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

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.

37 pages, 11 figures, 54 references

References in corpus (4)

• Weaving knotted vector fields with tunable helicity
• Magnetic field generation by intermittent convection
• Alpha-effect dynamos with zero kinetic helicity
• Negative magnetic eddy diffusivities from test-field method and multiscale stability theory

Cited by in corpus (6)

• Computation of kinematic and magnetic $\alpha$-effect and eddy diffusivity tensors by Padé approximation
• Pointwise vanishing velocity helicity of a flow does not preclude magnetic field generation
• Negative magnetic eddy diffusivity due to oscillogenic $\alpha$-effect
• Generalized quenching of large-scale magnetic dynamos in anisotropic flows
• Calculating turbulent transport tensors by averaging single plume dynamics and application to dynamos
• What makes a steady flow to favour kinematic magnetic field generation: A statistical analysis