An efficient method for computing the eigenfunctions of the dynamo equation

Abstract

We present an elegant method of determining the eigensolutions of the induction and the dynamo equation in a fluid embedded in a vacuum. The magnetic field is expanded in a complete set of functions. The new method is based on the biorthogonality of the adjoint electric current and the vector potential with an inner product defined by a volume integral over the fluid domain. The advantage of this method is that the velocity and the dynamo coefficients of the induction and the dynamo equation do not have to be differentiated and thus even numerically determined tabulated values of the coefficients produce reasonable results. We provide test calculations and compare with published results obtained by the classical treatment based on the biorthogonality of the magnetic field and its adjoint. We especially consider dynamos with mean-field coefficients determined from direct numerical simulations of the geodynamo and compare with initial value calculations and the full MHD simulations.

accepted for Astronomy & Astrophysics

References in corpus (6)

• Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo
• Alpha effect and turbulent diffusion from convection
• Nonlinear magnetic diffusivity and alpha tensors in helical turbulence
• Saturation and time dependence of geodynamo models
• A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields
• Statistical dynamo theory: Mode excitation

Cited by in corpus (4)

• Oscillatory dynamos and their induction mechanisms
• Global dynamo models from direct numerical simulations and their mean-field counterparts
• Mode analysis of numerical geodynamo models
• Spectral properties of oscillatory and non-oscillatory α^2-dynamos