Rescaled vorticity moments in the 3D Navier-Stokes equations
Duration: 42 mins 24 secs
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| Description: |
Gibbon, J (Imperial College London)
Monday 02 December 2013, 10:15-11:00 |
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| Created: | 2013-12-03 14:04 |
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| Collection: | Mathematics for the Fluid Earth |
| Publisher: | University of Cambridge |
| Copyright: | Rob Leonard |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Co-authors: D. D. Donzis (Texas A and M), A. Gupta (University of Rome Tor Vergata), R. M. Kerr (University of Warwick), R. Pandit (Indian Institute of Science Bangalore), D. Vincenzi (CNRS, Universite de Nice)
The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations is addressed using a new set of variables whose evolution has been calculated through three sets of numerical simulations. These variables are defined on a periodic box [0,L]3 such that Dm(t)=(ϖ−10Ωm)αm where αm=2m/(4m−3) \& the set of frequencies Ωm for 1≤m≤∞ are defined by Ωm(t)=(L−3\I|\boldmathω|2mdV)1/2m\,; the fixed frequency ϖ0=νL−2. All three simulations unexpectedly show that the Dm are ordered for m=1,...,9 such that Dm+1<Dm. Moreover, the Dm squeeze together such that Dm+1/Dm↗1 as m increases. This regime is shown to connected to the depletion of nonlinearity. The first simulation is of very anisotropic decaying turbulence\,; the second pair is of decaying isotropic turbulence from random initial conditions \& of forced isotropic turbulence at constant Grashof number\,; the third 40963 simulation is of very high Reynolds number forced, stationary, isotropic turbulence. |
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