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| Titel |
Multifractality in the Atmospheric Boundary Layer |
| VerfasserIn |
José María Vindel, Carlos Yagüe, Jose Manuel Redondo |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250036344
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| Zusammenfassung |
| According to the Kolmogorov theory (K41), scaling exponents of the velocity structure
functions, ζp, follow a linear relation with respect to the order, p, of these functions.
However, experiments in fully developed turbulence show a deviation from this linear form;
this phenomenon is known as intermittency of the turbulence. More precisely, in case of
intermittency and in fully developed turbulence, ζp vs. p must describe a concave
curve according to the Hölder inequality. However, from the analysis of the several
stratification situations in the Atmospheric Boundary Layer, we have found out the
possibility of a convex curvature. Indeed, unstable conditions of stratification present a
concave curvature, but the convex one is showed in very stable situations, where the
appearance of bursts of turbulence, due to the breaking up of internal waves, confers a
sporadic and intermittent character to the turbulence, what prevent a fully developed
turbulence.
The absence of intermittency can be explained from a monofractal point of view.
However, in order to explain both types of deviation (concave and convex) of the
scaling exponents from the linear form, the multifractal analysis should be used.
According to this analysis, it is possible to relate the scaling exponents and the fractal
dimension through the Legendre transformation. The representation of the dimensions
corresponding to the different fractals of the system constitutes the multifractal
spectrum or singularity spectrum, and the concave (convex) curvature of ζp vs. p
is translated in a concave (convex) spectrum; moreover, the greater the deviation
is, the wider the spectrum is, in a way that in the monofractal case, the spectrum
is reduced to just a point. Therefore, the former mentioned relationship between
type of stratification and type of curvature is showed in the singularity spectra. |
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