Anisotropy in turbulent flows and in turbulent transport
By Luca Biferale, I. Procaccia. 2004
306 citations recorded by the source corpus.
Abstract The problem of anisotropy and its effects on the statistical theory of high Reynolds number ( 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 5 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 rate of decay of anisotropy upon reducing the scales are explained and systematized, showing that isotropy is eventually recovered at small scales.
Subfields: Computational Mechanics, Global and Planetary Change
View Paper: https://www.semanticscholar.org/paper/392c2966201d5f34ed89f355fcfee6bfe5aafb95
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
In Global and Planetary Change
Citations in the corpus
- Cascades and transitions in turbulent flows (2018, background): “Indeed, theoretical arguments based on invariance under rotation of the NSE suggest that both increments should have the same scaling behaviour for large enough Re and that the observed deviation must be due to some sub-leading effect (see [134] and Sec.”
- Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation (2009, background): “This discrepancy may result from finite Reynolds number effects (He et al. 1998, Hill 2001, L’vov et al. 1997) and anisotropy (Biferale & Procaccia 2005).”