A Note on General Classification of Motions in a Baroclinic Atmosphere

Abstract

In the present note we make an attempt to classify the basic types of dynamical processes in the atmosphere such as gravitational and acoustic waves and horizontal eddy motions by solving the problem of small oscillations in the baroclinic atmosphere.

We have found a certain invariant with the help of which one can estimate the final stationary state of the atmosphere under arbitrary conditions without the analysis of the wave processes which cause the field change. The most natural way of obtaining the special equations for the numerical forecasting is that of computing the first derivative in time of the invariant in the second approximation (quadratic terms being taken into account).

The filtrating role of the quasi-static approximation is being investigated in the note. Quasi-static approximation filtrates the internal acoustic waves and somewhat increases the frequencies of the gravitational waves.

It has, in particular, been shown that the time required for establishing the quasi-static balance in the atmosphere is equal to some minutes.