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Dissipation and enstrophy statistics in turbulence : are the simulations and mathematics converging?
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Kerr, Robert M. (Robert McDougall) (2012) Dissipation and enstrophy statistics in turbulence : are the simulations and mathematics converging? Journal of Fluid Mechanics, Volume 700 . pp. 1-4. doi:10.1017/jfm.2012.111 ISSN 0022-1120.
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Official URL: http://dx.doi.org/10.1017/jfm.2012.111
Abstract
Since the advent of cluster computing over 10 years ago there has been a steady output of new and better direct numerical simulation of homogeneous, isotropic turbulence with spectra and lower-order statistics converging to experiments and many phenomenological models. The next step is to directly compare these simulations to new models and new mathematics, employing the simulated data sets in novel ways, especially when experimental results do not exist or are poorly converged. For example, many of the higher-order moments predicted by the models converge slowly in experiments. The solution with a simulation is to do what an experiment cannot. The calculation and analysis of Yeung, Donzis & Sreenivasan (J. Fluid Mech., this issue, vol. 700, 2012, pp. 5–15) represents the vanguard of new simulations and new numerical analysis that will fill this gap. Where individual higher-order moments of the vorticity squared (the enstrophy) and kinetic energy dissipation might be converging slowly, they have focused upon ratios between different moments that have better convergence properties. This allows them to more fully explore the statistical distributions that eventually must be modelled. This approach is consistent with recent mathematics that focuses upon temporal intermittency rather than spatial intermittency. The principle is that when the flow is nearly singular, during ‘bad’ phases, when global properties can go up and down by many orders of magnitude, if appropriate ratios are taken, convergence rates should improve. Furthermore, in future analysis it might be possible to use these ratios to gain new insights into the intermittency and regularity properties of the underlying equations.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Engineering -- Data processing, Computer-aided engineering, Engineering models -- Research, Engineering -- Statistical methods, Engineering mathematics | ||||
Journal or Publication Title: | Journal of Fluid Mechanics | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0022-1120 | ||||
Official Date: | June 2012 | ||||
Dates: |
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Volume: | Volume 700 | ||||
Page Range: | pp. 1-4 | ||||
DOI: | 10.1017/jfm.2012.111 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 23 December 2015 | ||||
Date of first compliant Open Access: | 23 December 2015 |
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