The k^-3 and k^-5/3 Energy Spectrum of Atmospheric Turbulence

We present an explanation of the observed turbulent energy spectrum of the atmosphere (Nastrom and Gage (1985)) encompassing several octaves of scales. Energy injection occurs over the long synoptic scales. From there energy is transferred through nonlinear wave-wave interactions upscale to the planetary waves and downscale through the mesoscale waves and eventually to dissipation. The observed spectral shape: k^-3 over the synoptic and subsynoptic scales and k^-5/3 over the mesoscales, where k is the horizontal wavenumber, reveals the nature of the turbulent cascades.