CHAPTER III - Application to the Theory of Motion of a Viscous Fluid and to the Theory of Turbulence

Abstract

This chapter presents examples of the use of dimensional analysis in the mathematical solution of certain physical problems. The chapter discusses the problem of diffusion of vorticity in the one dimensional unsteady motion of a viscous incompressible fluid of infinite extent. The exact solutions of the equations of motion of a viscous incompressible fluid are reviewed. The chapter discusses the boundary layer in the flow of a viscous fluid past a flat plate, and reviews isotropic turbulent motion of an incompressible fluid. Many fluid motions observed in nature and the majority of motions with which one deals with in engineering are characterized by the presence of disorderly, unsteady, fluid motions superposed on a basic fluid motion which can be represented as a certain statistically average motion. Fluid motions of such a kind are called turbulent. The velocity, pressure, and other quantities at each point of the flow in turbulent fluid motion undergo irregular fluctuating variations about certain average values.