Symmetry induced turbulent scaling laws for arbitrary moments and their validation with DNS and experimental data: A fact-check

A fact-check is presented to a Webinar recently held at the Australasian Fluid Mechanics Society (AFMS) on symmetries and its applications in turbulence [M. Oberlack, Oct. 14th, 2020: https://www.afms.org.au/events.html]. More than a dozen of statements made therein prove to be misleading and partly even mathematically incorrect. No knowledge in Lie-group symmetry theory is required to recognize, for example, that the presented scaling theory for turbulent channel and pipe flow is misleading: Instead of matching the determined scaling laws to the relevant fluctuation correlations, they are matched to the irrelevant correlations of the full velocity field, which in configurations with a strong mean flow, as in channel or pipe flow, effectively just equate to the exponentiated mean velocity field. In other words, the presented approach only proves to be a curve-fitting process for the exponentiated mean velocity, and not for the physically interesting and relevant fluctuation correlations. But not only misleading, also mathematically incorrect statements are made: For example, two nonphysical invariants are used, which generate the scalings not only in the wrong way, but also give a false picture of the intermittency and the non-Gaussian behavior in turbulence. Ultimately, the main message with the fact-check here is that the Lie-group symmetry method alone, like any other analytical method, cannot bypass the closure problem of turbulence, as is falsely claimed.