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Experimental evidence of a phase transition in the multifractal spectra of turbulent temperature fluctuations at a forest canopy top

Published online by Cambridge University Press:  01 June 2020

S. Dupont Open the ORCID record for S. Dupont [Opens in a new window] ,
F. Argoul Open the ORCID record for F. Argoul [Opens in a new window] ,
E. Gerasimova-Chechkina ,
M. R. Irvine Open the ORCID record for M. R. Irvine [Opens in a new window]  and
A. Arneodo Open the ORCID record for A. Arneodo [Opens in a new window]
S. Dupont*
Affiliation:
INRAE, Bordeaux Sciences Agro, ISPA, F-33140Villenave d’Ornon, France
F. Argoul
Affiliation:
Laboratoire Ondes et Matière d’Aquitaine, CNRS UMR5798, Université de Bordeaux, 33405Talence, France
E. Gerasimova-Chechkina
Affiliation:
Laboratory of Physical Foundation of Strength, Institute of Continuous Media Mechanics UB RAS, Perm, Russia
M. R. Irvine
Affiliation:
INRAE, Bordeaux Sciences Agro, ISPA, F-33140Villenave d’Ornon, France
A. Arneodo
Affiliation:
Laboratoire Ondes et Matière d’Aquitaine, CNRS UMR5798, Université de Bordeaux, 33405Talence, France
*
†Email address for correspondence: [email protected]
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Abstract

Ramp–cliff patterns visible in scalar turbulent time series have long been suspected to enhance the fine-scale intermittency of scalar fluctuations compared to longitudinal velocity fluctuations. Here, we use the wavelet transform modulus maxima method to perform a multifractal analysis of air temperature time series collected at a pine forest canopy top for different atmospheric stability regimes. We show that the multifractal spectra exhibit a phase transition as the signature of the presence of strong singularities corresponding to sharp temperature drops (respectively jumps) bordering the so-called ramp (respectively inverted ramp) cliff patterns commonly observed in unstable (respectively stable) atmospheric conditions and previously suspected to contaminate and possibly enhance the internal intermittency of (scalar) temperature fluctuations. Under unstable (respectively stable) atmospheric conditions, these ‘cliff’ singularities are indeed found to be hierarchically distributed on a ‘Cantor-like’ set surrounded by singularities of weaker strength typical of intermittent temperature fluctuations observed in homogeneous and isotropic turbulence. Under near-neutral conditions, no such a phase transition is observed in the temperature multifractal spectra, which is a strong indication that the statistical contribution of the ‘cliffs’ is not important enough to account for the stronger intermittency of temperature fluctuations when compared to corresponding longitudinal velocity fluctuations.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Nonlinear Dynamical Systems: Fractals Turbulent Flows: Intermittency
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A15
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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