ABSTRACT
Turbulence results from the unstable growth of infinitesimal disturbances existing in a flow. Studies on its origin begin with the small disturbance theory of instability which one consider in terms of a number of illustrative examples. The theory considers the change of total energy of a system resulting from an infinitesimal disturbance introduced to the initial state of the system. Two examples, one from mechanics and one from conduction, elaborate the application of the energy method to instability problems. Before addressing the instability in fluid mechanics problems, this chapter considers a transitory problem from conduction. Elementary examples somewhat conceal the complexities involved with instability problems. There are two approaches to the integration of equation, the statistical and computational. The present state of the statistical approach, including recent impressive advances, is far from providing an answer to turbulence.
