Behavior of hydrodynamic and magnetohydrodynamic turbulence in a rotating sphere with precession and dynamo action

Etchevest, M.; Fontana, M.; Dmitruk, P.

doi:10.1103/physrevfluids.7.103801

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…The connection between the periodic box of a Fourier model and the spherical shell of an Earth-like model is that they have essentially the same ideal MHD statistical mechanics [14]. However, no spectral transform methods for studying MHD turbulence in a spherical shell exist yet, and although non-transform methods [15][16][17] have been used, they will always have insufficient resolution. Thus, we use Fourier spectral transform methods in a periodic box because they are efficient and, again, serve as a surrogate for transform methods more explicitly designed for spherical shells, until such methods are available.…”

Section: Introductionmentioning

confidence: 99%

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence, Part 2

Shebalin

2023

Fluids

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We continue our study of the transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a 1283 periodic grid. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time. The six runs that previously went to near equilibrium are here extended into equilibrium. As before, we neglect dissipation as we are primarily concerned with behavior at the largest scale where this behavior has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. These six runs have various combinations of imposed rotation and mean magnetic field and represent the five cases of ideal, homogeneous, incompressible, and MHD turbulence: Case I (Run 1), with no rotation or mean field; Case II (Runs 2a and 2b), where only rotation is imposed; Case III (Run 3), which has only a mean magnetic field; Case IV (Run 4), where rotation vector and mean magnetic field direction are aligned; and Case V (Run 5), which has non-aligned rotation vector and mean field directions. Statistical mechanics predicts that dynamic Fourier coefficients are zero-mean random variables, but largest-scale coherent magnetic structures emerge and manifest themselves as Fourier coefficients with very large, quasi-steady, mean values compared to their standard deviations, i.e., there is ‘broken ergodicity.’ These magnetic coherent structures appeared in all cases during transition to near equilibrium. Here, we report that, as the runs were continued, these coherent structures remained quasi-steady and energetic only in Cases I and II, while Case IV maintained its coherent structure but at comparatively low energy. The coherent structures that appeared in transition in Cases III and V were seen to collapse as their associated runs extended into equilibrium. The creation of largest-scale, coherent magnetic structure appears to be a dynamo process inherent in ideal MHD turbulence, particularly in Cases I and II, i.e., those cases most pertinent to planets and stars. Furthermore, the statistical theory of ideal MHD turbulence has proven to apply at the largest scale, even when dissipation and forcing are included. This, along with the discovery and explanation of dynamically broken ergodicity, is essentially a solution to the ‘dynamo problem’.

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Section: Introductionmentioning

confidence: 99%

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence, Part 2

Shebalin

2023

Fluids

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Interplay between geostrophic vortices and inertial waves in precession-driven turbulence

et al. 2022

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The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame, where precession gives rise to a background shear flow, which becomes linearly unstable and breaks down into turbulence. We observe that this precession-driven turbulence is in general characterized by coexisting two-dimensional (2D) columnar vortices and three-dimensional (3D) inertial waves, whose relative energies depend on the precession parameter Po. The vortices resemble the typical condensates of geostrophic turbulence, are aligned along the rotation axis (with zero wavenumber in this direction, kz = 0), and are fed by the 3D waves through nonlinear transfer of energy, while the waves (with [Formula: see text]) in turn are directly fed by the precessional instability of the background flow. The vortices themselves undergo inverse cascade of energy and exhibit anisotropy in Fourier space. For small Po < 0.1 and sufficiently high Reynolds numbers, the typical regime for most geo- and astrophysical applications, the flow exhibits strongly oscillatory (bursty) evolution due to the alternation of vortices and small-scale waves. On the other hand, at larger Po > 0.1 turbulence is quasi-steady with only mild fluctuations, the coexisting columnar vortices and waves in this state give rise to a split (simultaneous inverse and forward) cascade. Increasing the precession magnitude causes a reinforcement of waves relative to vortices with the energy spectra approaching the Kolmogorov scaling, and therefore, the precession mechanism counteracts the effects of the rotation.

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A parametric study of precession driven dynamos inside a sphere

Liao,

2024

Physics of Fluids

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The dynamo actions of an electrically conducting fluid in a precessing sphere are investigated over a wide range of parameters by direct numerical simulation using a Galerkin spectral method. The focus of this work is to identify the most promising parameter regimes for the dynamo action and to investigate the characteristics of the magnetic field generated by precession. The influence of different nutation angles (30°,60°,90°) and different precession ratios on the ability to drive dynamo action are investigated. The optimal angle for dynamo actions is found at 90°, followed by 60° with retrograde precession. A moderate precession ratio around 0.3 is shown to be more feasible for dynamo actions. A rich set of self-sustained dynamo solutions are obtained in the parameter space we explored, including steady, periodic, quasi-periodic, and turbulent dynamos. The structure of the generated magnetic fields is analyzed by using helical wave decomposition. None of the precession driven dynamos we obtained produce a predominantly dipolar field, contrary to the convection driven dynamos. The long-time evolution of the magnetic dipole moment is investigated and different types of polarity reversals are observed.

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Behavior of hydrodynamic and magnetohydrodynamic turbulence in a rotating sphere with precession and dynamo action

Cited by 3 publications

References 28 publications

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence, Part 2

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence, Part 2

Interplay between geostrophic vortices and inertial waves in precession-driven turbulence

A parametric study of precession driven dynamos inside a sphere

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