Effect of spatial dimension on a model of fluid turbulence

Daniel Clark, Richard D J G Ho, Arjun Berera

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

A numerical study of the d-dimensional eddy damped quasi-normal Markovian equations is performed to investigate the dependence on spatial dimension of homogeneous isotropic fluid turbulence. Relationships between structure functions and energy and transfer spectra are derived for the d-dimensional case. Additionally, an equation for the d-dimensional enstrophy analogue is derived and related to the velocity derivative skewness. Comparisons are made to recent four-dimensional direct numerical simulation results. Measured energy spectra show a magnified bottleneck effect which grows with dimension whilst transfer spectra show a varying peak in the nonlinear energy transfer as the dimension is increased. These results are consistent with an increased forward energy transfer at higher dimensions, further evidenced by measurements of a larger asymptotic dissipation rate with growing dimension. The enstrophy production term, related to the velocity derivative skewness, is seen to reach a maximum at around five dimensions and may reach zero in the limit of infinite dimensions, raising interesting questions about the nature of turbulence in this limit.
Original languageEnglish
Article numberA40
Pages (from-to)1-29
Number of pages29
JournalJournal of Fluid Mechanics
Early online date15 Feb 2021
Publication statusPublished - 10 Apr 2021

Keywords / Materials (for Non-textual outputs)

  • physics.flu-dyn
  • cond-mat.stat-mech


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