and dissipation of vorticity in a turbulent fluid* in 1930s. Taylor inferred his thoughts on turbulent dissipation partly from the wind tunnel measurements of a turbulent flow past a uniform grid, concluding the paper with the following statement: “It seems that the stretching of vortex filaments must be regarded as the principal mechanical cause of the high rate of dissipation which is associated with turbulent motion” [@Tay37].

A pioneering event in incorporating geometry of the flow in the mathematical study of possible singularity formation in the 3D NSE took place in P. Constantin’s paper *Geometric statistics in turbulence* [@Co94]. This approach was based on a singular integral representation for the stretching factor in the evolution of the vorticity magnitude, and the key observation was that the kernel had a geometric flavor; more precisely, it was *depleted* by the *local coherence* of the *vorticity direction* (this has been referred to as ‘geometric depletion of the nonlinearity’). The first quantification of this phenomenon appeared in [@CoFe93], revealing that postulating the Lipschitz-continuity [^3] of the vorticity direction in the regions of intense vorticity suffices to guarantee that the flow initiated at a regular initial configuration does not develop a singularity.

Subsequent results include 