Horizontal velocity structure functions in the upper troposphere and lowerstratosphere 2. Theoretical considerations

The Kolmogorov equation for tile third-order velocity structure function is derived for atmospheric mesoscale motions on an f plane. A possible soluti on is a negative third-order structure function, varying linearly with sepa ration distance and mean dissipation, just as in three-dimensional turbulen ce, but with another scaling constant. On the basis of the analysis and the observed stratospheric third-order structure function, it is argued that t here is a forward energy cascade in the mesoscale range of atmospheric moti ons. Tile off-diagonal part of the general tenser equation is also studied. In this equation there is an explicit Coriolis term that may be crucial fo r the understanding of the kinetic energy spectrum at scales larger than 10 0km.