Publication Date:
2014-12-03
Description:
Longitudinal and transverse structure functions, Dll = (δulδui) and Dll = (δμlδμi), can be calculated from aircraft data. Here, δ denotes the increment between two points separated by a distance r, ul and ut the velocity components parallel and perpendicular to the aircraft track respectively and () an average. Assuming statistical axisymmetry and making a Helmholtz decomposition of the horizontal velocity, u =ur+ud, where ur is the rotational and ud the divergent component of the velocity, we derive expressions relating the structure functions Drr= (δur.δur) and Ddd=(δud .δud to Dll and Dtt. Corresponding expressions are also derived in spectral space. The decomposition is applied to structure functions calculated from aircraft data. In the lower stratosphere, Drr and Ddd both show a nice r2=3-dependence for r 2 T2; 20U km. In this range, the ratio between rotational and divergent energy is a little larger than unity, excluding gravity waves as the principal agent behind the observations. In the upper troposphere, Drr and Ddd show no clean r2=3-dependence, although the overall slope of Ddd is close to 2=3 for r 2 T2; 400U km. The ratio between rotational and divergent energy is approximately three for r 〈100 km, excluding gravity waves also in this case. We argue that the possible errors in the decomposition at scales of the order of 10 km are marginal. © 2014 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
