Fractal aircraft trajectories and 23/9 dimensional atmospheric turbulence

Analysis of the horizontal structure of the atmosphere using nearly 1000 satellite images of clouds has showed that from planetary scales down to at least 1 km, they are multiscaling with statistics very close to those predicted by cascade processes: there is no "meso-scale gap" between isotropic two dimensional and isotropic three dimensional turbulence. Lidar data of aerosols directly shows how this is possible: it shows that the scaling in the horizontal and vertical directions are quite different. In fact, the ratio of the multifractal exponents is close to those predicted by the unified scaling model of stratification (= (Kolmorogov 1/3 / Bogliano-Obhukhov 3/5) =5/9). Using data from trajectories of scientific aircraft flights in the stratosphere (roughly 2000km long) during a "Mach cruise" flight mode (in which an autopilot maintains a constant Mach number) we show that <Dz2>^aDx2Hz where z and x are the vertical and horizontal coordinates of the aircraft: the trajectory is fractal with Hz^a 0.545 close to the predicted 5/9=0.555... thus giving direct quantitative supporting this picture. In addition, we find that the temperature and velocity exponents are indeed in the correct ratio - although not surprisingly, their values are nonclassical. If other aircraft trajectories are found to be fractal - and this seems likely - then these results have potentially far reaching consequences for the interpretation of aircraft data. This is because the statistics on fractal and standard (i.e. linear) sections are fundamentally different. This finding could thus explain a number of apparently contradictory claims about the nature and limits of scaling of the horizontal wind particularly in the meso-scale.