Effect of spatial dimension on a model of fluid turbulence
arXiv:2008.05018 · doi:10.1017/jfm.2020.1173
Abstract
A numerical study of the -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 -dimensional case. Additionally, an equation for the -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.
arXiv comment29 pages, 9 figures. In press Journal of Fluid Mechanics, 2021
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