In an effort to enhance the reader's physical understanding, this chapter begins with a discussion of fundamental concepts including parcel oscillations in a stable atmosphere, wave propagation, and the fluid motions associated with vertically propagating internal gravity waves. this followed by a brief review of the theory of of small-amplitude mountain waves, beginning with the case of air flowing over a series of sinusoidal ridges in a basic state with uniform wind speed and stability. The Linear theory is then extended to cover isolated mountains and situations with vertical variations in the basic-state wind speed and stability.The effects of nonlinearity on the flow are introduced in a discussion of downslope windstorms. Three different theoretical models of the downslope windstorm are compared. The first argues that the development of strong downslope winds is analogous to the transition from subcritical to supercritical flow in a hydraulic jump. The second proposes that downslope winds are produced by the superposition of partially reflected waves generated at atmospheric interfaces where there is a rapid change in the static stability, such as the tropopause. The third suggests that strong winds are produced by processes that become active when vertically propagating waves become unstable and "break" in the upper troposphere.The problem of forecasting downslope winds is discussed. recent observational and theoretical investigations of the gust structure embedded in the downslope wind current are reviewed. The paper concludes with a selective overview of recent work on the flow around isolated three-dimensional mountains.

[This publication is referenced in the "Synthesis of knowledge of extreme fire behavior: volume I for fire managers" (Werth et al 2011).]