The infinite Reynolds number limit and the quasi dissipative anomaly

TL;DR

This paper critically reviews Onsager's 1949 analysis, clarifying that setting viscosity to zero is not equivalent to taking the infinite Reynolds number limit, highlighting a key conceptual distinction in fluid dynamics.

Contribution

It clarifies the difference between the zero-viscosity limit and the infinite Reynolds number limit in Onsager's work, correcting a common misconception.

Findings

Onsager's analysis was based on setting viscosity to zero, not on the infinite Reynolds number limit.

The distinction impacts the interpretation of the quasi-dissipative anomaly.

The paper emphasizes the importance of correctly understanding the limiting processes in turbulence theory.

Abstract

From a critical review of Onsager's pioneering paper which was published in 1949 we conclude that his analysis was at odds with other workers in the field because instead of taking the infinite Reynolds number limit he simply set the viscosity equal to zero which is not the same thing.