2.1 Inviscid Flows

Finding solutions with the Navier-Stokes equations that were introduced in Chapter 1 is a formidable challenge, particularly for flows where convective acceleration is present. When, however, the Reynolds number is sufficiently high, of the order of 10 ⁵ or more, viscosity effects usually are of importance to the flow only in the boundary layer near a body or a wall or possibly in confined regions in the wake of a body. In many problems, such as the case of waves on a free surface, viscosity effects many be of secondary importance in most of the flow field.

In solving such flows, it is convenient and useful to first omit viscosity terms completely. Since this reduces the order of the differential equations, this means that fewer boundary conditions can be applied. The zero normal velocity condition generally is the most important condition and so is retained, whereas the no-slip velocity condition is ignored. For many flows, viscous effects can be included later by considering the boundary layer flow using the slip velocity found from the inviscid flow at the outer edge of the boundary layer.

Most 19th-century fluid mechanics was concerned with the study of inviscid flows. ^[1] There was no clear understanding of the effects of the Reynolds number on the flow, and the study of turbulence was left largely untouched. This was, however, a time of great ferment in the fields of fluid mechanics, electricity and magnetism, and thermodynamics. Particularly in the first two areas, scientists...