Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2407.17627

What makes a steady flow to favour kinematic magnetic field generation: A statistical analysis

Francisco Stefano de Almeida·Roman Chertovskih·Sílvio Gama·Rui Gonçalves
View original source ↗Read source document ↗Export metadata ↓

Abstract

To advance our understanding of the magnetohydrodynamic (MHD) processes in liquid metals, in this paper we propose an approach combining the classical methods in the dynamo theory based on numerical simulations of the partial differential equations governing the evolution of the magnetic field with the statistical methods. In this study, we intend to answer the following ``optimization'' question: Can we find a statistical explanation what makes a flow to favour magnetic field generation in the linear regime (i.e. the kinematic dynamo is considered), where the Lorenz force is neglected? The flow is assumed to be steady and incompressible, and the magnetic field generation is governed by the magnetic induction equation. The behaviour of its solution is determined by the dominant (i.e. with the largest real part) eigenvalue of the magnetic induction operator. Considering an ensemble of 2193 randomly generated flows, we solved the kinematic dynamo problem and performed an attempt to find a correlation between the dominant eigenvalue and the standard quantities used in hydrodynamics -- vorticity and kinetic helicity. We have found that there is no visible relation between the property of the flow to be a kinematic dynamo and these quantities. This enables us to conclude that the problem requires a more elaborated approach to ``recognize'' if the flow is a dynamo or not; we plan to solve it using contemporary data-driven approach based on deep neural networks.

Explore related subjects

physics.flu-dynmath.OC

Keep this discovery

BibTeXRIS

Francisco Stefano de Almeida, Roman Chertovskih, Sílvio Gama, Rui Gonçalves. 2024-07-24. What makes a steady flow to favour kinematic magnetic field generation: A statistical analysis. https://doi.org/10.1007/978-3-031-81724-3_59

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

KEEP EXPLORING

Related papers

arXiv2026

Correlative effects of induced magnetic field-buoyancy on reactive solute dispersion dynamics in couple-stress fluids

We investigate the dispersion of a reactive solute in a couple-stress fluid flowing between two parallel plates under the combined effects of pressure-driven flow, buoyancy, and an induced magnetic field. The model incorporates first-order heterogeneous reactions at both channel walls alongside a bulk reaction. Using Mei's multiscale homogenization technique accurate to third order, we develop a higher-order asymptotic formulation to determine the effective longitudinal dispersion coefficient and concentration field. Analytical predictions are complemented by Brownian dynamics simulations and finite-difference solutions, while the Aris method of moments quantifies transient mean displacement, spatial variance, and effective dispersivity. The hydrodynamic analysis reveals a singular branch in the velocity solution when the Hartmann number equals half the couple-stress parameter and identifies a characteristic quarter-power scaling between the Hartmann number and couple-stress parameter, separating couple-stress- and magnetically dominated regimes. The model recovers classical Taylor-dispersion behavior in the non-reactive Newtonian limit and agrees well with experimental measurements. Couple-stress rheology and magnetic damping suppress shear-induced dispersion, whereas buoyancy enhances dispersion through additional transverse velocity gradients. A distinct saturation regime of the dispersion coefficient emerges with an increasing couple-stress parameter, while unequal wall absorption induces persistent transverse asymmetry, and stronger absorption enhances solute removal near the source. Numerical and stochastic results validate the analytical framework while resolving higher-order concentration structures and particle-scale wall adsorption.

physics.flu-dyn↗
arXiv2026

DiffSWE2d: a differentiable Shallow Water Equations solver for end-to-end flood and tsunami modelling

Solving inverse and optimisation problems with traditional shallow water equations (SWE) solvers can be computationally expensive, particularly when gradients with respect to model inputs or parameters must be estimated through repeated forward simulations. In this paper, we introduce DiffSWE2d, an open-source differentiable shallow water equations solver for end-to-end flood and tsunami modelling implemented in PyTorch. By leveraging automatic differentiation, DiffSWE2d represents the time-marching physics as a differentiable computational graph, enabling gradients to be propagated directly through the numerical solver. We validate the solver against two established benchmark cases and demonstrate its application to tsunami waveform inversion, showing its ability to infer model inputs through gradient-based optimisation. DiffSWE2d provides a flexible framework for integrating physics-based hydrodynamic modelling with modern optimisation and machine learning methods. The source code and reproducible examples are publicly available at: https://github.com/ZhonghouXu/DiffSWE2d

physics.flu-dyn↗
arXiv2026

Low inertia limit of elasto-inertial turbulence

Pipe and channel flows of viscoelastic fluids display chaotic dynamics at unusually low speeds, a phenomenon referred to as elasto-inertial turbulence, EIT. First reported in experiments a century ago, recent theoretical studies and model computations predict a variety of scenarios for the phenomenon's origin, ranging from hoop stress modes to center modes and to Tollmien-Schlichting waves. Lacking experimental confirmation, the relevant scenario in actual flows of polymer solutions remains unknown. We here determine the transition threshold of EIT in pipe experiments, covering three decades in elasticity number. Across this entire parameter range, the transition features center mode structures at onset. Eventually the instability diverges at a lower inertia (upper elasticity) limit, which is a robust signature of this center mode scenario. Finally, we report the first experimental observation of a traveling wave in viscoelastic pipe flow, and the sequences of localized structures found, are in excellent agreement with a center mode traveling wave, the "arrowhead" solution, discovered in model simulations.

physics.flu-dyn↗