Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group
arXiv:chao-dyn/9810025 · doi:10.1103/PhysRevE.59.6753
Abstract
The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we firstly consider the needed general theory and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.
35 pages, REVTEX, 1 figure, Phys. Rev. E, submitted
References in corpus (4)
- The Extraction of Anisotropic Contributions in Turbulent Flows
- Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multi-scaling
- Invariants for Correlations of Velocity Differences in Turbulent Fields
- Exact Result for the 3rd Order Correlations of Velocity in Turbulence with Helicity
Cited by in corpus (49)
- Particles and fields in fluid turbulence
- Cascades and transitions in turbulent flows
- Anisotropy in Turbulent Flows and in Turbulent Transport
- Recovering Isotropic Statistics in Turbulence Simulations: The Kolmogorov 4/5th-Law
- The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer
- Anisotropic Homogeneous Turbulence: hierarchy and intermittency of scaling exponents in the anisotropic sectors
- Turbulence with Pressure: Anomalous Scaling of a Passive Vector Field
- Nonperturbative Spectrum of Anomalous Scaling Exponents in the Anisotropic Sectors of Passively Advected Magnetic Fields
- Drag Reduction by Polymers in Turbulent Channel Flows: Energy Redistribution Between Invariant Empirical Modes
- Isotropy vs anisotropy in small-scale turbulence
- Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
- Scaling properties in the production range of shear dominated flows
- Derivative moments in turbulent shear flows
- Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field
- Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents
- Anomalous and dimensional scaling in anisotropic turbulence
- An experimental study on the multiscale properties of turbulence in bubble-laden flows
- Anisotropy, inhomogeneity and inertial range scalings in turbulent convection
- Spectrum of Anisotropic Exponents in Hydrodynamic Systems with Pressure
- The decay of homogeneous anisotropic turbulence
- Effects of non-universal large scales on conditional structure functions in turbulence
- Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind
- Anomalous scaling and anisotropy in models of passively advected vector fields
- Universality of anisotropic fluctuations from numerical simulations of turbulent flows
- Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum
- A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations
- Scaling Exponents in Anisotropic Hydrodynamic Turbulence
- Small-scale anisotropy and intermittency in high and low-latitude solar wind
- Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models
- The State of the Art in Hydrodynamic Turbulence: Past Successes and Future Challenges
- On the elimination of the sweeping interactions from theories of hydrodynamic turbulence
- Disentangling Scaling Properties in Anisotropic Fracture
- Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flows
- Anisotropic fluctuations in turbulent sheared flows
- Temporal surrogates of spatial turbulent statistics: the Taylor hypothesis revisted
- Statistical analysis of the velocity and scalar fields in reacting turbulent wall-jets
- Steady state existence of passive vector fields under the Kraichnan model
- Intermittency and regularity issues in 3D Navier-Stokes turbulence
- Estimating von-Karman's constant from Homogeneous Turbulence
- Statistical Physics of Fracture Surfaces Morphology
- Intermittency in the isotropic component of helical and non-helical turbulent flows
- Inhomogeneous Anisotropic Passive Scalars
- Strong anisotropy of superfluid He counterflow turbulence
- Some relations between Lagrangian models and synthetic random velocity fields
- Anisotropy in Homogeneous Rotating Turbulence
- Statistics of pressure and of pressure-velocity correlations in isotropic turbulence
- Is the subdominant part of the energy spectrum due to downscale energy cascade hidden in quasi-geostrophic turbulence?
- Sign-symmetry of temperature structure functions
- Anomalous scaling of low-order structure functions of turbulent velocity