Extreme dissipation and intermittency in turbulence at very high Reynolds numbers: Extreme dissipation in turbulence

Gerrit E. Elsinga, Takashi Ishihara, Julian C.R. Hunt

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or model for predicting the extrema as a function of the Reynolds number. Here, we introduce a new model for the dissipation probability density function (PDF) based on the concept of significant shear layers, which are thin regions of elevated local mean dissipation. At very high Reynolds numbers, these significant shear layers develop layered substructures. The flow domain is divided into the different layer regions and a background region, each with their own PDF of dissipation. The volume-weighted regional PDFs are combined to obtain the overall PDF, which is subsequently used to determine the dissipation variance and maximum. The model yields Reynolds number scalings for the dissipation maximum and variance, which are in agreement with the available data. Moreover, the power law scaling exponent is found to increase gradually with the Reynolds numbers, which is also consistent with the data. The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients.

Original languageEnglish
Article number0591
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume476
Issue number2243
DOIs
Publication statusPublished - 2020

Keywords

  • dissipation rate statistics
  • flow structures
  • shear layers
  • velocity gradients

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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