scholarly journals Force balance in convectively driven dynamos with no inertia

2019 ◽  
Vol 879 ◽  
pp. 793-807
Author(s):  
David W. Hughes ◽  
Fausto Cattaneo
Keyword(s):  
Strong Field ◽  
Plane Layer ◽  
Weak Field ◽  
Momentum Equation ◽  
Force Balance ◽  
Dominant Contribution ◽  
Dynamo Action ◽  
Thermal Equation ◽  
Magnetic Part ◽  
Viscous Forces

We study dynamo action in rotating, plane layer Boussinesq convection in the absence of inertia. This allows a decomposition of the velocity into a thermal part driven by buoyancy, and a magnetic part driven by the Lorentz force. We have identified three families of solutions, defined in terms of what is the dominant contribution to the velocity. In weak field dynamos the dominant contribution is the thermal component, in super strong field dynamos the dominant contribution is magnetic and in strong field dynamos the two components are comparable. For each of these solutions we investigate the force balance in the momentum equation to determine the relative importance of the viscous, buoyancy, Coriolis and magnetic forces. We do this by extracting the solenoidal part of the individual terms in the momentum equation, thereby removing their pressure contributions. This is numerically preferable to the more common practice of taking the curl of the momentum equation, which introduces an extra derivative. We find that, irrespective of the type of dynamo solution, the dynamics is controlled by the horizontal forces (in projection). Furthermore, in the progression from weak to strong to super strong dynamos, we find that the viscous forces in the thermal equation become negligible, thereby leading to a balance between buoyancy and Coriolis forces. On the other hand, no corresponding trend is observed in the magnetic part of the momentum equation: the viscous stresses always remain significant. This can be attributed to the different degrees of smoothness of the Coriolis and Lorentz forces, the latter having contributions from strong, filamentary structures. We discuss how our findings relate to dynamo solutions in which viscosity plays no role whatsoever – so-called Taylor states.

scholarly journals Strong-field spherical dynamos

2016 ◽  
Vol 789 ◽  
pp. 500-513 ◽  
Author(s):  
Emmanuel Dormy
Keyword(s):  
Strong Field ◽  
Numerical Models ◽  
Weak Field ◽  
Force Balance ◽  
Inertial Effects ◽  
Viscous Effects ◽  
Field Limit ◽  
Magnetic Prandtl Number ◽  
Number Ratio ◽  
Magnetic Diffusivity

Numerical models of the geodynamo are usually classified into two categories: dipolar modes, observed when the inertial term is small enough; and multipolar fluctuating dynamos, for stronger forcing. We show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong-field limit. This solution coexists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length scale, and the strong-field branch, in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimising the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is misleading.

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.

Dynamo action in rapidly rotating Rayleigh–Bénard convection at infinite Prandtl number

2017 ◽  
Vol 825 ◽  
pp. 385-411 ◽  
Author(s):  
Fausto Cattaneo ◽  
David W. Hughes
Keyword(s):  
Prandtl Number ◽  
Weak Solutions ◽  
Strong Solutions ◽  
Momentum Equation ◽  
Finite Amplitude ◽  
Force Balance ◽  
Small Cells ◽  
Back Reaction ◽  
Dynamo Action ◽  
Magnetic Forces

In order better to understand the processes that lead to the generation of magnetic fields of finite amplitude, we study dynamo action driven by turbulent Boussinesq convection in a rapidly rotating system. In the limit of infinite Prandtl number (the ratio of viscous to thermal diffusion) the inertia term drops out of the momentum equation, which becomes linear in the velocity. This simplification allows a decomposition of the velocity into a thermal part driven by buoyancy, and a magnetic part driven by the Lorentz force. While the former velocity defines the kinematic dynamo problem responsible for the exponential growth of the magnetic field, the latter encodes the magnetic back reaction that leads to the eventual nonlinear saturation of the dynamo. We argue that two different types of solution should exist: weak solutions in which the saturated velocity remains close to the kinematic one, and strong solutions in which magnetic forces drive the system into a new strongly magnetised state that is radically different from the kinematic one. Indeed, we find both types of solutions numerically. Interestingly, we also find that, in our inertialess system, both types of solutions exist on the same subcritical branch of solutions bifurcating from the non-magnetic convective state, in contrast with the more traditional situation for systems with finite inertia in which weak and strong solutions are thought to exist on different branches. We find that for weak solutions, the force balance is the same as in the non-magnetic case, with the horizontal size of the convection varying as the one-third power of the Ekman number (the ratio of viscous to Coriolis forces), which gives rise to very small cells at small Ekman numbers (i.e. high rotation rates). In the strong solutions, magnetic forces become important and the convection develops on much larger horizontal scales. However, we note that even in the strong cases the solutions never properly satisfy Taylor’s constraint, and that viscous stresses continue to play a role. Finally, we discuss the relevance of our findings to the study of planetary dynamos in rapidly rotating systems such as the Earth.

scholarly journals Global MHD phenomena and their importance for stellar surfaces

2010 ◽  
Vol 6 (S273) ◽  
pp. 141-147
Author(s):  
Rainer Arlt
Keyword(s):  
Magnetic Fields ◽  
Mean Field ◽  
Momentum Equation ◽  
Small Scale ◽  
Dynamo Action ◽  
Complex Activity ◽  
Mhd Instabilities ◽  
Stellar Magnetic Fields ◽  
Mean Field Dynamo

AbstractThis review is an attempt to elucidate MHD phenomena relevant for stellar magnetic fields. The full MHD treatment of a star is a problem which is numerically too demanding. Mean-field dynamo models use an approximation of the dynamo action from the small-scale motions and deliver global magnetic modes which can be cyclic, stationary, axisymmetric, and non-axisymmetric. Due to the lack of a momentum equation, MHD instabilities are not visible in this picture. However, magnetic instabilities must set in as a result of growing magnetic fields and/or buoyancy. Instabilities deliver new timescales, saturation limits and topologies to the system probably providing a key to the complex activity features observed on stars.

scholarly journals The confrontation between general relativity and experiment

2009 ◽  
Vol 5 (S261) ◽  
pp. 198-199
Author(s):  
Clifford M. Will
Keyword(s):  
General Relativity ◽  
Gravitational Wave ◽  
Equivalence Principle ◽  
Gamma Ray ◽  
Strong Field ◽  
Weak Field ◽  
X Ray ◽  
Spacetime Geometry ◽  
Tests Of General Relativity ◽  
Laser Interferometric

AbstractWe review the experimental evidence for Einstein's general relativity. A variety of high precision null experiments confirm the Einstein Equivalence Principle, which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars.

scholarly journals Iron Complexes of a Proton-Responsive SCS Pincer Ligand with Sensitive Electronic Structure

2021 ◽  
Author(s):  
Kazimer Skubi ◽  
Reagan Hooper ◽  
Brandon Mercado ◽  
Melissa Bollmeyer ◽  
Samantha MacMillan ◽  
...  
Keyword(s):  
Strong Field ◽  
Alkali Metal Cation ◽  
Weak Field ◽  
Pincer Ligands ◽  
Zero Field ◽  
Zero Field Splitting ◽  
Pincer Ligand ◽  
Intermediate Spin ◽  
X Ray Absorption ◽  
Phosphine Complex

SCS pincer ligands have an interesting combination of strong-field and weak-field donors that is also present in the nitrogenase active site. Here, we explore the electronic structures of iron(II) and iron(III) complexes with such a pincer ligand, bearing a monodentate phosphine, thiolate S donor, amide N donor, ammonia, or CO. The ligand scaffold features a protonresponsive thioamide site, and the protonation state of the ligand greatly influences the reduction potential of iron in the phosphine complex. The N–H bond dissociation free energy can be quantitated as 56 ± 2 kcal/mol. EPR spectroscopy and SQUID magnetometry measurements show that the iron(III) complexes with S and N as the fourth donors have an intermediate spin (S = 3/2) ground state with large zero field splitting, and X-ray absorption spectra show high Fe–S covalency. The Mössbauer spectrum changes drastically with the position of a nearby alkali metal cation in the iron(III) amido complex, and DFT calculations explain this phenomenon through a change between having the doubly-occupied orbital as dz2 or dyz, as the former is more influenced by the nearby positive charge.

scholarly journals Maintaining Constant Pulse-Duration in Highly Dispersive Media Using Nonlinear Potentials

Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 570
Author(s):  
Haider Zia
Keyword(s):  
Strong Field ◽  
Propagation Distance ◽  
Weak Field ◽  
Dispersive Media ◽  
Signal Pulse ◽  
Nonlinear Phenomenon ◽  
Numerical Example ◽  
Ultrafast Optical ◽  
Nonlinear Potentials ◽  
Temporal Broadening

A method is shown for preventing temporal broadening of ultrafast optical pulses in highly dispersive and fluctuating media for arbitrary signal-pulse profiles. Pulse pairs, consisting of a strong-field control-pulse and a weak-field signal-pulse, co-propagate, whereby the specific profile of the strong-field pulse precisely compensates for the dispersive phase in the weak pulse. A numerical example is presented in an optical system consisting of both resonant and gain dispersive effects. Here, we show signal-pulses that do not temporally broaden across a vast propagation distance, even in the presence of dispersion that fluctuates several orders of magnitude and in sign (for example, within a material resonance) across the pulse’s bandwidth. Another numerical example is presented in normal dispersion telecom fiber, where the length at which an ultrafast pulse does not have significant temporal broadening is extended by at least a factor of 10. Our approach can be used in the design of dispersion-less fiber links and navigating pulses in turbulent dispersive media. Furthermore, we illustrate the potential of using cross-phase modulation to compensate for dispersive effects on a signal-pulse and fill the gap in the current understanding of this nonlinear phenomenon.

Binary pulsars as probes of relativistic gravity

1992 ◽  
Vol 341 (1660) ◽  
pp. 135-149 ◽  
Keyword(s):  
Binary Systems ◽  
Strong Field ◽  
Field Tests ◽  
Weak Field ◽  
Multidimensional Space ◽  
Alternative Theory ◽  
Theory Approach ◽  
Binary Pulsars ◽  
Weak Field Limit ◽  
Self Gravity

Until now, most experiments have succeeded in testing relativistic gravity only in its extreme weak-field limit. Because of the strong self-gravity of neutron stars, observations of pulsars in binary systems provide a unique opportunity for probing the strong-field régime of relativistic gravity. The two basic approaches to using binary pulsar measurements as probes of relativistic gravity are reviewed: the phenomenological (‘parametrized post-keplerian’ formalism) and the alternative-theory approach (multidimensional space of possible theories). The experimental constraints recently derived from the actual timing observations of three binary pulsars are summarized. General relativity passes these new, strong-field tests with complete success.

scholarly journals Lightwave-controlled electron dynamics in graphene

2019 ◽  
Vol 205 ◽  
pp. 05002
Author(s):  
Christian Heide ◽  
Takuya Higuchi ◽  
Konrad Ullmann ◽  
Heiko B. Weber ◽  
Peter Hommelhoff
Keyword(s):  
Strong Field ◽  
Polarized Light ◽  
Laser Pulses ◽  
Weak Field ◽  
Ultrashort Laser Pulses ◽  
Electron Dynamics ◽  
Matter Interaction ◽  
Linearly Polarized ◽  
Light Matter Interaction ◽  
Optical Cycle

We demonstrate that currents induced in graphene by ultrashort laser pulses are sensitive to the exact shape of the electric-field waveform. By increasing the field strength, we found a transition of the light–matter interaction from the weak-field to the strong-field regime at around 2 V/nm, where intraband dynamics influence interband transitions. In this strong-field regime, the light-matter interaction can be described by the wavenumber trajectories of electrons in the reciprocal space. For linearly polarized light the electron dynamics are governed by repeated sub-optical-cycle Landau-Zener transitions between the valence- and conduction band, resulting in Landau-Zener-Stuckelberg interference, whereas for circular polarized light this interference is supressed.

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