In Chapter 2, we showed that flow disturbances can be decomposed into fluctuations in vorticity, entropy, and volume. The next two chapters focus on the evolution of vorticity in flows, with particular emphasis on the development of coherent vortical structures. Such large-scale structures, embedded on a background of acoustic waves and broadband, smaller-scale turbulence, dominate the unsteady flow fields in combustors. These large-scale structures play important roles in processes such as combustion instabilities, mixing and entrainment, flashback, and blowoff. For example, we will discuss vortex–flame interactions repeatedly in discussions of combustion instabilities in later chapters.

High Reynolds number flows are effectively inviscid outside the boundary layer. Vorticity in the flow largely originates, then, from boundary layers in approach flow passages or other walls. Free shear layers arise at points of boundary layer separation, initiating a sequence of large-scale flow instabilities as this vorticity is then stretched and amplified by the base flow.

Coherent structures arise because the base flow configuration, u0(y) or ū(y), is unstable. Many of the same instabilities that are focused on in the next two chapters that play such important roles in unsteady combustor dynamics also manifest themselves in a variety of other instances, including in spectacular, large-scale fashion in nature. To illustrate, Figure 3–1(a) illustrates cloud patterns showing the Kelvin- Helmholtz instability, discussed in Sections 3.4 and 4.1. Figure 3–1(b) illustrates the Bénard/von Kármán instability over a Japanese island visualized from space, to be discussed in Section 4.2.