A note on the notion "statistical symmetry"

Abstract

A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short note is to provide this missing information and to clarify this notion on the basis of a few instructive examples.

arXiv comment8 pages; extension of main footnote in Section 1

References in corpus (2)

• A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence
• On the physical inconsistency of a new statistical scaling symmetry in incompressible Navier-Stokes turbulence

Cited by in corpus (9)

• A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined 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'
• On the use of applying Lie-group symmetry analysis to turbulent channel flow with streamwise rotation
• A closer look at predicting turbulence statistics of arbitrary moments when based on a non-modelled symmetry approach
• Symmetries and turbulence modeling. A critical examination
• Comment on 'Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence'