Direct evidence for 23/9 elliptical dimensional atmospheric turbulence from fractal aircraft trajectories

Details Direct evidence for 23/9 elliptical dimensional atmospheric turbulence from fractal aircraft trajectories Direct evidence for 23/9 elliptical dimensional atmospheric turbulence from fractal aircraft trajectories

Dec 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufmng21a0424l&link_type=abstract

American Geophysical Union, Fall Meeting 2001, abstract #NG21A-0424

Statistics

3250 Fractals And Multifractals, 3379 Turbulence

Scientific paper

Recent analysis of nearly 1000 satellite images of clouds showed that from planetary scales down to at least 1 km, they are multiscaling with statistics very close to those predicted by cascade processes. Since the atmosphere is ``thin'' at planentary scales, but ``voluminous'' at kilometric scales, this is already indirect evidence for the unified scaling model of stratification proposed by Schertzer and Lovejoy 1985 in which for the horizontal wind field, Kolmorogov scaling holds in the horizontal (basic exponent =1/3), while Bogliano-Obhukhov scaling holds in the vertical (basic exponent =3/5), the resulting ``unified scaling'' model having an elliptical dimension of 2+Hz with Hz = (1/3)/(3/5)=5/9=0.555. In this talk, we study data from 31 trajectories of scientific aircraft flights in the stratosphere. The segments chosen were roughly 2000km long and were taken during a ``Mach cruise'' flight mode in which an autopilot maintains a constant Mach number. The resulting flight along an iso-Mach involved correlated temperature and wind fluctuations so that =deltax**(2Hz) where z and x are the vertical and horizontal coordinates of the aircraft. Empirically, over the range 1 to 1000km, we found Hz=0.545 close to the predicted 5/9=0.555. Since Hz*1, this trajectory is fractal. We also systematically compared horizontal and vertical statistics of wind and temperature and found that the ratio of horizontal and vertical structure functions =Hz. This is direct quantitative evidence in favour of the unified scaling model. In contrast, the standard model assumes isotropic 3-D at small scales and isotropic 2D turbulence at larege scales seperated by a meso-scale gap (i.e. two different regimes with Hz=1, 0 respectively).

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