The growth of meteorological disturbances

Extract

1. Introduction. A considerable amount of attention has been paid to the problem of determining the conditions which decide whether a liquid heated from below is stable or unstable. The motion consequent upon the disturbance of an unstable ideal gas does not, however, seem to have been treated so far, and this problem forms the subject of the present paper. Heat conduction and viscosity are at first neglected, and we are therefore dealing with the small motions of a gas slightly disturbed from a position of equilibrium under the influence of gravity. The condition for the stability of such a gas is well known, namely, the temperature gradient must be less than the adiabatic gradient. Furthermore, it is known that there is a sharp distinction between slow large-scale (meteorological) and rapidly varying small-scale (acoustical) phenomena. The present paper confirms these points and derives the time scale of meteorological phenomena. Heat conduction and viscosity are then shown to set a lower limit to the dimensions of such disturbances, while the effect of the earth's rotation is shown to be negligible.