Clustering of polarity reversals of the geomagnetic field

A model for the geomagnetic field reversal rate and constraints on the heat flux variations at the core-mantle boundary

A striking feature of many natural magnetic fields generated by dynamo action is the occurrence of polarity reversals. Paleomagnetic measurements revealed that the Earth's magnetic field has been characterised by few hundred stochastic polarity switches during its history. The rate of reversals changes in time, maybe obeying some underlying regular pattern. While chaotic dynamical systems can describe the short-term behaviour of the switches of the Earth's magnetic polarity, modelling the long-term variations of the reversal rate is somewhat problematic, as they occur on timescales of tens to hundreds of millions of years, of the order of mantle convection timescales. By investigating data of geomagnetic reversal rates, we find the presence of cycles with variable frequency and show that the transition towards periods where reversals do not occur for tens of million years (superchrons) can be described by a second-order phase transition that we interpret to be driven by variations of the heat flux at the core-mantle boundary (CMB). The model allows us to extract from the reversal sequence quantitative information on the susceptibility of the reversal rate caused by changes in the CMB heat flux amplitude, thus providing direct information on the deep inner layers of the Earth.

Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves

We demonstrate via direct numerical simulations that a periodic, oscillating mean flow spontaneously develops from turbulently generated internal waves. We consider a minimal physical model where the fluid self-organizes in a convective layer adjacent to a stably stratified one. Internal waves are excited by turbulent convective motions, then nonlinearly interact to produce a mean flow reversing on timescales much longer than the waves' period. Our results demonstrate for the first time that the three-scale dynamics due to convection, waves, and mean flow is generic and hence can occur in many astrophysical and geophysical fluids. We discuss efforts to reproduce the mean flow in reduced models, where the turbulence is bypassed. We demonstrate that wave intermittency, resulting from the chaotic nature of convection, plays a key role in the mean-flow dynamics, which thus cannot be captured using only second-order statistics of the turbulent motions.

Magnetic field reversals and long-time memory in conducting flows

Employing a simple ideal magnetohydrodynamic model in spherical geometry, we show that the presence of either rotation or finite magnetic helicity is sufficient to induce dynamical reversals of the magnetic dipole moment. The statistical character of the model is similar to that of terrestrial magnetic field reversals, with the similarity being stronger when rotation is present. The connection between long-time correlations, 1/f noise, and statistics of reversals is supported, consistent with earlier suggestions.

Long-term memory in experiments and numerical simulations of hydrodynamic and magnetohydrodynamic turbulence

We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von Kármán swirling flow between two counterrotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field and a case with self-sustained magnetic fields. Evidence of long-term memory and 1/f noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von Kármán flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large-scale magnetic field.

Magnetic reversals in a modified shell model for magnetohydrodynamics turbulence

The aim of the paper is the study of dynamo action using a simple nonlinear model in the framework of magnetohydrodynamic turbulence. The nonlinear behavior of the system is described by using a shell model for velocity field and magnetic field fluctuations, modified for the magnetic field at the largest scale by a term describing a supercritical pitchfork bifurcation. Turbulent fluctuations generate a dynamical situation where the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field. Despite its simplicity, the model has the capability to describe a long time series of reversals from which we infer results about the statistics of persistence times and scaling laws of cancellations between opposite polarities for different magnetic diffusivity coefficients. These properties of the model are compared with real paleomagnetic data, thus revealing the origin of long-range correlations in the process.

Waiting-time distributions of magnetic discontinuities: clustering or Poisson process?

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.

Determining role of Krein signature for three-dimensional Arnold tongues of oscillatory dynamos

Using a homotopic family of boundary eigenvalue problems for the mean-field alpha;{2} dynamo with helical turbulence parameter alpha(r)=alpha_{0}+gammaDeltaalpha(r) and homotopy parameter beta[0,1] , we show that the underlying network of diabolical points for Dirichlet (idealized, beta=0 ) boundary conditions substantially determines the choreography of eigenvalues and thus the character of the dynamo instability for Robin (physically realistic, beta=1 ) boundary conditions. In the (alpha_{0},beta,gamma) space the Arnold tongues of oscillatory solutions at beta=1 end up at the diabolical points for beta=0 . In the vicinity of the diabolical points the space orientation of the three-dimensional tongues, which are cones in first-order approximation, is determined by the Krein signature of the modes involved in the diabolical crossings at the apexes of the cones. The Krein space-induced geometry of the resonance zones explains the subtleties in finding alpha profiles leading to spectral exceptional points, which are important ingredients in recent theories of polarity reversals of the geomagnetic field.

Statistical analysis of random lasing emission properties in nematic liquid crystals

A statistical analysis of random lasing events observed in dye-doped nematic-liquid-crystal films is reported. The occurrence of random laser action in such complex fluids is due to residual resonances in the multiple scattering of spontaneously emitted photons. The Shannon entropy and a local-Poisson test are used here in order to quantitatively characterize the chaotic behavior of laser spikes and gain further understanding of the mechanisms underlying the lasing effect in strongly scattering organized fluids arising by an unexpected interplay of localization and amplification.