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The method of Lie symmetry groups is a successful tool to either model dynamical rules that should admit a certain given set of symmetries, or to provide insight into the structure of the solution space for a given closed set of dynamical equations, including the possibility to even allow for their full integration.

The equations of turbulence, however, are different, both conceptually and practically. These equations are mathematically unclosed and need to be modelled empirically. Therefore, from the unclosed and unmodelled theory itself, caution has to be exercised when extracting new symmetry-based information from it.

For Navier-Stokes turbulence, no breakthrough with symmetries has been achieved yet and is still in a very immature state. Up to date, all systematic results to predict the statistical scaling behaviour of turbulent flows with Lie-group symmetries, are either not rigorous to convince or are not correct to be adopted.

The goal of this blog is to shed the correct light onto the method of Lie symmetry groups when applied to turbulence. For a more detailed discussion, see Zenodo.

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