Initial evolution of three-dimensional turbulence en route to the Kolmogorov state: Emergence and transformations of coherent structures, self-similarity, and instabilities

The development of singular structures and the path to turbulence in fluids is a fundamental problem that has puzzled researchers for a long time. In this work, we study numerically the evolution of a large-scale initial condition under the hyperviscous incompressible Navier-Stoke equations. Our observations revealed the emergence of shrinking vortex pancakes, which lead to vortex ribs and, eventually, vortex ropes, as depicted in the figure. Eventually, a fully developed turbulent state was achieved prior to its viscous decay.