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

TL;DR

This paper develops a $d$-dimensional EDQNM closure model to identify critical dimensions for dynamo action, providing a framework for future studies with various physical effects.

Contribution

It introduces a novel $d$-dimensional model to determine critical dimensions for dynamo action, extending understanding in magnetohydrodynamics.

Findings

Identifies lower and upper critical dimensions for dynamo action.

Provides a flexible model adaptable to various physical effects.

Lays groundwork for future studies on dynamo phenomena.

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.