The Kolmogorov equation for the third-order velocity structure function is derived for atmospheric mesoscale motions on an f plane. A possible solution is a negative third-order structure function, varying linearly with separation distance and mean dissipation, just as in three-dimensional turbulence, but with another scaling constant. On the basis of the analysis and the observed stratospheric third-order structure function, it is argued that there is a forward energy cascade in the mesoscale range of atmospheric motions. The off-diagonal part of the general tensor equation is also studied. In this equation there is an explicit Coriolis term that may be crucial for the understanding of the kinetic energy spectrum at scales larger than 100 km. ¿ 2001 American Geophysical Union