On the spectral equations and the statistical energy spectrum of atmospheric motions in the frequency domain¹

The kinetic energy spectral equations in the frequency domain was derived for the large-scale atmospheric motions. Some of the more important implications revealed by the spectral equations are: (1) the shape of the spectral density function ϕ_il (v), is controlled by the out-of-phase relationships among various meteorological variables; (2) the rotation of the earth has an explicit influence on ϕ_il (v) as well as on the average level of the atmospheric kinetic energy, and (3) an atmosphere that is efficient in spreading its kinetic energy among its various frequency components, so that there is no particular tendency for spectral peaks to form, should have a red-noise spectrum. A detailed discussion of these as well as of other implications is given in the text.