Laws of turbulence decay from direct numerical simulations

John Panickacheril John, Diego A. Donzis, Katepalli R. Sreenivasan

Research output: Contribution to journalArticlepeer-review


Inspection of available data on the decay exponent for the kinetic energy of homogeneous and isotropic turbulence (HIT) shows that it varies by as much as 100%. Measurements and simulations often show no correspondence with theoretical arguments, which are themselves varied. This situation is unsatisfactory given that HIT is a building block of turbulence theory and modelling. We take recourse to a large base of direct numerical simulations and study decaying HIT for a variety of initial conditions. We show that the Kolmogorov decay exponent and the Birkhoff-Saffman decay are both observed, albeit approximately, for long periods of time if the initial conditions are appropriately arranged. We also present, for both cases, other turbulent statistics such as the velocity derivative skewness, energy spectra and dissipation, and show that the decay and growth laws are approximately as expected theoretically, though the wavenumber spectrum near the origin begins to change relatively quickly, suggesting that the invariants do not strictly exist. We comment briefly on why the decay exponent has varied so widely in past experiments and simulations. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

Original languageEnglish (US)
Article number20210089
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2218
StatePublished - Mar 7 2022


  • decaying turbulence
  • incompressible turbulence
  • scaling laws
  • universality

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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