It is common to observe patterns in thin, semi-continuous layers of cirrus clouds that are highly suggestive of wave-like motion in the middle and upper troposphere. Astute observers may even have seen clouds that appear to mark a sequence of breaking waves near a large mountain or mountain range. These are indeed indications that waves can exist in the atmosphere, but are a misleading indication because these waves are only evident because they are made visible by clouds whose presence may not be directly related to the waves. There is the possibility that waves could exist in clear air, and also that waves could exist on such a large scale that they are not evident to observers looking up from Earth's surface. An example of a wave-filled atmosphere is shown in Figure 5.1. Studies of atmospheric waves have uncovered a wide range of wave types, all having different dynamical bases, different characteristics, and existing under different atmospheric conditions. All waves have a simple dynamical basis in common – they are driven by restoring forces that act in opposition to a displacement from an equilibrium position. The elasticity of air gives rise to sound waves. If the restoring force is gravity, the atmosphere will support gravity waves. If the restoring force is both gravity and the Coriolis force, the atmosphere will support inertia-gravity waves, while the Coriolis force alone gives rise to inertial waves. If the variation of Coriolis force with latitude provides the restoring force, Rossby waves will result. These waves are all particular solutions of the governing equations. We will explore only two simple wave types in order to illustrate the approaches needed for their analysis.

Sound waves are unlike other atmospheric waves in that they are longitudinal waves, in which the oscillation is in the direction of propagation. By contrast, transverse waves have an oscillation perpendicular to their direction of propagation.