Anisotropy in large eddy simulations determined from SO(3) symmetry group

Hofbauer, T.; Palma, J. M. L. M.; Biferale, Luca; Gama, S.

doi:10.1080/14685240500125435

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…Previously, it has been fruitfully applied to study anisotropic systems in analytical, numerical, and experimental works (Arad et al 1999b;Biferale and Procaccia 2005). Recently, Hofbauer et al (2005) have used the SO(3) decomposition to test the performances of a variety of SGS models, and check how these reproduce the isotropic and anisotropic fluctuations of the turbulent velocity field.…”

Section: Introductionmentioning

confidence: 98%

Anisotropies and Universality of Buoyancy-Dominated Turbulent Fluctuations: A Large-Eddy Simulation Study

Antonelli

Lanotte

Mazzino

2007

Journal of the Atmospheric Sciences

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Turbulent fluctuations of both velocity and temperature fields, issuing from high-resolution large-eddy simulations, have been analyzed in convective boundary layers. The numerically simulated flows are strongly anisotropic at large scales: this is due both to the action of buoyancy and to the imposed geostrophic wind. Their relative weight is varied so that one experiment's results are much more convective than the other. To properly disentangle anisotropic properties, the authors exploit both standard statistical indicators, like skewness coefficients, and the three-dimensional rotational group decomposition SO(3). Two main conclusions can be drawn. First, despite the strong anisotropies at large scales, isotropy is statistically recovered at scales much smaller than the large ones. Second, relevant statistical indicators of turbulence such as the scaling exponents, of both velocity and temperature fields, are remarkably close for the two experiments. Implications of these findings for the problem of subgrid-scale modeling are discussed.

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Section: Introductionmentioning

confidence: 98%

Anisotropies and Universality of Buoyancy-Dominated Turbulent Fluctuations: A Large-Eddy Simulation Study

Antonelli

Lanotte

Mazzino

2007

Journal of the Atmospheric Sciences

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Anisotropy in turbulent flows and in turbulent transport

2005

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The problem of anisotropy and its effects on the statistical theory of high Reynoldsnumber (Re) turbulence (and turbulent transport) is intimately related and intermingled with the problem of the universality of the (anomalous) scaling exponents of structure functions. Both problems had seen tremendous progress in the last five years. In this review we present a detailed description of the new tools that allow effective data analysis and systematic theoretical studies such as to separate isotropic from anisotropic aspects of turbulent statistical fluctuations. Employing the invariance of the equations of fluid mechanics to all rotations, we show how to decompose the (tensorial) statistical objects in terms of the irreducible representation of the SO(d) symmetry group (with d being the dimension, d = 2 or 3). This device allows a discussion of the scaling properties of the statistical objects in well defined sectors of the symmetry group, each of which is determined by the "angular momenta" sector numbers (j, m). For the case of turbulent advection of passive scalar or vector fields, this decomposition allows rigorous statements to be made: (i) the scaling exponents are universal, (ii) the isotropic scaling exponents are always leading, (iii) the anisotropic scaling exponents form a discrete spectrum which is strictly increasing as a function of j. This emerging picture offers a complete understanding of the decay of anisotropy upon going to smaller and smaller scales. Next we explain how to apply the SO(3) decomposition to the statistical Navier-Stokes theory. We show how to extract information about the scaling behavior in the isotropic sector. Doing so furnishes a systematic way to assess the universality of the scaling exponents in this sector, clarifying the anisotropic origin of the many measurements that claimed the opposite. A systematic analysis of Direct Numerical Simulations (DNS) of the Navier-Stokes equations and of experiments provides a strong support to the proposition that also for the non-linear problem there exists foliation of the statistical theory into sectors of the symmetry group. The exponents appear universal in each sector, and again strictly increasing as a function of j. An approximate calculation of the anisotropic exponents based on a closure theory is reviewed. The conflicting experimental measurements on the decay of anisotropy are explained and systematized, showing agreement with the theory presented here.

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Anisotropy in large eddy simulations determined from SO(3) symmetry group

Cited by 2 publications

References 26 publications

Anisotropies and Universality of Buoyancy-Dominated Turbulent Fluctuations: A Large-Eddy Simulation Study

Anisotropies and Universality of Buoyancy-Dominated Turbulent Fluctuations: A Large-Eddy Simulation Study

Anisotropy in turbulent flows and in turbulent transport

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