Modeling the fine-scale turbulence within and above an Amazon forest using Tsallis generalized...

Modeling the fine-scale turbulence within and above an Amazon forest using Tsallis‘

generalized thermostatistics. I. Wind velocity

Maurício J. A. Bolzan , Fernando M. Ramos, Leonardo D. A. Sá, Reinaldo R.

Rosa

1. Centro de Previsão de Tempo e Estudos Climáticos, INPE, Brazil 

2. Laboratório Associado de Computação e Matemática Aplicada, INPE, Brazil

3. Instituto de Pesquisa e Desenvolvimento, UNIVAP, Brazil

3,1

2

22

Abstract

In this work, we used the Tsallis’ Non-Extensive Thermostatistics for modelling the Probability Density Functions (PDFs) of wind velocity measured in LBA campaign. The theoretical PDF results show good agreement with experimental PDFs and for both heights, below and above the forest canopy.

THE DATA AND EXPERIMENTAL SITE

60 meters height localized in Reserva Biológica do Jaru, Rondônia;

Measured simultaneasly at the three differents heights (66m, 42m, 28m);

Variables u, v, w e T Sampling rate of the

measurements: 60 Hz.

The Thermostatistics Non-Extensive

Based on the scaling properties of multifractals, a generalization of Boltzmann-Gibbs thermostatistics has been proposed by Tsallis (1988) through the introduction of a family of non-extensive entropy functionals Sq(p) with a single parameter q.

For a system with W microstates and with the probability , its entropy is given by:

W

i

qii

W

i

qi

q ppq

k

q

pkS

11

11

0ip

PDF MODEL

• In this work, was adopted the PDF model generalization given by (Beck et al., 2001), which proposed a PDF that Model is given by :

)1/(132

3

1)()1(1

1)(

q

rrrrq

rq uuusignCuqZ

up

where

)(qf

00 ,

,0

B

Bau nnmmn

rn

)(sec momentondf

RESULTS FOR WIND VELOCITY

ABOVE CANOPY BELOW CANOPY

CONCLUSION

Summarizing, we have shown that the generalized thermostatistics provides a simple and accurate framework for modeling the statistical behavior of fully developed mechanics turbulence in the inertial subrange;

According to this framework, intermittency and nonextensivity are linked by the entropic parameter q defined in the Tsallis’ theory. This parameter represents a measurable quantity, flow independent and robust to variations in the Reynolds number, that can be used to objectively quantify the occurrence of intermittency in turbulent flows.

ACKNOLEMENTS

This work was supported by FAPESP (97/09926-9). MJAB acknowledges the suppot given by CAPES and FMR also acknowledges the support given by CNPq-Brazil through the research grant 300171/97-8.