Magnetic field generation by pointwise zero-helicity three-dimensional steady flow of incompressible electrically conducting fluid

TL;DR

This paper introduces six families of three-dimensional steady flows with zero kinetic helicity density, demonstrating through numerical analysis that such flows can still generate large-scale magnetic fields via dynamo mechanisms, challenging previous assumptions.

Contribution

It presents new classes of zero-helicity flows and shows they can sustain magnetic dynamos, expanding understanding of flow properties influencing magnetic field generation.

Findings

Zero helicity density does not prevent large-scale dynamo action.

Flows can generate small-scale magnetic fields at low magnetic diffusivity.

Kinetic helicity and its spectrum are not sole determinants of dynamo capability.

Abstract

We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density, nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic $\alpha$-effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field for sufficiently small magnetic molecular diffusivity. These findings indicate that kinetic helicity and helicity spectrum are not the quantities controlling the dynamo properties of a flow regardless of whether scale separation is present or not.