Presentation on theme: "Modeling the fine-scale turbulence within and above an Amazon forest using Tsallis generalized thermostatistics. I. Wind velocity Maurício J. A. Bolzan,"— Presentation transcript:
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
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:
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 : where
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.