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Rescaled vorticity moments in the 3D Navier-Stokes equations

Presented by: 
J Gibbon Imperial College London
Monday 2nd December 2013 - 10:15 to 11:00
INI Seminar Room 1
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 $D_{m}(t) = \left(\varpi_{0}^{-1}\Omega_{m}\right)^{\alpha_{m}}$ where $\alpha_{m}= 2m/(4m-3)$ \& the set of frequencies $\Omega_{m}$ for $1 \leq m \leq \infty$ are defined by $\Omega_{m}(t) = \left(L^{-3}\I |\mbox{\boldmath$\omega$}|^{2m}dV\right)^{1/2m}$\,; the fixed frequency $\varpi_{0} = \nu L^{-2}$. All three simulations unexpectedly show that the $D_{m}$ are ordered for $m = 1\,,...,\,9$ such that $D_{m+1}

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons