerned mainly, though not entirely, with the development of infinitesimal disturbances and with the associated concept of exponential stability or instability. Crucial experiments were made by a number of scientists and engineers, including Reynolds, Bénard, Taylor and Schubauer and Skramstad, and good agreement was established between the observations and the results of theory. This stage may be said to cover the period 1880 to 1950 approximately.