A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence

Abstract

We present a critical examination of the recent article by Waclawczyk et al. (2014) which proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. We first show that both symmetries are unphysical in that they induce inconsistencies due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Yet, aside from this particular issue, the article by Waclawczyk et al. (2014) is flawed in more than one respect, ranging from an incomplete proof, to a self-contradicting statement up to an incorrect claim. All these aspects will be listed, discussed and corrected, thus obtaining a completely opposite conclusion in our study than the article by Waclawczyk et al. (2014) is proposing.

27 pages; Updated reference list and minor text improvements; Comment published in Phys. Rev. E. arXiv admin note: text overlap with arXiv:1412.3061

References in corpus (7)

• Symmetries in Physics: Philosophical Reflections
• The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence
• On the physical inconsistency of a new statistical scaling symmetry in incompressible Navier-Stokes turbulence
• A note on the notion "statistical symmetry"
• Application of Lie-group symmetry analysis to an infinite hierarchy of differential equations at the example of first order ODEs
• An example elucidating the mathematical situation in the statistical non-uniqueness problem of turbulence
• Revisiting the Lie-group symmetry method for turbulent channel flow with wall transpiration

Cited by in corpus (12)

• On the physical inconsistency of a new statistical scaling symmetry in incompressible Navier-Stokes turbulence
• A note on the notion "statistical symmetry"
• Is the log-law a first principle result from Lie-group invariance analysis?
• An example elucidating the mathematical situation in the statistical non-uniqueness problem of turbulence
• Revisiting the Lie-group symmetry method for turbulent channel flow with wall transpiration
• Covariance and objectivity in mechanics and turbulence
• Conformal invariance and the Lundgren-Monin-Novikov equations for vorticity fields in 2D turbulence: Refuting a recent claim
• Comment on 'Lie symmetry analysis of the Lundgren-Monin-Novikov equations for multi-point probability density functions of turbulent flow'
• A closer look at predicting turbulence statistics of arbitrary moments when based on a non-modelled symmetry approach
• On the use of applying Lie-group symmetry analysis to turbulent channel flow with streamwise rotation
• Symmetries and turbulence modeling. A critical examination
• Comment on 'Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence'