scholarly journals Dynamo action of the anisotropic turbulence under the influence of coriolis and Lorentz forces.

1984 ◽  
Vol 36 (9) ◽  
pp. 341-350
Author(s):  
Hidefumi WATANABE
Keyword(s):  
Dynamo Action ◽  
Anisotropic Turbulence ◽  
Lorentz Forces

scholarly journals Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo

1997 ◽  
Vol 4 (4) ◽  
pp. 201-205 ◽  
Author(s):  
R. Hide
Keyword(s):  
Boundary Conditions ◽  
Outer Core ◽  
Angular Speed ◽  
Current Fluctuations ◽  
Geological Time ◽  
Dynamo Action ◽  
Lorentz Forces ◽  
In Series ◽  
Geomagnetic Polarity ◽  
New Evidence

Abstract. In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions.  New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ) (where τ denotes time) by a steady applied couple.  The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ) by a torque xf (x) due to Lorentz forces associated with the electric current x(τ) in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD) geodynamo).   The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel) autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1) - βzf(x), dy/dt = α(1 - x²) - κy, dz/dt = xf (x) -λz,          where f (x) = 1 - ε + εσx, in cases when the dimensionless parameters (α, β, κ, λ, σ) are all positive and 0 ≤ ε ≤ 1. Within those regions of (α, β, κ, λ, σ) parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0) to occur at all, there are in general extensive regions where x(τ) exhibits large amplitude regular or irregular (chaotic) fluctuations.  But these fluctuating régimes shrink in size as increases from zero, and they disappear altogether when ε = 1, leaving only steady régimes of dynamo action.

On the role of rotation in the generation of magnetic fields by fluid motions

1982 ◽  
Vol 306 (1492) ◽  
pp. 223-234 ◽  
Keyword(s):  
Magnetic Fields ◽  
Axial Symmetry ◽  
Fluid Motion ◽  
Liquid Core ◽  
Flow Speed ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Coriolis Forces ◽  
Lorentz Forces

It is generally accepted that the magnetic fields of planets and stars are produced by the self-exciting dynamo process (first proposed by Larmor) and that observed near-alignments of magnetic dipole axes with rotation axes are due to the influence of Coriolis forces on underlying fluid motions. The detailed role of rotation in the generation of cosmical magnetic fields has yet to be elucidated but useful insight can be obtained from general considerations of the governing magnetohydrodynamic equations. A magnetic field B cannot be maintained or amplified by fluid motion u against the effects of ohmic decay unless (a) the magnetic Reynolds number R = ULno is sufficiently large, and (b) the patterns of B and u are sufficiently complicated (where U is a characteristic flow speed, a characteristic length and J and o are typical values of the magnetic permeability and electrical conductivity respectively). Axisymmetric magnetic fields will always decay (a result that suggests that palaeomagnetic and archaeomagnetic data might show evidence that departures from axial symmetry in the geomagnetic field are systematically less during the decay phase of a polarity ‘ reversal ’ or * excursion ’ than during the recovery phase). Dynamo action is stimulated by Coriolis forces, which promote departures from axial symmetry in the pattern of uwhen B is weak, and is opposed by Lorentz forces, which increase in influence as B grows in strength. If equilibrium is attained when Coriolis and Lorentz forces are roughly equal in magnitude then the system becomes ‘ magnetostrophic' and the strengths of the internal and external parts of the field, and respectively, satisfy B i < B 8 R 1/2 and B e < B 8 R -1/2 if B 8 = UL~1 *X)/c f)i » (p being the mean density of the fluid and Q the angular speed of rotation). The slow and dispersive ‘magnetohydrodynamic inertial wave’ with a frequency that depends on the square of the Alfven speed [B]/(up) 1/2 and inversely on Q exemplifies magnetostrophic flow. Such waves probably occur in the electrically conducting fluid interiors of planets and stars, where they play an important role in the generation of magnetic fields as well as in other processes, such as the topographic coupling between the Earth’s liquid core and solid mantle.

scholarly journals Force balance in numerical geodynamo simulations: a systematic study

2019 ◽  
Vol 219 (Supplement_1) ◽  
pp. S101-S114 ◽  
Author(s):  
T Schwaiger ◽  
T Gastine ◽  
J Aubert
Keyword(s):  
Parameter Space ◽  
Dominant Role ◽  
Second Order ◽  
Force Balance ◽  
Dynamo Action ◽  
Onset Of Convection ◽  
First Order ◽  
Viscous Forces ◽  
Magnetic Diffusivity ◽  
Lorentz Forces

SUMMARY Dynamo action in the Earth’s outer core is expected to be controlled by a balance between pressure, Coriolis, buoyancy and Lorentz forces, with marginal contributions from inertia and viscous forces. Current numerical simulations of the geodynamo, however, operate at much larger inertia and viscosity because of computational limitations. This casts some doubt on the physical relevance of these models. Our work aims at finding dynamo models in a moderate computational regime which reproduce the leading-order force balance of the Earth. By performing a systematic parameter space survey with Ekman numbers in the range 10−6 ≤ E ≤ 10−4, we study the variations of the force balance when changing the forcing (Rayleigh number, Ra) and the ratio between viscous and magnetic diffusivities (magnetic Prandtl number, Pm). For dipole-dominated dynamos, we observe that the force balance is structurally robust throughout the investigated parameter space, exhibiting a quasi-geostrophic (QG) balance (balance between Coriolis and pressure forces) at zeroth order, followed by a first-order Magneto-Archimedean-Coriolis (MAC) balance between the ageostrophic Coriolis, buoyancy and Lorentz forces. At second order, this balance is disturbed by contributions from inertia and viscous forces. Dynamos with a different sequence of the forces, where inertia and/or viscosity replace the Lorentz force in the first-order force balance, can only be found close to the onset of dynamo action and in the multipolar regime. To assess the agreement of the model force balance with that expected in the Earth’s core, we introduce a parameter quantifying the distance between the first- and second-order forces. Analysis of this parameter shows that the strongest-field dynamos can be obtained close to the onset of convection (Ra close to critical) and in situations of reduced magnetic diffusivity (high Pm). Decreasing the Ekman number gradually expands this regime towards higher supercriticalities and lower values of Pm. Our study illustrates that most classical numerical dynamos are controlled by a QG-MAC balance, while cases where viscosity and inertia play a dominant role are the exception rather than the norm.

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan &amp; Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

Decay of anisotropic turbulence.

AIAA Journal ◽  
1973 ◽  
Vol 11 (4) ◽  
pp. 546-548 ◽  
Author(s):  
HENRY J. TUCKER ◽  
S. FlRASAT ALI
Keyword(s):  
Anisotropic Turbulence
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