arXiv subjects

Anna Guseva

Publications and source records attributed to Anna Guseva.

8 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 $D\sim \alpha \Omega'$, magnetic dissipation parameter $\kappa$, 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↗

arXiv2025

Magnetic field morphologies in convective zones influenced by a turbulent surface layer

Spectropolarimetric observations show that many low-mass stars possess large-scale poloidal magnetic fields with considerable dipole component, which in some cases exhibit temporal dynamics - cycles or reversals. Although it is widely accepted that their magnetic fields are generated by the dynamo process, it is hard to reproduce coherent oscillations of large-scale magnetic fields with a dipolar symmetry as observed for the Sun when turbulent and compressible regimes are explored. Most previous 3D numerical studies partially avoided this problem by considering a numerical domain with low density stratification, which may correspond to neglecting surface effects where density drops considerably. To address this question, we perform direct numerical simulations of convective dynamos in extreme parameter regimes of both strong turbulence and strong density stratification, using software MagIC. Our simulations exhibit rotationally-influenced large-scale convective motions surrounded by a turbulent compressible surface layer. We find complex time variations of the magnetic field in flow regimes of predominantly dipolar configuration with respect to the few large-scale harmonics. In such regimes, turbulent surface layer induces global magnetic pumping mechanism, transporting magnetic energy into the deep interiors of our dynamo model. Dipole magnetic fields are found in regimes of transition between solar- and anti-solar differential rotation, and interact dynamically with it. The spatial distribution and temporal behavior of the large-scale fields is consistent with observations of low-mass stars, which suggest magnetic pumping could promote time-dependent magnetic fields with a dipolar symmetry as observed for the Sun and other solar-like stars. Our results suggest a parameter path in which dynamo models with a complex multiscale dynamics should be explored.

astro-ph.SR↗

arXiv2024

Run-away transition to turbulent strong-field dynamo

Planets and stars are able to generate coherent large-scale magnetic fields by helical convective motions in their interiors. This process, known as hydromagnetic dynamo, involves nonlinear interaction between the flow and magnetic field. Nonlinearity facilitates existence of bi-stable dynamo branches: a weak field branch where the magnetic field is not strong enough to enter into the leading order force balance in the momentum equation at large flow scales, and a strong field branch where the field enters into this balance. The transition between the two with enhancement of convection can be either subcritical or supercritical, depending on the strength of magnetic induction. In both cases, it is accompanied by topological changes in velocity field across the system; however, it is yet unclear how these changes are produced. In this work, we analyse transitions between the weak and strong dynamo regimes using a data-driven approach, separating different physical effects induced by dynamically active flow scales. Using Dynamic Mode Decomposition, we decompose the dynamo data from direct numerical simulations into different components (modes), identify the ones relevant for transition, and estimate relative magnitudes of their contributions Lorentz force and induction term. Our results suggest that subcritical transition to a strong dynamo is facilitated by a subharmonic instability, allowing for a more efficient mode of convection, and provide a modal basis for reduced-order models of this transition.

physics.flu-dyn↗

arXiv2024

Data-driven scale identification in oscillatory dynamos

Parker's mean-field model includes two processes generating large-scale oscillatory dynamo waves: stretching of magnetic field lines by small-scale helical flows, and by differential rotation. In this work, we investigate the capacity of data-driven modal analysis, Dynamic Mode Decomposition, to identify coherent magnetic field structures of this model. In its canonical form, the only existing field scale corresponds to the dynamo instability. To take into account multi-scale nature of the dynamo, the model was augmented with coherent in time flow field, forcing small-scale magnetic field with a faster temporal evolution. Two clusters of DMD modes were obtained: the ``slow" cluster, located near the dynamo wave frequency and associated with its nonlinear self-interaction, and the ``fast" cluster, centered around the forcing frequency and resulting from the interaction between the wave and the flow. Compared to other widely used methods of data analysis, such as Fourier transform, DMD provides a natural spatiotemporal basis for the dynamo, related to its nonlinear dynamics. We assess how the parameters of the DMD model, rank and delay, influence its accuracy, and finally discuss the limitations of this approach when applied to randomly forced, more complex dynamo flows.

astro-ph.SR↗

arXiv2022

Transition to chaos and modal structure of magnetized Taylor-Couette flow

Taylor-Couette flow is often used as a simplified model for complex rotating flows in the interior of stars and accretion disks. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in Taylor-Couette geometry become unstable to a travelling or standing wave in an external magnetic field if the fluid is conducting; there is an instability even when the flow is hydrodynamically stable. This magnetorotational instability leads to the development of chaotic states and, eventually, turbulence, when the cylinder rotation is sufficiently fast. The transition to turbulence in this flow can be complex, with the coexistence of parameter regions with spatio-temporal chaos and regions with quasi-periodic behaviour, involving one or two additional modulating frequencies. Although the unstable modes of a periodic flow can be identified with Floquet analysis, here we adopt a more flexible equation-free data-driven approach. We analyse the data from the transition to chaos in the magnetized Taylor-Couette flow and identify the flow structures related to the modulating frequencies with Dynamic Mode Decomposition; this method is based on approximating nonlinear dynamics with a linear infinite-dimensional Koopman operator. With the use of these structures, one can construct a nonlinear reduced model for the transition.

physics.flu-dyn↗

arXiv2021

Linear instability and resonance effects in large-scale opposition flow control

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional setup consists of measuring wall-normal velocity in the buffer layer and opposing it at the wall. This work explores the possibility of implementing this strategy with a detection plane in the logarithmic layer, where control could be feasible experimentally. We apply control on a channel flow at $Re_\tau = 932$, only on the eddies with relatively large wavelengths ($\lambda / h > 0.1$). Similarly to the buffer layer opposition control, our control strategy results in a virtual-wall effect for the wall-normal velocity, creating a minimum in its intensity. However, it also induces a large response in the streamwise velocity and Reynolds stresses near the wall, with a substantial drag increase. When the phase of the control lags with respect to the detection plane, spanwise-homogeneous rollers are observed near the channel wall. We show that they are a result of a linear instability. In contrast, when the control leads with respect to the detection plane, this instability is inactive and oblique waves are observed. Their wall-normal profiles can be predicted linearly as a response of the turbulent channel flow to a forcing with the advection velocity of the detection plane. The linearity, governing the flow, opens a possibility to affect large scales of the flow in a controlled manner, when enhanced turbulence intensity or mixing is desired.

physics.flu-dyn↗

arXiv2017

Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow

We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy $Ω_o/Ω_i=(r_o/r_i)^{-3/2}$. In this quasi-Keplerian regime a non-magnetic system would be Rayleigh-stable for all Reynolds numbers $Re$, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers $Rm$. For $Re=10^4$ and $Rm=10^5$ we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, even though neither could exist without the other. This dynamo solution results in significantly increased outward angular momentum transport, with the bulk of the transport being by Maxwell rather than Reynolds stresses.

physics.flu-dyn↗

arXiv2017

Transport properties of the Azimuthal Magnetorotational Instability

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles $ω\propto r^{q}$. We perform direct numerical simulations of a steep profile close to the Rayleigh line $q \gtrsim -2 $ and a quasi-Keplerian profile $q \approx -3/2$ and cover wide ranges of Reynolds ($Re\le 4\cdot10^4$) and magnetic Prandtl numbers ($0\le Pm \le 1$). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with $Rm_c \approx 50$, and angular momentum transport scales as $\sqrt{Pm} Re^2$ in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by $Rm$. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as $Rm$ increases. For the profile close to the Rayleigh line, the instability shares these properties as long as $Pm\gtrsim0.1$, but exhibits a markedly different character if $Pm\rightarrow 0$, where the onset of instability is governed by the Reynolds number, with $Re_c \approx 1250$, transport is via Reynolds stresses and scales as $Re^2$. At intermediate $Pm=0.01$ we observe a continuous transition from one regime to the other, with a crossover at $Rm=\mathcal{O}(100)$. Our results give a comprehensive picture of angular momentum transport of the MRI with an imposed azimuthal field.

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