arXiv subjects

Steve Tobias

Publications and source records attributed to Steve Tobias.

4 recordsLinked to original sources

arXiv2026

Data-driven discovery of dynamo cycle equations

Many low-mass stars like the Sun host periodic, oscillatory magnetic fields that lead to variable levels of stellar activity, driving space weather that affects the habitability and detection of exoplanets. Owing to the intrinsic difficulty in modeling stellar magnetohydrodynamics across scales, realistic numerical simulations of this process are very challenging, and developing reduced-order models is of interest. In this work, we develop a framework to recover such models directly from numerical data by using a combination of Dynamic Mode Decomposition (DMD) to identify coherent magnetic structures, and the Sparse Identification of Nonlinear Dynamics (SINDy) framework to model their dynamics. We compare these models to those obtained using the classic mathematical method of weakly nonlinear (WNL) analysis. This approach is implemented on a one-dimensional mean-field dynamo model that parameterizes the main components of a convective dynamo in a low-mass star -- helical convection and differential rotation. We recover oscillatory dynamo models as a function of the dynamo strength parameter $D\sim αΩ'$, magnetic dissipation parameter $κ$, and a comprehensive dynamo model that predicts the magnetic state for a combination of these two parameters. Our results suggest that equations discovered with SINDy are more robust than equations from WNL analysis, and can predict the saturation amplitude of magnetic fields in parameter regimes far from the onset of dynamo action characterized by stiff nonlinearities. This includes unstable, and typically unknown, subcritical branches. Further to this, SINDy is able to find equations in parameter regimes where the nonlinearity is not analytic and WNL analysis cannot be applied. These properties of data-driven SINDy models suggest them as a viable alternative for modeling of stellar dynamo cycles directly from the data.

astro-ph.SR↗

arXiv2018

Rotationally induced coherence in turbulent kinematic dynamos

We consider rotating, kinematic dynamos at low magnetic Prandtl number $Pm$. We show that the inclusion of rotation leads to an increase in spatio-temporal coherence and a modification of the turbulent spectrum. These effects make the flow more efficient in driving the dynamo, in the sense that the energy injection rate required to reach the critical value of the magnetic Reynolds number $Rm_c$ is reduced in comparison with a non-rotating dynamo (Seshasayanan et al. 2017). For random dynamos it is known that the growth-rate would largely be determined by the spectral index of the flow at the resistive scale. Here, however, we demonstrate that the dynamo growth-rate in rotating flows is increased by the rotationally induced long-lived large scale eddies with a coherence time greater than the local turnover time. These eddies play the major role in determining the dynamo growth-rate.

physics.flu-dyn↗

arXiv2016

Forcing-dependent dynamics and emergence of helicity in rotating turbulence

The effects of large scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of numerical simulations, varying systematically the nature of the mechanical force in time. We demonstrate that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relatively to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We find that the nature of the mechanical force in time and the emergence of helicity have direct implications on the cascade dynamics of these flows, determining the anisotropy in the flow, the energy condensation at large scales and the power-law energy spectra that are consistent with previous findings and phenomenologies under strong and weak-wave turbulent conditions.

physics.flu-dyn↗

arXiv2015

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions.

astro-ph.SR↗