This chapter is concerned with the dynamics of atmospheric motions that characteristically have cyclical structure in space and periodic fluctuations in time. Such type of motion is what we call waves. As far as weather disturbances are concerned, the two most important types of waves in the atmosphere are known as internal gravity waves and Rossby waves. Following some brief preliminary remarks in Section 5.1, we discuss the physical nature and the restoring mechanisms responsible for the existence of these waves in Sections 5.2, 5.5 and 5.6. We formulate the simplest possible models for them and deduce the intrinsic properties of the free wave modes in Sections 5.3, 5.4 and 5.7. We also delineate their structures arising from a given external forcing in Section 5.8. A brief discussion of the observed statistical properties of Rossby waves in the atmosphere is given in Section 5.9. The chapter ends in Section 5.10 with a discussion of the fundamental dynamics of a unique subclass of wave motions known as edge waves that turns out to have wide ramifications.

Preliminary remarks

Wave is a generic term for vibrations in a physical medium, whether it is a string, a membrane, a three-dimensional structure, water in an ocean or air in the atmosphere. A wave has cyclic structure in space and/or periodic fluctuations in time. A localized disturbance in the atmosphere may be thought of as an ensemble of constituent waves. There are distinctly different types of waves in the atmosphere and oceans.