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
On the Oscillation in Model Z
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
The paper deals with nonlinear decaying oscillations appearing in model Z. A method, based on the balance equations, is proposed which allows us to estimate whether or not the time behaviour of the solutions is correct. For this purpose the balance equation of energy and a new variable J = Bθ/s are used. The equation for J has conservative form. The oscillatory solution is characterized by two time scales. We speculate that the small time scale (the period of the oscillations) is connected to diffusion of azimuthal field through the boundary layer while the large time scale (the decay time of the oscillations) is linked to the diffusion of the meridional field (created in the boundary layer) into the volume of the core. The large meridional convection at the core-mantle boundary (CMB) plays a crucial role in this process.
INTRODUCTION
The solution of model Z has been found in many cases with account taken of both viscous and electromagnetic core-mantle coupling (Braginsky 1978; Braginsky & Roberts 1987; Braginsky 1988; Braginsky 1989; Cupal & Hejda 1989). Apart from Braginsky (1989), the time evolution of the solution was used simply as an aid to obtain the steady-state solution. Cupal & Hejda (1992) found numerically a transient solution of model Z having the form of a decaying oscillation. The accuracy of such solutions depends on the numerical method used, on the density of space and time discretization, and for that matter, on the character of the solution itself. An important question is which characteristics of the time behaviour of the solution reflect the real (physical) behaviour of the system and which follow from the limitations of the numerical method.
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- Solar and Planetary Dynamos , pp. 9 - 18Publisher: Cambridge University PressPrint publication year: 1994