A salient feature of stably stratified fluids is their ability to sustain buoyancy oscillations. The history of linear buoyancy oscillations is reviewed. The expression of their frequency was first given by Lord Rayleigh (1883) for linear oscillations in an incompressible fluid. Hesselberg (1924) used parcel arguments to describe the oscillation in a dry compressible atmosphere. His expression for the buoyancy oscillation neglected a factor of g and was corrected by Väisälä (1925). Brunt (1927) independently obtained the same expression. The correct expression for the oscillation in a saturated atmosphere was given by Lalas and Einaudi (1974) and discussed by Durran and Klemp (1982). It is shown that all these expressions are contained in a general formulation of the frequency by Eckart (1960).

Nonlinear solutions of the oscillations in dry, moist, and saturated atmospheres are presented. Emphasis is placed on the energetics of the oscillation. The traditional energetics is compared to the available energetics. The traditional approach indicates that the parcel does not conserve its total energy but rather that there is an exchange of energy with the environment. This exchange is associated with the rate of working of the pressure field on the parcel. In the available approach the parcel conserves the sum of its kinetic and available energies. For the particular case of parcel theory, the available energy is the available potential energy and is directly related to the convective available potential energy (CAPE). The local theory of the available energetics is extended to the case of a saturated atmosphere.