A note on the “principle of material frame-indifference in the limit of two-dimensional turbulence”

In this note we show that the setting up of the “principle of material frame-indifference in the limit of two-dimensional turbulence” by Speziale in the 1980s, which has been applied to turbulence modelling for the past two decades as seen from the literature, is unsound—in fact, there is an inconsistency in dealing with the fluctuating pressure which leads to contradicting the physical facts of turbulence. We conclude that this so-called “principle of material frame-indifference in the limit of two-dimensional turbulence” for turbulence modelling should be discarded.