The Optimum Theory of Turbulence

This chapter discusses that the optimum theory represents an approach toward the understanding of turbulent flows without the introduction of heuristic assumptions that are commonly used in other theories of turbulence. As there does not seem to be a generally accepted definition of turbulence, this chapter shall regard, for the present purpose, a fluid flow as turbulent if the details of the velocity field are too complex to be of interest and only the information about certain average properties is needed. The chapter highlights that the optimum theory is hardly appropriate for all turbulent systems of this general nature and a more suitable mathematical definition of turbulence will be required later. The main point is that turbulent fluid systems are characterized by an information gap that is neither possible nor desirable to fill. The optimum theory represents an alternative approach in which the lack of information about properties of the fluctuating velocity field is reflected by the theoretical results. Instead of a theoretical prediction of the physically realized average properties, bounds on those properties are obtained. The idea of the optimum theory is to consider not the manifold of solutions of the basic equations for a particular problem, but a larger manifold of vector fields, which includes the actual solutions. This manifold of fields shares with the solutions kinematic relationships such as boundary conditions and the energy balance. © 1978, Academic Press Inc.