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On how a turbulent system replicates itself at smaller scales

On how a turbulent system replicates itself at smaller scales.
Marta Antonelli 1, Andrea Mazzino 2, Umberto Rizza 2(1) Univ. di Genova, D.to di Fis., (2) CNR-ISAC, Sez. di Lecce
One of the most intriguing features characterizing a turbulent system is the emergence of huge fluctuations covering a wide range of spatial and temporal scales. Although the equations ruling the dynamics of such fluctuations are fully deterministic, the probabilistic description turns out to be the most appropriate (Frisch, 1995).
In such context characterized by many degrees of freedom (e.g. the whole set of moments of the probability density function (pdf) describing the process), one of the biggest challenges is to find out statistical features of turbulent systems that remain unchanged at different scales. Such issue is related to the possible existence of some form of scale invariance for turbulent systems, an issue attracting a great deal of attention both in theoretical and applicative domains ranging from science to engineering (Meneveau and Katz, 2000). The most relevant application of scale invariance is related to the long-standing problem of parameterizing small-scale motion in large-eddy simulation models (LES) of turbulence.
With such motivation in mind, we have identified a way through which a turbulent system replicates itself at smaller and smaller scales. The system we have considered is a turbulent atmospheric boundary layer in convective regimes simulated by a LES model with 128x128x128 grid points.
There, we have focused the attention on the temperature field that is characterized (see figures) by the presence of intense (thermal) plumes.
Weak fluctuations are present where the colours are homogeneous (e.g. in the inner part of plumes) while strong temperature excursions take place where colours change abruptly. Despite the fact that such fluctuations cover a wide range of scales, we have identified a similarity law connecting fluctuations occurring at different scales. Such law emerges by analyzing the rescaling properties of the pdf of temperature excursions between points separated by a distance, say r. Interestingly enough, the parameter appearing in the rescaling law depends neither on the degrees of convection nor on the elevation from the ground. For details, see Antonelli et al, 2003. The next step of our research is oriented toward the experimental verification of our new findings. For such purpose an experiment in field is in program at the Lecce Section of ISAC.
The authors are particularly grateful to Chin-Hoh Moeng and Peter Sullivan, of the NCAR (Boulder, Colorado) for providing us with their LES code as well as many useful discussions.

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