An upper critical dimension for dynamo action: A $d$-dimensional closure model study

Abstract

We construct a $d$-dimensional Eddy Damped Quasi-Normal Markovian (EDQNM) Closure Model to study dynamo action in arbitrary dimensions. In particular, we find lower $d_L$ and upper $d_U$ critical dimensions for sustained dynamo action in this incompressible problem. Our model is adaptable for future studies incorporating helicity, compressible effects and a wide range of magnetic Reynolds and Prandtl numbers.

arXiv comment15 pages, 5 figures

References in corpus (15)

• Astrophysical magnetic fields and nonlinear dynamo theory
• Particles and fields in fluid turbulence
• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Dynamo theories
• Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers
• Advances in mean-field dynamo theory and applications to astrophysical turbulence
• Turbulence in non-integer dimensions by fractal Fourier decimation
• Galactic Dynamos
• Lecture notes: Astrophysical fluid dynamics
• Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+εdimensions
• Small-scale-field Dynamo
• Dynamo effect in the Kraichnan magnetohydrodynamic turbulence
• Kazantsev dynamo in turbulent compressible flows
• Effect of spatial dimension on a model of fluid turbulence
• Lagrangian Irreversibility and Eulerian Dissipation in Fully-Developed Turbulence