Abstract
Scale interactions between a variety of motions in the atmosphere and ocean have many theoretical and practical implications from predictability at the weather scales to reliability at the slow seasonal and climate scales. Two classes of wavy motions are prominent at the hydrostatic limit, for instance: the fast inertia-gravity waves and the slow Rossby waves. Although only Rossby waves are believed to be of direct meteorological significance, neglecting the fast oscillations may corrupt numerical integrations leading to unrealistic results and eventually to a complete model crash. Reliability of long seasonal and climate scales depends upon a proper representation of, at least, the statistics of the weather scale phenomena under given boundary conditions. The predictability of the weather scale phenomena, on the other hand, depends on the proper evolution of the system from a given initial condition. It has long been shown that a balance between stringent and permissive control of the high-frequency oscillations can allow improvements to weather forecasting. Behind these concepts are the ways by which Rossby waves can interact, horizontally and vertically, with high-frequency oscillations, or with other slow frequency oscillations and even with topography. Thus, in the present work we make a review of Rossby wave theory, considering its generation mechanisms and their interactions, including a brief discussion of some applications for the atmosphere.