No new scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence

TL;DR

This paper critiques a recent claim of new scaling laws for passive scalar in decaying isotropic turbulence, demonstrating that these laws are not new and that the Lie-group symmetry method used is not fundamentally different from classical approaches.

Contribution

The paper clarifies that the supposed new scaling laws are not novel and argues that the Lie-group symmetry analysis is not a first-principle method, challenging recent claims in the literature.

Findings

The scaling laws by Sadeghi & Oberlack are not new and are already known from Bahri (2016).

Lie-group symmetry analysis in turbulence is akin to trial-and-error, not a first-principle approach.

Classical dimensional analysis provides more general scaling laws than the Lie-group method used in the criticized study.

Abstract

In the study by Sadeghi & Oberlack [JFM 899, A10 (2020)] it is claimed that new scaling laws are derived for the case of passive scalar dynamics under the influence of a constant mean gradient in decaying homogeneous isotropic turbulence. However, these scaling laws are not new and have already been derived and discussed in Bahri (2016). No novel analytical achievements are made by Sadeghi & Oberlack, as the title of their study misleadingly wants to suggest. In fact, the already established self-similar scaling laws obtained by Bahri through simple dimensional analysis are already more general in the application than the ones obtained by Sadeghi & Oberlack through an overly complicated and therefore unnecessarily performed Lie-group symmetry analysis. The claim that it has the virtue of not being an ad-hoc method is not true. Because, instead of using an a priori set of scales as the classical method, the Lie-group method has to make use of an a priori set of symmetries, namely to select the correct relevant symmetries from an infinite and thus unclosed set. For example, a nonphysical scaling symmetry is selected which in the course of the analysis has to be discarded since it is not compatible with the data simulated. Hence, the Lie-group symmetry method in turbulence is just another common trial-and-error method and not a first-principle method that can bypass the closure problem.