This contribution is based on the Kato theorem and on some work which I started with Edriss Titi and continued with Wiedemann and Szekelyhidi.
To the best of my knowledge the Kao theorem provides the simplest relation between the anomalous energy dissipation and the appearance of turbulence.
Both if and only if and sufficient conditions for such anomalous energy dissipation have been provided.
But what is striking is that these conditions are in full agreement with observations coming from engineering science or fluid mechanic litterature.