Well-known examples of artistic renditions of ‘coherent vortex structures’ appearing in nature include the woodblock print *Great Wave off Kanagawa* by Katsushika Hokusai, Vincent Van Gogh’s *Starry Night* and Leonardo Da Vinci’s drawings of eddy motion. Da Vinci’s studies were in fact among the first scientific studies of turbulent motion which then assumed a more rigorous form in the fundamental works of A.N. Kolmogorov [@Ko41-1; @Ko41-2; @Ko41-3], L. Onsager [@On45; @On49], G.I. Taylor [@Ta35; @Tay37] and others in the first half of the 20th century. One of the cornerstones of the turbulence phenomenology is the concept of the energy cascade: there is a nonlinear transfer of energy from larger to smaller scales; once a sufficiently small scale is reached, the diffusion takes over and the energy starts to dissipate in the form of heat. Despite much progress over the decades, a complete, rigorous theory of turbulence remains elusive; in particular, the question as to the role that coherent vortex structures play in the theory of turbulent dissipation.

A flow of 3D incompressible, viscous, Newtonian fluid is described by the 3D Navier-Stokes equations (NSE), $$\frac{\partial \pmb{u}}{\partial t} + (\pmb{u}\cdot \nabla)\pmb{u}=-\nabla p + \nu \triangle \pmb{u} + \pmb{f},$$ supplemented with the incompressibility 