A hipótese de turbulência localmente isotrópica e a universalidade da constante de Kolmogorov

Abstract

According to the Kolmogorov's fully developed turbulence theory established in 1941, there is an equilibrium range in which phenomenological quantities associated to the turbulence flow are described by laws of universal character. The main objection to this theory was given by Landau, who critized the universality of these laws arguing that an universal statistical equilibrium state would not be reached since there is a dependence on energy transference between the eddies belonging to the inertial range with the largest ones, which are external to this interval, thus non-universal. From the discussion between Kolmogorov and Landau, emerged in 1962 a theory proposed to be a correction to the 1941's theory. Following the new ideas, an intermittent energy cascade should exist in the inertial range thus, as a consequence, corrections to the scaling laws prediced by 1941's theory should to be taken in account. Since that, intermittency has became the central problem in fully developed turbulence. Another question which still remains from the discussion between Kolmogorov and Landau is that concerning to the universality of the second order structure constant, known as the Kolmogorov constant. Some theoreticians claim that this constant should be Reynolds' number dependent, however experimental evidences contradict themselves. 14 In this work, based on structure function of several orders of velocity, temperature and a passive scalar, anisotropy is related to a strange behavior of velocity odd-order structure functions. The Kolmogorov constant is determined in diferent flows and appear to be universal with the Reynolds' number. In addiction, the scatter and the dependence with the Reynolds' number found in the literature are explained as a consequence of anisotropy in the intertial subrange and imprecise determination of the dissipation rate. On other hand, experimental verification of intemittency in inertial subrange through the correlation of the rate dissipation R²,²(r) is explained to be an undesired efect of anisotropy on the equations whose derivation is based on the isotropy assumption. The existence of intermittency correction coeficent μ of the second order structure funtion GR2 is attributed to be a consequence of an arbitrary choice of the inertial subrange, nite Reynolds' number efect and another singularities. These conclusions lead to the idea that the classical theory of 1941 is correct in its original form and the discrepancies observed are due the nonexistence of a real fully developed turbulence state.