Is the loglaw a first principle result from Liegroup invariance analysis?
Abstract
The invariance method of Liegroups in the theory of turbulence carries the high expectation of being a first principle method for generating statistical scaling laws. The purpose of this comment is to show that this expectation has not been met so far. In particular for wallbounded turbulent flows, the prospects for success are not promising in view of the facts we will present herein. Although the invariance method of Liegroups is able to generate statistical scaling laws for wallbounded turbulent flows, like the loglaw for example, these invariant results yet not only fail to fulfil the basic requirements for a first principle result, but also are strongly misleading. The reason is that not the functional structure of the loglaw itself is misleading, but that its invariant Liegroup based derivation yielding this function is what is misleading. By revisiting the study of Oberlack (2001) we will demonstrate that all Liegroup generated scaling laws derived therein do not convince as first principle solutions. Instead, a rigorous derivation reveals complete arbitrariness rather than uniqueness in the construction of invariant turbulent scaling laws. Important to note here is that the key results obtained in Oberlack (2001) are based on several technical errors, which all will be revealed, discussed and corrected. The reason and motivation why we put our focus solely on Oberlack (2001) is that it still marks the core study and central reference point when applying the method of Liegroups to turbulence theory. Hence it is necessary to shed the correct light onto that study. Nevertheless, even if the method of Liegroups in its full extent is applied and interpreted correctly, strong natural limits of this method within the theory of turbulence exist, which, as will be finally discussed, constitute insurmountable obstacles in the progress of achieving a significant breakthrough.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.3069
 Bibcode:
 2014arXiv1412.3069F
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 35 pages, 6 lists CAScode