Imperial College London
Professor John Gibbon

ProfessorJohnGibbon

Faculty of Natural Sciences, Department of Mathematics

Senior Research Investigator
 
 
 
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Contact

 

j.d.gibbon Website

 
 
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Location

 

6M41Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Vincenzi:2021:1361-6544/abe096,
author = {Vincenzi, D and Gibbon, JD},
doi = {1361-6544/abe096},
journal = {Nonlinearity},
pages = {5821--5843},
title = {How close are shell models to the 3D Navier-Stokes equations?},
url = {http://dx.doi.org/10.1088/1361-6544/abe096},
volume = {34},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of spatial variation, they accurately reproduce the main statistical properties of fully-developed homogeneous and isotropic turbulence. Moreover, they enjoy regularity properties which still remain open for the three-dimensional (3D) Navier–Stokes equations (NSEs). The goal of this study is to make a rigorous comparison between shell models and the NSEs. It turns out that only the estimate of the mean energy dissipation rate is the same in both systems. The estimates of the velocity and its higher-order derivatives display a weaker Reynolds number dependence for shell models than for the 3D NSEs. Indeed, the velocity-derivative estimates for shell models are found to be equivalent to those corresponding to a velocity gradient averaged version of the 3D Navier–Stokes equations (VGA-NSEs), while the velocity estimates are even milder. Numerical simulations over a wide range of Reynolds numbers confirm the estimates for shell models.
AU  - Vincenzi,D
AU  - Gibbon,JD
DO  - 1361-6544/abe096
EP  - 5843
PY  - 2021///
SN  - 0951-7715
SP  - 5821
TI  - How close are shell models to the 3D Navier-Stokes equations?
T2  - Nonlinearity
UR  - http://dx.doi.org/10.1088/1361-6544/abe096
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000672960700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://iopscience.iop.org/article/10.1088/1361-6544/abe096
UR  - http://hdl.handle.net/10044/1/90886
VL  - 34
ER  -
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