Leis de escala e análise do fenômeno de intermitência em turbulência bem desenvolvida

Abstract

This study presents a review of the statistical theory for the inertial range of welldeveloped turbulent flows. The main focus of the study is on the experimental estimation of the so called intermittency exponent through recently developed statistical methods and its possible dependence on large scale mechanisms. The analysis employed allows to observe that even in very high Reynolds number, as those occurring in atmospheric boundary layer flows, clear scaling laws (power laws) are never observed in the inertial range. Comparing the non-scaling invariant models proposed in the literature, it is observed that the logarithmic scaling (SREENIVASAN; BERSHADSKII, 2006b) is suitable for all turbulence scenarios analyzed. Likewise, the classic isotropicincompressibility relation S⊥ 2 (r)/Sk 2(r), which relates longitudinal and transversal second rank tensors (structure functions), it is not constant but slightly dependent on the scale r in the inertial range. A recently developedmethodology for estimation of the intermittency coefficient (BASU et al., 2007) was modified according to the logarithmic scaling model in order to include the non-scaling invariance behavior. The new methodology allows obtaining more accurate estimations of the intermittency coefficient, even for short and noisy time series, as typically observed in sonic anemometry. The efficiency of the method is assessed by analysis of synthetic multifractal series and compared to wavelet-based multifractal formalism. Finally, the proposed methodology is applied to an atmospheric surface layer dataset and the variability of the estimations are assessed by employing a multifractal bootstrap method (PALU , 2008). Intermittency coefficients for velocity components and temperature are found to present large variability but no clear dependence on stability condition. It suggests that atmospheric stability does not directly affect the small-scale intermittency, therefore, other mechanisms may be responsible for the large variability found in the estimations.