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 dL and upper dU 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.