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Rigorous remarks about scaling laws in turbulent fluids
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Flandoli, Franco, Gubinelli, M., Hairer, Martin and Romito, M. (2008) Rigorous remarks about scaling laws in turbulent fluids. Communications in Mathematical Physics, Vol.278 (No.1). pp. 1-29. doi:10.1007/s00220-007-0398-9 ISSN 0010-3616.
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Official URL: http://dx.doi.org/10.1007/s00220-007-0398-9
Abstract
A definition of scaling law for suitable families of measures is given and investigated. First, a number of necessary conditions are proved. They imply the absence of scaling laws for 2D stochastic Navier-Stokes equations and for the stochastic Stokes (linear) problem in any dimension, while they imply a lower bound on the mean vortex stretching in 3D. Second, for the 3D stochastic Navier-Stokes equations, necessary and sufficient conditions for scaling laws to hold are given, translating the problem into bounds for energy and enstrophy of high and low modes respectively. Unlike in the 2D case, the validity or invalidity of such conditions in 3D remains open.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Turbulence, Scaling laws (Statistical physics) | ||||
Journal or Publication Title: | Communications in Mathematical Physics | ||||
Publisher: | Springer | ||||
ISSN: | 0010-3616 | ||||
Official Date: | February 2008 | ||||
Dates: |
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Volume: | Vol.278 | ||||
Number: | No.1 | ||||
Number of Pages: | 29 | ||||
Page Range: | pp. 1-29 | ||||
DOI: | 10.1007/s00220-007-0398-9 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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