Relating statistics to dynamics in axisymmetric homogeneous turbulence

The structure and the dynamics of homogeneous turbulence are modified by the presence of body forces such that the Coriolis or the buoyancy forces, which may render a wide range of turbulence scales anisotropic. The corresponding statistical characterization of such effects is done in physical space using structure functions, as well as in spectral space with spectra of two-point correlations, providing two complementary viewpoints. In this framework, second-order and third-order structure functions are put in parallel with spectra of two-point second- and third-order velocity correlation functions, using passage relations. Such relations apply in the isotropic case, or for isotropically averaged statistics, which, however, do not reflect the actual more complex structure of anisotropic turbulence submitted to rotation or stratification. This complexity is demonstrated in this paper by orientation-dependent energy and energy transfer spectra produced in both cases by means of a two-point statistical model for axisymmetric turbulence. We show that, to date, the anisotropic formalism used in the spectral transfer statistics is especially well-suited to analyze the refined dynamics of anisotropic homogeneous turbulence, and that it can help in the analysis of isotropically computed third-order structure function statistics often used to characterize anisotropic contexts.Comment: Physica

Lagrangian evolution of velocity increments in rotating turbulence: The effects of rotation on non-Gaussian statistics

The effects of rotation on the evolution of non-Gaussian statistics of velocity increments in rotating turbulence are studied in this paper. Following the Lagrangian evolution of the velocity increments over a fixed distance on an evolving material element, we derive a set of equations for the increments which provides a closed representation for the nonlinear interaction between the increments and the Coriolis force. Applying a restricted-Euler-type closure to the system, we obtain a system of ordinary differential equations which retains the effects of nonlinear interaction between the velocity increments and the Coriolis force. A priori tests using direct numerical simulation data show that the system captures the important dynamics of rotating turbulence. The system is integrated numerically starting from Gaussian initial data. It is shown that the system qualitatively reproduces a number of observations in rotating turbulence. The statistics of the velocity increments tend to Gaussian when strong rotation is imposed. The negative skewness in the longitudinal velocity increments is weakened by rotation. The model also predicts that the transverse velocity increment in the plane perpendicular to the rotation axis will have positive skewness, and that the skewness will depend on the Rossby number in a non-monotonic way. Based on the system, we identify the dynamical mechanisms leading to the observations. (c) 2010 Elsevier B.V. All rights reserved

Working with young Afro-Caribbean offenders Some dilemmas and opportunities

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