Developing homogeneous isotropic turbulence

We investigate the self-similar evolution of the transient energy spectrum, which precedes the establishment of the Kolmogorov spectrum in homogeneous isotropic turbulence in three dimensions using the EDQNM closure model. The transient evolution exhibits self-similarity of the second kind and has a non-trivial dynamical scaling exponent, which results in the transient spectrum having a scaling that is steeper than the Kolmogorov k−5/3k−5/3 spectrum. Attempts to detect a similar phenomenon in DNS data are inconclusive, owing to the limited range of scales available.

Research highlights
► The self-similar establishment of the Kolmogorov spectrum before the onset of dissipation is studied in the EDQNM model.
► The transient spectrum is found to be steeper than the usual Kolmogorov spectrum.
► The Kolmogorov spectrum is set up quasi-instantaneously from right to left after the onset of dissipation.