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A Helmholtz decomposition of structure functions and spectra calculated from aircraft data
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. (GEOFYSIKALISK STRÖMNMEKANIK)
2015 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 762, R4- p.Article in journal (Refereed) Published
Abstract [en]

Longitudinal and transverse structure functions, D-ll = <delta u(l)delta u(l)> and D-tt = delta u(t)delta u(t), can be calculated from aircraft data. Here, d denotes the increment between two points separated by a distance r, u(l) and u(t) 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 = u(r) + u(d), where u(r) is the rotational and u(d) the divergent component of the velocity, we derive expressions relating the structure functions D-rr = delta u(r). delta u(r) and D-dd = delta u(d). delta u(d) to D-ll and D-tt. Corresponding expressions are also derived in spectral space. The decomposition is applied to structure functions calculated from aircraft data. In the lower stratosphere, D-rr and D-dd both show a nice r(2/3)-dependence for r epsilon [2, 20] 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, D-rr and D-dd show no clean r(2/3)-dependence, although the overall slope of D-dd is close to 2/3 for r epsilon [2, 400] 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.

Place, publisher, year, edition, pages
2015. Vol. 762, R4- p.
Keyword [en]
atmospheric flows, meteorology, stratified flows
National Category
Fusion, Plasma and Space Physics
URN: urn:nbn:se:kth:diva-158373DOI: 10.1017/jfm.2014.685ISI: 000345575200015ScopusID: 2-s2.0-84915820588OAI: diva2:780836

QC 20150115

Available from: 2015-01-15 Created: 2015-01-07 Last updated: 2015-01-15Bibliographically approved

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Lindborg, Erik
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