Multi-scale coherent structures and their role in the energy cascade in homogeneous isotropic turbulence

In order to investigate the physical mechanism of the energy cascade in homogeneous isotropic turbulence, we introduce Galilean-invariant energy and its transfer rate in the real space as a function of position, time and scale. By using a database of direct numerical simulations (DNS) of homogeneous isotropic turbulence, it is shown that (i) fully developed turbulence consists of multi-scale coherent vortices of tubular shapes, (ii) the energy at each scale is mainly confined in vortex tubes with the radii of the same order of the length scale, and (iii) the energy transfer takes place around pairs (especially, anti-parallel pairs) of such vortex tubes. Based on these observations, it is suggested that the energy cascade can be caused, in the real space, by the process of the stretching and creation of smaller (i.e. thinner) vortex tubes by the straining field around pairs of larger (i.e. fatter) vortex tubes Indeed, it is quite easy to find such events (in our DNS fields) which strongly support this scenario of the energy cascade.