Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2410.14449

The role of magnetic boundaries in kinematic and self-consistent magnetohydrodynamic simulations of precession-driven dynamo action in a closed cylinder

André Giesecke·Mike Wilbert·Ján Šimkanin·Rainer Grauer·Frank Stefani
View original source ↗Read source document ↗Export metadata ↓

Abstract

We numerically examine dynamo action generated by a flow of an electrically conducting fluid in a precessing cylindrical cavity. We compare a simplified kinematic approach based on the solution of the magnetic induction equation with a prescribed velocity field with the results from a self-consistent three-dimensional simulation of the complete set of magnetohydrodynamic equations. In all cases, we observe a minimum for the onset of dynamo action in a transitional regime, within which the hydrodynamic flow undergoes a change from a large-scale to a more small-scale, turbulent behaviour. However, significant differences in the absolute values for the critical magnetic Reynolds number occur depending on the physical properties of the external layers surrounding the flow active domain. The strong influence of the electromagnetic properties of outer layers with the large variation of the critical magnetic Reynolds number can be related to the existence of two different branches with dynamo action. In contrast to the kinematic models, the nonlinear MHD simulations reveal a small scale dynamo solution with the magnetic energy remaining significantly smaller than the kinetic energy of the flow. In irregular intervals, we observe dynamo bursts with a local concentration of the magnetic field, resulting in a global increase of the magnetic energy by a factor of 3 to 5. However, diffusion of the local patches caused by strong local shear is too rapid, causing these features to exist for only a short period so that their dynamical impact on the dynamo remains small.

Explore related subjects

physics.flu-dynastro-ph.EPastro-ph.SR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

André Giesecke, Mike Wilbert, Ján Šimkanin, Rainer Grauer, Frank Stefani. 2025-04-04. The role of magnetic boundaries in kinematic and self-consistent magnetohydrodynamic simulations of precession-driven dynamo action in a closed cylinder. https://arxiv.org/abs/2410.14449

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Data-driven low-dimensional model for the onset of turbulence in plane Couette flow

We construct low-dimensional dynamical systems for low-Reynolds-number turbulence in plane Couette flow using Kernel Quantile Regression. Exploiting the finite-dimensional structure of attractors in dissipative systems, reduced-order models are learned from direct numerical simulation data using a small set of physically meaningful observables. The resulting discrete-time models accurately reproduce periodic and chaotic dynamics near the onset of turbulence. The minimum number of variables required for accurate prediction is found to be consistent with embedding theory based on the attractor dimension. For chaotic regimes, the models capture both short-term trajectory evolution and long-term statistical properties, including probability density functions. By incorporating the Reynolds number as an additional input variable, we further develop a parameter-dependent model that successfully reproduces the bifurcation structure over a range of Reynolds numbers, including bifurcations between training points. These results demonstrate the effectiveness of machine-learning-based reduced-order modeling for capturing the essential dynamics and statistics of weakly turbulent flows.

physics.flu-dyn↗
arXiv2026

Rapidly rotating internally heated convection: bounds on long-time averages

Convection on geophysical and astrophysical scales is subject to rapid rotation and strong heating from within the domain. In studying the long-time behaviour of the solutions for such a system, energy identities fail to capture the effects of rotation because the Coriolis force does no work, and rapid rotation can be prohibitive for direct numerical simulations. Instead, we derive an asymptotically reduced model for rapidly rotating convection driven by uniform internal heating between isothermal stress-free boundaries in a plane periodic layer. The main contribution is the proof of bounds on the mean temperature, and the mean vertical convective heat transport, in terms of the Rayleigh and Ekman numbers, in the limit of infinite Prandtl number. The first quantity represents the mixing of the flow, and the second the asymmetry in heat leaving the bottom and top boundaries due to convection, and unlike Rayleigh-Bénard convection, the two are not a priori related. We employ alternative estimation techniques to those used in previous studies (Grooms \& Whitehead, 2014 \textit{Nonlinearity}, 28, 29) and identify two distinct scaling behaviours for both quantities. Finally, our bounds are optimised, within the methodology, and provide a rigorous constraint for future studies of rotation-dominated internally heated convection.

physics.flu-dyn↗
arXiv2026

Baroclinic wave dynamics in the Ekman-free rotating rectangular annulus with localized forced plume

We report numerical simulations of a rotating rectangular annulus that isolates the Ekman-free bulk of the cylindrical baroclinic annulus, subjected to bi-directional temperature gradients imposed by a uniformly cooled inner wall and a localized forced heated plume at the outer bottom. The finite-volume OpenFOAM solver is employed across combinations of source Richardson number $Ri_0 = 99, 4, 1$ and Rossby number $Ro = 0.3, 0.1, 0.07$. A non-dimensional scaling of the governing equations identifies geostrophic-hydrostatic balance as the leading-order bulk state, a result confirmed a posteriori by the $x$ and $z-$momentum budgets. Baroclinic waves of mode $m=2$ at $Ro=0.3$ transition to $m=3$ as $Ro$ decreases, consistent with the contraction of the Eady deformation radius $L_ρ= NH/f$; Complex Empirical Orthogonal Function (CEOF) analysis characterizes the wave regime and detects a Hopf-bifurcated vacillating state at $Ri_0 = 99,~Ro = 0.1$. The plume morphology, classified through the Morton length scale and source flux-balance parameter, transitions from weak, laterally-swept structures at $Ri_0 = 99$ to sustained columnar plumes traversing the full baroclinic depth at $Ri_0 \leq 4$. The plume entrainment coefficient $Γ(z)$ shows opposite rotational sensitivities at low and high $Ri_0$, which we organize through a local plume Rossby number $Ro_p = w/(2Ωb)$. A mixing-length argument predicts a bulk turbulent heat flux $\overline{u'T'} \propto Ri_0^{-1/2}$, anticipating an order-of-magnitude enhancement from $Ri_0 = 99$ to $Ri_0 = 1$, in agreement with the simulations. A regime map in the $(Ri_0, Ro)$ plane reveals that, within the explored range, the plume-regime and wave-selection problems are approximately separable: $Ri_0$ sets the plume regime while $Ro$ selects the dominant baroclinic wave mode.

physics.flu-dyn↗