Horizontal velocity structure functions in the upper
troposphere and lower stratosphere: 2. Theoretical considerations
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.
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