Matthias Rheinhardt

Bio: Matthias Rheinhardt is an academic researcher from University of Helsinki. The author has contributed to research in topics: Magnetic field & Dynamo. The author has an hindex of 17, co-authored 49 publications receiving 1132 citations. Previous affiliations of Matthias Rheinhardt include Aalto University & Royal Institute of Technology.

Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo

Abstract: Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction ef...

Mean-field view on rotating magnetoconvection and a geodynamo model

Abstract: A comparison is made between direct numerical simulations of magnetohydrodynamic processes in a rotating spherical shell and their mean–field description. The mean fields are defined by azimuthal averaging. The coefficients that occur in the traditional representation of the mean electromotive force considering derivatives of the mean magnetic field up to the first order are calculated with the fluid velocity taken from the direct numerical simulations by two different methods. While the first one does not use specific approximations, the second one is based on the first–order smoothing approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. For the investigated example of rotating magnetoconvection the mean magnetic field derived from the direct numerical simulation is well reproduced on the mean–field level. For the simple geodynamo model a discrepancy occurs, which is probably a consequence of the neglect of higher–order derivatives of the mean magnetic field in the mean electromotive force. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

Abstract: The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) to meteorological cloud microphysics and engineering applications in combustion. Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to be used. The code can also evolve Lagrangian (inertial and noninertial) particles, their coagulation and condensation, as well as their interaction with the fluid.

Magnetic Quenching of α and Diffusivity Tensors in Helical Turbulence

Abstract: The effect of a dynamo-generated mean magnetic field of Beltrami type on the mean electromotive force is studied. In the absence of the mean magnetic field the turbulence is assumed to be homogeneous and isotropic, but it becomes inhomogeneous and anisotropic with this field. Using the test-field method the dependence of the α and turbulent diffusivity tensors on the magnetic Reynolds number ReM is determined for magnetic fields that have reached approximate equipartition with the velocity field. The tensor components are characterized by a pseudoscalar α and a scalar turbulent magnetic diffusivity ηt. Increasing ReM from 2 to 600 reduces ηt by a factor ≈5, suggesting that the quenching of ηt is, in contrast to the two-dimensional case, only weakly dependent on ReM. Over the same range of ReM, however, α is reduced by a factor ≈14, which can be explained by a corresponding increase of a magnetic contribution to the α-effect with opposite sign. Within this framework, the corresponding kinetic contribution to the α-effect turns out to be independent of ReM for 2 ≤ ReM ≤ 600. The level of fluctuations of α and ηt is only 10% and 20% of the respective kinematic reference values.

Test-field method for mean-field coefficients with MHD background

Abstract: Aims. The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods. A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results. Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. Furthermore, results for the turbulent diffusivity tensor are given, which are inaccessible to the imposed-field method. For MHD backgrounds, new mean-field effects are found that depend on the occurrence of cross-correlations between magnetic and velocity fluctuations. For strong imposed fields, � is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Dynamo Models of the Solar Cycle

Abstract: This chapter details a series of dynamo models applicable to the sun and solar-type stars. After introducing the theoretical framework known as mean-field electrodynamics, a series of increasingly complex dynamo models are constructed, with the primary aim of reproducing the various basic observed characteristics of the solar magnetic activity cycle. Global and local magnetohydrodynamcial simulations of solar convection, and dynamo action therein, are also considered, and the resulting magnetic cycles compared and contrasted to those obtained in the simpler dynamo models. The focus throughout the chapter is on the sun, simply because the amount of available observational material on the solar magnetic field and its cycle dwarfs anything else in the astrophysical realm, in terms of spatial and temporal resolution, sensitivity, and time span.

Solar Dynamo Theory

Abstract: The Sun's magnetic field is the engine and energy source driving all phenomena collectively defining solar activity, which in turn structures the whole heliosphere and significantly impacts Earth's atmosphere down at least to the stratosphere. The solar magnetic field is believed to originate through the action of a hydromagnetic dynamo process operating in the Sun's interior, where the strongly turbulent environment of the convection zone leads to flow-field interactions taking place on an extremely wide range of spatial and temporal scales. Following a necessarily brief observational overview of the solar magnetic field and its cycle, this review on solar dynamo theory is structured around three areas in which significant advances have been made in recent years: (a) global magnetohydrodynamical simulations of convection and magnetic cycles, (b) the turbulent electromotive force and the dynamo saturation problem, and (c) flux transport dynamos, and their application to model cycle fluctuations and grand ...