Fractal aircraft trajectories and nonclassical turbulent exponents
Résumé
The dimension (D) of aircraft trajectories is fundamental in interpreting airborne data. To estimate D, we studied data from 18 trajectories of stratospheric aircraft flights 1600 km long taken during a "Mach cruise" (near constant Mach number) autopilot flight mode of the ER-2 research aircraft. Mach cruise implies correlated temperature and wind fluctuations so that approximate toDeltax(z)(H) where Z is the (fluctuating) vertical and x the horizontal coordinate of the aircraft. Over the range approximate to3-300 km, we found H(z)approximate to0.58+/-0.02 close to the theoretical 5/9=0.56 and implying D=1+H(z)=14/9, i.e., the trajectories are fractal. For distances <3 km aircraft inertia smooths the trajectories, for distances >300 km, D=1 again because of a rise of 1 m/km due to fuel consumption. In the fractal regime, the horizontal velocity and temperature exponents are close to the nonclassical value 1/2 (rather than 1/3). We discuss implications for aircraft measurements as well as for the structure of the atmosphere.