Caracterização de turbulência completamente desenvolvida através de cumulantes e processos multiplicativos

Abstract

In this work we study drainings that present fully developed turbulence, that is, drainings characterized for raised Reynolds numbers. After a theoretical revision based on the model of Kolmogorov of 1941, we study the concept of intermittency in small scales through cumulants, defined as the logarithms moments of the increments of speed of the wind. We will get the cumulants of first, second and third order for data gotten in wind tunnel, atmosphere and Large Eddy Simulation (LES). We search to characterize the intermittency through the coefficient of intermittency for the log-normal model, that can be gotten for the adjustment of the cumulantes of second order. The technique based on cumulantes is an alternative for classic methods, as analysis of functions structure of sixth order and correlation of the waste rate of energy. In accordance with Malécot et al. (2000), the cumulants of first and second order are proportional and therefore we can determine a coefficient β, whose behavior it is supposedly universal with the Reynolds number. Of complementary form, we study the attainment of random processes based in the models log-normal and log-Poisson [Kiyono 2009] and of multiplicatives cascade processes, gotten from gaussians variables of average zero and constant variance. The generated series present behavior of fully developed turbulence and therefore they can be used as test of precision of the method based on cumulants. The coefficient β indicates that the cumulants can be written by a power law.