Fractal aircraft trajectories and nonclassical turbulent exponents
Bibliographic record
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 $1600\phantom{\rule{0.3em}{0ex}}\mathrm{km}$ 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 $\ensuremath{\approx}3--300\phantom{\rule{0.3em}{0ex}}\mathrm{km}$, we found ${\mathrm{H}}_{z}\ensuremath{\approx}0.58\ifmmode\pm\else\textpm\fi{}0.02$ close to the theoretical $5∕9=0.56$ and implying $D=1+{H}_{z}=14∕9$, i.e., the trajectories are fractal. For distances $<3\phantom{\rule{0.3em}{0ex}}\mathrm{km}$ aircraft inertia smooths the trajectories, for distances $>300\phantom{\rule{0.3em}{0ex}}\mathrm{km}$, $\mathrm{D}=1$ again because of a rise of $1\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{km}$ 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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".