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In this work, we study numerically the temporal evolution of an initiallyrandom large-scale velocity field under governed by the hyperviscousincompressible Navier-Stoke equations. Three stages are clearly observed duringthe evolution. First, the initial condition development is characterized by aspectrum evolving in a self-similar way with a wave number front $k_*(t)$propagating toward high values exponentially in time. This evolutioncorresponds to the formation and shrinking of think vortex pancakesexponentially in time, as it has been previously reported in simulations of theincompressible Euler equations. At the second stage, pancakes become unstable,rolling up on the edges and breaking up in the middle, leading to the emergenceof vortex ribs -- quasi-periodic arrangements of vortex filaments. Thosefilaments then twist creating structures akin to ropes. At the last stage, afully developed turbulent state is observed, characterized by a Kolmogorovenergy spectrum and exhibiting a decay law compatible with standard turbulentpredictions in the case of an integral scale saturated at the scale of the box.

Initial evolution of 3D turbulence en route to the Kolmogorov state:  emergence and transformations of coherent structures, self-similarity and  instabilities