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- W2014302216 abstract "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 $1600phantom{rule{0.3em}{0ex}}mathrm{km}$ 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 $⟨ensuremath{Delta}Z⟩ensuremath{approx}{ensuremath{Delta}x}^{{H}_{z}}$ where $Z$ is the (fluctuating) vertical and $x$ the horizontal coordinate of the aircraft. Over the range $ensuremath{approx}3--300phantom{rule{0.3em}{0ex}}mathrm{km}$, we found ${mathrm{H}}_{z}ensuremath{approx}0.58ifmmodepmelsetextpmfi{}0.02$ close to the theoretical $5∕9=0.56$ and implying $D=1+{H}_{z}=14∕9$, i.e., the trajectories are fractal. For distances $<3phantom{rule{0.3em}{0ex}}mathrm{km}$ aircraft inertia smooths the trajectories, for distances $>300phantom{rule{0.3em}{0ex}}mathrm{km}$, $mathrm{D}=1$ again because of a rise of $1phantom{rule{0.3em}{0ex}}mathrm{m}∕mathrm{km}$ 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." @default.
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- W2014302216 date "2004-09-16" @default.
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- W2014302216 title "Fractal aircraft trajectories and nonclassical turbulent exponents" @default.
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- W2014302216 doi "https://doi.org/10.1103/physreve.70.036306" @default.
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