We compute horizontal velocity structure functions using quasiglobal data accumulated by specially equipped commercial aircraft on 7630 flights from August 1994 to December 1997. Using the ozone concentration measurements, we classify the results as tropospheric or stratospheric. We further divide the results into four absolute latitude bands. For separation distance r between 10 and 100 km, the lower stratospheric diagonal third-order structure functions are proportional to negative r. This implies a downscale energy cascade, and we estimate the mean energy dissipation rate to be ⟨&egr;⟩≈6¿10-5 m2 s-3. For r between 300 and 1500 km, a positive r3 dependence was visible for the polar stratospheric data. This may be the result of a two-dimensional (2D) turbulence downscale enstrophy cascade, and we estimate the average enstrophy flux to be &Pgr;ω≈2¿10-15 s-3 and the energy spectral constant to be K≈2. The negative sign of these third-order functions at mesoscales in both the upper troposphere and lower stratosphere provide no support for an inverse energy cascade 2D turbulence. At scales above ~100 km, the second-order structure functions increase with latitude in the troposphere and decrease with latitude in the stratosphere. The off-diagonal third-order functions in the stratosphere show a remarkably clean negative r2 dependency from 10 to 1000 km in scale. ¿ 2001 American Geophysical Union