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arXiv · 2008.05018

Effect of spatial dimension on a model of fluid turbulence

Daniel Clark·Richard Ho·Arjun Berera
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Abstract

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 non-linear 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.

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physics.flu-dyncond-mat.stat-mechhep-th

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Daniel Clark, Richard Ho, Arjun Berera. 2020-08-11. Effect of spatial dimension on a model of fluid turbulence. https://doi.org/10.1017/jfm.2020.1173

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