Book contents
- Frontmatter
- Contents
- Preface
- List of Participants
- Magnetic Noise and the Galactic Dynamo
- On the Oscillation in Model Z
- Nonlinear Dynamos in a Spherical Shell
- The Onset of Dynamo Action in Alpha-lambda Dynamos
- Multifractality, Near-singularities and the Role of Stretching in Turbulence
- Note on Perfect Fast Dynamo Action in a Large-amplitude SFS Map
- A Thermally Driven Disc Dynamo
- Magnetic Instabilities in Rapidly Rotating Systems
- Modes of a Flux Ring Lying in the Equator of a Star
- A Nonaxisymmetric Dynamo in Toroidal Geometry
- Simulating the Interaction of Convection with Magnetic Fields in the Sun
- Experimental Aspects of a Laboratory Scale Liquid Sodium Dynamo Model
- Influence of the Period of an ABC Flow on its Dynamo Action
- Numerical Calculations of Dynamos for ABC and Related Flows
- Local Helicity, a Material Invariant for the Odd-dimensional Incompressible Euler Equations
- On the Quasimagnetostrophic Asymptotic Approximation Related to Solar Activity
- Simple Dynamical Fast Dynamos
- A Numerical Study of Dynamos in Spherical Shells with Conducting Boundaries
- Non-axisymmetric Shear Layers in a Rotating Spherical Shell
- Testing for Dynamo Action
- Alpha-quenching in Cylindrical Magnetoconvection
- On the Stretching of Line Elements in Fluids: an Approach from Differential Geometry
- Instabilities of Tidally and Precessionally Induced Flows
- Probability Distribution of Passive Scalars with Nonlinear Mean Gradient
- Magnetic Fluctuations in Fast Dynamos
- A Statistical Description of MHD Turbulence in Laboratory Plasmas
- Compressible Magnetoconvection in Three Dimensions
- The Excitation of Nonaxisymmetric Magnetic Fields in Galaxies
- Localized Magnetic Fields in a Perfectly Conducting Fluid
- Turbulent Dynamo and the Geomagnetic Secular Variation
- On-Off Intermittency: General Description and Feedback Model
- Dynamo Action in a Nearly Integrable Chaotic Flow
- The Dynamo Mechanism in the Deep Convection Zone of the Sun
- Shearing Instabilities in Magnetoconvection
- On the Role of Rotation of the Internal Core Relative to the Mantle
- Evolution of Magnetic Fields in a Swirling Jet
- Analytic Fast Dynamo Solution for a Two-dimensional Pulsed Flow
- On Magnetic Dynamos in Thin Accretion Disks Around Compact and Young Stars
- The Strong Field Branch of the Childress–Soward Dynamo
- Evidence for the Suppression of the Alpha-effect by Weak Magnetic Fields
- Turbulent Magnetic Transport Effects and their Relation to Magnetic Field Intermittency
- Proving the Existence of Negative Isotropic Eddy Viscosity
- Dynamo Action Induced by Lateral Variation of Electrical Conductivity
- Spherical Inertial Oscillation and Convection
- Hydrodynamic Stability of the ABC Flow
- Dynamos with Ambipolar Diffusion
- Subject Index
The Onset of Dynamo Action in Alpha-lambda Dynamos
Published online by Cambridge University Press: 11 May 2010
- Frontmatter
- Contents
- Preface
- List of Participants
- Magnetic Noise and the Galactic Dynamo
- On the Oscillation in Model Z
- Nonlinear Dynamos in a Spherical Shell
- The Onset of Dynamo Action in Alpha-lambda Dynamos
- Multifractality, Near-singularities and the Role of Stretching in Turbulence
- Note on Perfect Fast Dynamo Action in a Large-amplitude SFS Map
- A Thermally Driven Disc Dynamo
- Magnetic Instabilities in Rapidly Rotating Systems
- Modes of a Flux Ring Lying in the Equator of a Star
- A Nonaxisymmetric Dynamo in Toroidal Geometry
- Simulating the Interaction of Convection with Magnetic Fields in the Sun
- Experimental Aspects of a Laboratory Scale Liquid Sodium Dynamo Model
- Influence of the Period of an ABC Flow on its Dynamo Action
- Numerical Calculations of Dynamos for ABC and Related Flows
- Local Helicity, a Material Invariant for the Odd-dimensional Incompressible Euler Equations
- On the Quasimagnetostrophic Asymptotic Approximation Related to Solar Activity
- Simple Dynamical Fast Dynamos
- A Numerical Study of Dynamos in Spherical Shells with Conducting Boundaries
- Non-axisymmetric Shear Layers in a Rotating Spherical Shell
- Testing for Dynamo Action
- Alpha-quenching in Cylindrical Magnetoconvection
- On the Stretching of Line Elements in Fluids: an Approach from Differential Geometry
- Instabilities of Tidally and Precessionally Induced Flows
- Probability Distribution of Passive Scalars with Nonlinear Mean Gradient
- Magnetic Fluctuations in Fast Dynamos
- A Statistical Description of MHD Turbulence in Laboratory Plasmas
- Compressible Magnetoconvection in Three Dimensions
- The Excitation of Nonaxisymmetric Magnetic Fields in Galaxies
- Localized Magnetic Fields in a Perfectly Conducting Fluid
- Turbulent Dynamo and the Geomagnetic Secular Variation
- On-Off Intermittency: General Description and Feedback Model
- Dynamo Action in a Nearly Integrable Chaotic Flow
- The Dynamo Mechanism in the Deep Convection Zone of the Sun
- Shearing Instabilities in Magnetoconvection
- On the Role of Rotation of the Internal Core Relative to the Mantle
- Evolution of Magnetic Fields in a Swirling Jet
- Analytic Fast Dynamo Solution for a Two-dimensional Pulsed Flow
- On Magnetic Dynamos in Thin Accretion Disks Around Compact and Young Stars
- The Strong Field Branch of the Childress–Soward Dynamo
- Evidence for the Suppression of the Alpha-effect by Weak Magnetic Fields
- Turbulent Magnetic Transport Effects and their Relation to Magnetic Field Intermittency
- Proving the Existence of Negative Isotropic Eddy Viscosity
- Dynamo Action Induced by Lateral Variation of Electrical Conductivity
- Spherical Inertial Oscillation and Convection
- Hydrodynamic Stability of the ABC Flow
- Dynamos with Ambipolar Diffusion
- Subject Index
Summary
Solutions of the Navier-Stokes equation are computed in a deep, incompressible, spherical shell, including a parametrization of the Reynolds stresses arising from anisotropic turbulence. Thus the purely dynamical problem has solutions with marked differential rotation. The critical dynamo number for the onset of dynamo action is determined for different hydrodynamic models for both axisymmetric and nonaxisymmetric magnetic fields.
INTRODUCTION
Although kinematic dynamo models reveal some of the basic features of Solar and stellar magnetic fields, a fully satisfactory model must allow the dynamics to emerge as part of the solution of the governing system of equations. This has been attempted in a number of mean-field studies starting with Proctor (1977). It has been shown that solutions exist in which axisymmetric fields become saturated at a finite energy by the action of the macroscopic Lorentz force acting on the fluid.
The mean-field formalism is used in turbulent convection zones to parametrise the effects of the small scale dynamics on the magnetic field (Steenbeck et al. 1966). The influence of the small-scale turbulence on the macroscopic motions can be similarly modelled by the ‘Λ-effect’, representing the Reynolds stresses of anisotropic turbulence induced in a rotating, stratified medium (Rudiger 1989). The resulting mean-field equations describe the evolution of quantities averaged over time or length scales greater than those of the turbulence.
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- Solar and Planetary Dynamos , pp. 27 - 34Publisher: Cambridge University PressPrint publication year: 1994