On the instability of laminar flow and its transition to turbulence

Abstract

In recent years, there has been much progress in our understanding of the mechanism of transition from laminar flow to turbulent flow, but the problem remains not completely solved. Theoretically, the most easily tractable mechanism of transition is that following the development of the disturbances in the laminar motion caused by its inherent instability. When the disturbances are small, the equations describing the motion can be linearized, and the mathematical theory can be developed in great detail. Even in this case, it is well-known that the theory of the instability of parallel flows has involved a great deal of controversy, largely due to the difficulty of the mathematical problems involved.