arXiv subjects

Evan H. Anders

Publications and source records attributed to Evan H. Anders.

At least 19 recordsLinked to original sources

arXiv2026

The Unsteady Taylor--Vortex Dynamo is Fast

Astrophysical and geophysical fluids commonly generate organized magnetic fields, despite having enormous magnetic Reynolds numbers $\rm{Rm}$ and abundant small-scale turbulence. Flow-induced dynamo action produces these fields, with the ``kinematic dynamo problem'' devoted to determining the rate at which a flow exponentially amplifies weak magnetic fields. However, previous studies on high-Rm kinematic dynamos have generated flows via imposed volumetric forcing or oscillatory boundary conditions. In this letter, we investigate a system with three important attributes: realistic flow conditions, fast dynamo action (operational for $\rm{Rm}\to\infty$), and a subharmonic spatio-temporal structure. We show that unsteady Taylor--vortex flow, a regime observed in laboratory experiments, gives rise to fast dynamos with time and length scales twice those of the flow at high $\rm{Rm}$. By numerically integrating a Floquet system driven by periodic oscillations of Taylor vortices, we solve the kinematic dynamo problem up to $\rm{Rm} = 3.2 \cdot 10^6$, calculating the dynamo's growth rate as a function of Rm and streamwise wavenumber. We find the onset of instability and compute Finite-Time Lyapunov Exponents, which identify the regions of Lagrangian chaos required for fast dynamo action. To our knowledge, unsteady Taylor--vortex flow produces the most physically motivated fast dynamo to date.

physics.flu-dyn↗

arXiv2025

Meridional circulation molecular-weighted

Meridional circulation in stratified stellar/planetary interiors in the presence of stable molecular weight gradients remains poorly understood, thereby affecting angular momentum transport in evolutionary models. We extend the downward control principle of atmospheric sciences to include compositional stratification. Using a linearized analysis we show that stable compositional gradients slow down the penetration of circulation into the depths, emphasizing the importance of time-dependent solutions. However, additional effects such as horizontal turbulence or magnetic fields are needed to halt it completely. We also find limits demarcating linear and nonlinear regimes in terms of Schmidt and Rossby numbers. Nonlinear simulations exhibit compositional mixing due to meridional currents, enabling deeper penetration than otherwise. We propose slowly evolving and steady-state scenarios for the solar tachocline, and helioseismically observed heavy element abundances, while acknowledging the absence of constraints on the radial variation of the Schmidt number. In the context of stellar evolution, differential rotation profiles of solar-type main-sequence stars may follow analytical solutions extending from Banik & Menou (2024), thereby aiding further probes into magneto/hydrodynamic instabilities and outward angular momentum transport.

astro-ph.SR↗

arXiv2025

Morphological Regimes of Rotating Moist Convection

Moist convection is a physical process where the latent heat released by condensation acts as a buoyancy source that can enhance or even trigger an overturning convective instability. Since the saturation temperature often decreases with height, condensation releases latent heat preferentially in regions of upflow. Due to this inhomogeneous heat source, moist convection may be more sensitive to changes in flow morphology, such as those induced by rotation, than dry Rayleigh-Bénard convection. In order to study the effects of rotation on flows driven by latent heat release, we present a suite of numerical simulations that solve the Rainy-Bénard equations (Vallis et al. 2019). We identify three morphological regimes: a cellular regime and a plume regime broadly analogous to those found in rotating Rayleigh Bénard convection, and a novel funnel regime that lacks a clear analog within the regimes exhibited by dry convection. We measure energy fluxes through the system and report rotational scalings of the Reynolds and moist Nusselt numbers. We find that moist static energy transport, as measured by a moist Nusselt number, is significantly enhanced in the funnel regime without a corresponding enhancement in Reynolds number, indicating that this funnel regime produces structures with more favorable correlations between the temperature and vertical velocity.

physics.flu-dyn↗

arXiv2025

Multiple scales analysis of a nonlinear timestepping instability in simulations of solitons

The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in pseudospectral simulations of nonlinear wave propagation resulting in finite-time blow-up. The blow-up time scale is independent of the spatial resolution and spectral basis but sensitive to the timestepping scheme and the timestep size. The instability appears in multi-step and multi-stage implicit-explicit (IMEX) timestepping schemes of different orders of accuracy and has been found to manifest in simulations of soliton solutions of the Korteweg-de Vries (KdV) equation and traveling wave solutions of a nonlinear generalized Klein-Gordon equation. Focusing on the case of KdV solitons, we show that modal predictions from linear stability theory are unable to explain the instability because the spurious growth from linear dispersion is small and nonlinear sources of error growth converge too slowly in the limit of small timestep size. We then develop a novel multi-scale asymptotic framework that captures the slow, nonlinear accumulation of timestepping errors. The framework allows the solution to vary with respect to multiple time scales related to the timestep size and thus recovers the instability as a function of a slow time scale dictated by the order of accuracy of the timestepping scheme. We show that this approach correctly describes our simulations of solitons by making accurate predictions of the blow-up time scale and transient features of the instability. Our work demonstrates that studies of long-time simulations of nonlinear waves should exercise caution when validating their timestepping schemes.

math.NA↗

arXiv2025

3D Simulations Demonstrate Propagating Thermohaline Convection for Polluted White Dwarfs

Polluted white dwarfs (WDs) with small surface convection zones deposit significant concentrations of heavy elements to the underlying radiative interior, presumably driving thermohaline convection. Current models of polluted WDs frequently fail to account for this effect, although its inclusion can increase the inferred accretion rate by orders of magnitude. It has been argued that this instability cannot be treated as a continuous mixing process and thus should not be considered in these models. In this work, we study three-dimensional simulations of a thermohaline-unstable layer propagating into an underlying stable region, approximating the polluted WD scenario. We find that although thermohaline convection works to reduce driving gradients somewhat, the front continues to propagate and the system remains unstable. Importantly, the turbulent flux of metals broadly dominates over the diffusive flux in quantitative agreement with with existing mixing prescriptions implemented in some stellar evolution models (except slightly below the boundary of the propagating front, where recent prescriptions neglect overshoot-like effects). Thus, our results broadly support polluted WD models that include thermohaline mixing in their estimates of the settling rate.

astro-ph.SR↗

arXiv2024

Evolution of Semi-convective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets

Recent observational constraints on the internal structure of Jupiter and Saturn suggest that these planets have ``fuzzy" cores, i.e., gradients of the concentration of heavy elements that might span a large fraction of the planet's radius. These cores could be composed of a semi-convective staircase, i.e., multiple convective layers separated by diffusive interfaces arising from double-diffusive instabilities. However, to date, no study has demonstrated how such staircases can avoid layer mergers and persist over evolutionary time scales. In fact, previous work has found that these mergers occur rapidly, leading to only a single convective layer. Using 3D simulations, we demonstrate that rotation prolongs the lifetime of a convective staircase by increasing the timescale for both layer merger and erosion of the interface between the final two layers. We present an analytic model for the erosion phase, predicting that rotation increases the erosion time by a factor of approximately $\mathrm{Ro}^{-1/2}$, where $\mathrm{Ro}$ is the Rossby number of the convective flows (the ratio of the rotation period to the convective turnover time). For Jovian conditions at early times after formation (when convection is vigorous enough to mix a large fraction of the planet), we find the erosion time to be roughly $10^{9}~\mathrm{yrs}$ in the non-rotating case and $10^{11}~\mathrm{yrs}$ in the rotating case. If these timescales are confirmed with a larger suite of numerical simulations, the existence of convective staircases within the deep interiors of giant planets is a strong possibility, and rotation could be an important factor in the preservation of their fuzzy cores.

astro-ph.EP↗

arXiv2024

Iterative Methods for Navier--Stokes Inverse Problems

Even when the partial differential equation underlying a physical process can be evolved forward in time, the retrospective (backward in time) inverse problem often has its own challenges and applications. Direct Adjoint Looping (DAL) is the defacto approach for solving retrospective inverse problems, but it has not been applied to deterministic retrospective Navier--Stokes inverse problems in 2D or 3D. In this paper, we demonstrate that DAL is ill-suited for solving retrospective 2D Navier--Stokes inverse problems. Alongside DAL, we study two other iterative methods: Simple Backward Integration (SBI) and the Quasi-Reversible Method (QRM). Our iterative SBI approach is novel while iterative QRM has previously been used. Using these three iterative methods, we solve two retrospective inverse problems: 1D Korteweg--de Vries--Burgers (decaying nonlinear wave) and 2D Navier--Stokes (unstratified Kelvin--Helmholtz vortex). In both cases, SBI and QRM reproduce the target final states more accurately and in fewer iterations than DAL. We attribute this performance gap to additional terms present in SBI and QRM's respective backward integrations which are absent in DAL.

physics.flu-dyn↗

arXiv2024

Marginally-Stable Thermal Equilibria of Rayleigh-Bénard Convection

Natural convection is ubiquitous throughout the physical sciences and engineering, yet many of its important properties remain elusive. To study convection in a novel context, we derive and solve a quasilinear form of the Rayleigh-Bénard problem by representing the perturbations in terms of marginally-stable eigenmodes. The amplitude of each eigenmode is determined by requiring that the background state maintains marginal stability. The background temperature profile evolves due to the advective flux of every marginally-stable eigenmode, as well as diffusion. To ensure marginal stability and to obtain the eigenfunctions at every timestep, we perform a one-dimensional eigenvalue solve on each of the allowable wavenumbers. The background temperature field evolves to an equilibrium state, where the advective flux from the marginally-stable eigenmodes and the diffusive flux sum to a constant. These marginally-stable thermal equilibria (MSTE) are exact solutions of the quasilinear equations. The mean temperature profile has thinner boundary layers and larger Nusselt numbers than thermally-equilibrated 2D and 3D simulations of the full nonlinear equations. We find the Nusselt number scales like $\rm{Nu} \sim\rm{Ra}^{1/3}$. When an MSTE is used as initial conditions for a 2D simulation, we find that Nu quickly equilibrates without the burst of turbulence often induced by purely conductive initial conditions, but we also find that the kinetic energy is too large and viscously attenuates on a long viscous time scale. This is due to the thin temperature boundary layers which diffuse heat very effectively, thereby requiring high-velocity advective flows to reach an equilibrium.

physics.flu-dyn↗

arXiv2023

Modelling time-dependent convective penetration in 1D stellar evolution

1D stellar evolution calculations produce uncertain predictions for quantities like the age, core mass, core compactness, and nucleo-synthetic yields; a key source of uncertainty is the modeling of interfaces between regions that are convectively stable and those that are not. Theoretical and numerical work has demonstrated that there should be numerous processes adjacent to the convective boundary that induce chemical and angular momentum transport, as well as modify the thermal structure of the star. One such process is called convective penetration, wherein vigorous convection extends beyond the nominal convective boundary and alters both the composition and thermal structure. In this work, we incorporate the process of convective penetration in stellar evolution calculations using the stellar evolution software instrument mesa. We implement convective penetration according to the description presented by Anders et al. (2022a) to calculate a grid of models from the pre main sequence to He core depletion. The extent of the convective penetration zone is self-consistently calculated at each time step without introducing new free parameters. We find both a substantial penetration zone in all models with a convective core and observable differences to global stellar properties such as the luminosity and radius. We preset how the predicted radial extent of the penetration zone scales with the total stellar mass, age and the metallicity of the star. We discuss our results in the context of existing numerical and observational studies.

astro-ph.SR↗

arXiv2023

Internally heated and fully compressible convection: flow morphology and scaling laws

In stars and planets natural processes heat convective flows in the bulk of a convective region rather than at hard boundaries. By characterizing how convective dynamics are determined by the strength of an internal heating source we can gain insight into the processes driving astrophysical convection. Internally heated convection has been studied extensively in incompressible fluids, but the effects of stratification and compressibility have not been examined in detail. In this work, we study fully compressible convection driven by a spatially uniform heating source in 2D and 3D Cartesian, hydrodynamic simulations. We use a fixed temperature upper boundary condition which results in a system that is internally heated in the bulk and cooled at the top. We find that the flow speed, as measured by the Mach number, and turbulence, as measured by the Reynolds number, can be independently controlled by separately varying the characteristic temperature gradient from internal heating and the diffusivities. 2D simulations at a fixed Mach number (flow speed) demonstrate consistent power at low wavenumber as diffusivities are decreased. We observe convection where the velocity distribution is skewed towards cold, fast downflows, and that the flow speed is related to the length scale and entropy gradient of the upper boundary where the downflows are driven. We additionally find a heat transport scaling law which is consistent with prior incompressible work.

physics.flu-dyn↗

arXiv2023

The photometric variability of massive stars due to gravity waves excited by core convection

Massive stars die in catastrophic explosions, which seed the interstellar medium with heavy elements and produce neutron stars and black holes. Predictions of the explosion's character and the remnant mass depend on models of the star's evolutionary history. Models of massive star interiors can be empirically constrained by asteroseismic observations of gravity wave oscillations. Recent photometric observations reveal a ubiquitous red noise signal on massive main sequence stars; a hypothesized source of this noise is gravity waves driven by core convection. We present the first 3D simulations of massive star convection extending from the star's center to near its surface, with realistic stellar luminosities. Using these simulations, we make the first prediction of photometric variability due to convectively-driven gravity waves at the surfaces of massive stars, and find that gravity waves produce photometric variability of a lower amplitude and lower characteristic frequency than the observed red noise. We infer that the photometric signal of gravity waves excited by core convection is below the noise limit of current observations, so the red noise must be generated by an alternative process.

astro-ph.SR↗

arXiv2023

Rotation reduces convective mixing in Jupiter and other gas giants

Recent measurements of Jupiter's gravitational moments by the Juno spacecraft and seismology of Saturn's rings suggest that the primordial composition gradients in the deep interior of these planets have persisted since their formation. One possible explanation is the presence of a double-diffusive staircase below the planet's outer convection zone, which inhibits mixing across the deeper layers. However, hydrodynamic simulations have shown that these staircases are not long-lasting and can be disrupted by overshooting convection. In this paper we suggests that planetary rotation could be another factor for the longevity of primordial composition gradients. Using rotational mixing-length theory and 3D hydrodynamic simulations, we demonstrate that rotation significantly reduces both the convective velocity and the mixing of primordial composition gradients. In particular, for Jovian conditions at $t\sim10^{8}~\mathrm{yrs}$ after formation, rotation reduces the convective velocity by a factor of 6, and in turn, the kinetic energy flux available for mixing gets reduced by a factor of $6^3\sim 200$. This leads to an entrainment timescale that is more than two orders of magnitude longer than without rotation. We encourage future hydrodynamic models of Jupiter and other gas giants to include rapid rotation, because the decrease in the mixing efficiency could explain why Jupiter and Saturn are not fully mixed.

astro-ph.EP↗

arXiv2023

Convective boundary mixing in main-sequence stars: theory and empirical constraints

The convective envelopes of solar-type stars and the convective cores of intermediate- and high-mass stars share boundaries with stable radiative zones. Through a host of processes we collectively refer to as "convective boundary mixing" (CBM), convection can drive efficient mixing in these nominally stable regions. In this review, we discuss the current state of CBM research in the context of main-sequence stars through three lenses. (1) We examine the most frequently implemented 1D prescriptions of CBM -- exponential overshoot, step overshoot, and convective penetration -- and we include a discussion of implementation degeneracies and how to convert between various prescriptions. (2) Next, we examine the literature of CBM from a fluid dynamical perspective, with a focus on three distinct processes: convective overshoot, entrainment, and convective penetration. (3) Finally, we discuss observational inferences regarding how much mixing should occur in the cores of intermediate- and high-mass stars, and the implied constraints that these observations place on 1D CBM implementations. We conclude with a discussion of pathways forward for future studies to place better constraints on this difficult challenge in stellar evolution modeling.

astro-ph.SR↗

arXiv2022

Characterizing Observed Extra Mixing Trends in Red Giants using the Reduced Density Ratio from Thermohaline Models

Observations show an almost ubiquitous presence of extra mixing in low-mass upper giant branch stars. The most commonly invoked explanation for this is thermohaline mixing. One-dimensional stellar evolution models include various prescriptions for thermohaline mixing, but the use of observational data directly to discriminate between thermohaline prescriptions has thus far been limited. Here, we propose a new framework to facilitate direct comparison: Using carbon-to-nitrogen measurements from the SDSS-IV APOGEE survey as a probe of mixing and a fluid parameter known as the reduced density ratio from one-dimensional stellar evolution programs, we compare the observed amount of extra mixing on the upper giant branch to predicted trends from three-dimensional fluid dynamics simulations. Using this method, we are able to empirically constrain how mixing efficiency should vary with the reduced density ratio. We find the observed amount of extra mixing is strongly correlated with the reduced density ratio and that trends between reduced density ratio and fundamental stellar parameters are robust across choices for modeling prescription. We show that stars with available mixing data tend to have relatively low density ratios, which should inform the regimes selected for future simulation efforts. Finally, we show that there is increased mixing at low reduced density ratios, which is consistent with current hydrodynamical models of thermohaline mixing. The introduction of this framework sets a new standard for theoretical modeling efforts, as validation for not only the amount of extra mixing, but trends between the degree of extra mixing and fundamental stellar parameters is now possible.

astro-ph.SR↗

arXiv2022

The Stability of Prendergast Magnetic Fields

Convection in massive main sequence stars generates large scale magnetic fields in their cores which persists as they evolve up the red giant branch. The remnants of these fields may take the form of the Prendergast magnetic field, a combination of poloidal and toroidal field components which are expected to stabilize each other. Previous analytic and numerical calculations did not find any evidence for instability of the Prendergast field over short timescales. In this paper, we present numerical simulations which show a long timescale, linear instability of this magnetic field. We find the instability to be robust to changes in boundary conditions and it is not stabilized by strong stable stratification. The instability is a resistive instability, and the growth rate has a power-law dependence on the resistivity, in which the growth rate decreases as the resistivity decreases. We estimate the growth rate of the instability in stars by extrapolating this power-law to stellar values of the resistivity. The instability is sufficiently rapid to destabilize the magnetic field on timescales shorter than the stellar evolution timescale, indicating that the Prendergast field is not a good model to use in studies of magnetic fields in stars.

astro-ph.SR↗

arXiv2022

An Atlas of Convection in Main-Sequence Stars

Convection is ubiquitous in stars and occurs under many different conditions. Here we explore convection in main-sequence stars through two lenses: dimensionless parameters arising from stellar structure and parameters which emerge from the application of mixing length theory. We first define each quantity in terms familiar both to the 1D stellar evolution community and the hydrodynamics community. We then explore the variation of these quantities across different convection zones, different masses, and different stages of main-sequence evolution. We find immense diversity across stellar convection zones. Convection occurs in thin shells, deep envelopes, and nearly-spherical cores; it can be efficient of inefficient, rotationally constrained or not, transsonic or deeply subsonic. This atlas serves as a guide for future theoretical and observational investigations by indicating which regimes of convection are active in a given star, and by describing appropriate model assumptions for numerical simulations.

astro-ph.SR↗

arXiv2022

Moosinesq Convection in the Cores of Moosive Stars

Stars with masses $\gtrsim 4 \times 10^{27}M_{\rm{moose}} \approx 1.1 M_\odot$ have core convection zones during their time on the main sequence. In these moosive stars, convection introduces many uncertainties in stellar modeling. In this Letter, we build upon the Boussinesq approximation to present the first-ever simulations of Moosinesq convection, which captures the complex geometric structure of the convection zones of these stars. These flows are bounded in a manner informed by the majestic terrestrial Alces alces (moose) and could have important consequences for the evolution of these stars. We find that Moosinesq convection results in very interesting flow morphologies and rapid heat transfer, and posit this as a mechanism of biomechanical thermoregulation.

astro-ph.SR↗

arXiv2022

Convective Penetration in Early-Type Stars

Observations indicate that the convective cores of stars must ingest a substantial amount of material from the overlying radiative zone, but the extent of this mixing and the mechanism which causes it remain uncertain. Recently, Anders et al. (2021) developed a theory of convective penetration and calibrated it with 3D numerical hydrodynamics simulations. Here we employ that theory to predict the extent of convective boundary mixing in early-type main-sequence stars. We find that convective penetration produces enough mixing to explain core masses inferred from asteroseismology and eclipsing binary studies, and matches observed trends in mass and age. While there are remaining uncertainties in the theory, this agreement suggests that most convective boundary mixing in early-type main-sequence stars arises from convective penetration. Finally, we provide a fitting formula for the extent of core convective penetration for main-sequence stars in the mass range from $1.1-60 M_\odot$.

astro-ph.SR↗