GIBBON , John D.

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box $[0,\,L]^{3}$ is addressed through four sets of numerical simulations that calculate a new set of variables defined by $D_{m}(t) = \left(\varpi_{0}^{-1}\Omega_{m}\right)^{\alpha_{m}}$ for $1 \leq m \leq \infty$ where $\alpha_{m}=...

The periodic $3D$ Navier-Stokes equations are analyzed in terms of dimensionless, scaled, $L^{2m}$-norms of vorticity $D_m$ ($1 \leq m < \infty$). The first in this hierarchy, $D_1$, is the global enstrophy. Three regimes naturally occur in the $D_1-D_m$ plane. Solutions in the first regime, which lie between two concave curves, are shown to be...

The periodic $3D$ Navier-Stokes equations are analyzed in terms of dimensionless, scaled, $L^{2m}$-norms of vorticity $D_m$ ($1 \leq m < \infty$). The first in this hierarchy, $D_1$, is the global enstrophy. Three regimes naturally occur in the $D_1-D_m$ plane. Solutions in the first regime, which lie between two concave curves, are shown to be...

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box $[0,\,L]^{3}$ is addressed through four sets of numerical simulations that calculate a new set of variables defined by $D_{m}(t) = \left(\varpi_{0}^{-1}\Omega_{m}\right)^{\alpha_{m}}$ for $1 \leq m \leq \infty$ where $\alpha_{m}=...

We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are, respectively, the vorticity and current density in three-dimensional magnetohydrodynamics (MHD). We show by...