A key focus of this text is to relate the manner in which fluctuations in flow or thermodynamic variables propagate and interact in combustion systems. In this chapter, we demonstrate that combustor disturbances can be decomposed into three canonical types of fluctuations, referred to here as acoustic, entropy, and vorticity disturbances. This decomposition is highly illustrative in understanding the spatial/temporal dynamics of combustor disturbances [1]. For example, we show that unsteady flow motions can be decomposed into acoustic fluctuations, which propagate as waves at the speed of sound, and vorticity fluctuations, which are advected by the flow. This decomposition is important because, as shown in Chapters 11 and 12, two velocity disturbances of the same magnitude can lead to very different influences on the flame, depending on their phase speeds and space–time correlation. Aside 2.2 further emphasizes how this decomposition provides insight into behavior measured in a harmonically oscillating flow field.

This chapter is organized in the following manner. Section 2.1 introduces the basic approach for analyzing disturbances, and illustrates the formal process of perturbation expansions used throughout the text. Section 2.2 then considers small-amplitude disturbance propagation in homogeneous flows. This limit is helpful for understanding key aspects of the problem, as the disturbance modes do not interact and are not excited. Section 2.3 closely follows this material by treating the effects of boundary conditions, finite amplitude disturbances, and inhomogeneities, and shows how these effects cause interaction and/or excitation of these modes. Sec-tion 2.4 then considers the energy density and energy flux associated with these fluctuations.