Transition to Turbulence

Abstract

As already stressed in Chapter I, turbulence can only develop in rotational flows: it is due to the existence of shear in a basic flow that small perturbations will develop, through various instabilities, and eventually degenerate into turbulence. Some of these instabilities, at least during the initial stage of their development, may be understood within the framework of linear-instability theory, the main results of which will be recalled in this chapter. The non-linear instability studies may prove to be useful in the future in understanding transition to turbulence, but, to date, they are still in progress and have not led to any unified theory of transition. On the contrary, an extremely useful tool to understand the transition, and assess the various theories claiming to describe it, is the direct-numerical simulations of the Navier-Stokes equations: numerous examples of these calculations will be given here.