Flow at high Reynolds numbers

Abstract

Having discussed viscous flows at vanishing Reynolds numbers, we turn our attention to the diametrically opposite limit of inertia-dominated flows at high Reynolds numbers. Examining the changes in the structure of a flow with increasing Reynolds number, we encounter a broad variety of protocols accompanied by a rich phenomenology. In all cases, when the Reynolds number exceeds a critical threshold, flow instability arises and a small-scale turbulent motion is established. The theoretical study of the structure and dynamics of flows at high Reynolds numbers encompasses several complementary topics including potential-flow theory, boundary-layer theory, theory of hydrodynamic stability, theory of turbulent motion, and dynamics of vortex motion. Potential flow was considered in earlier sections; boundary-layer theory, hydrodynamic stability, and turbulent motion will be discussed in this chapter; and vortex motion will be the exclusive topic of Chapter 11.