arXiv subjects

Benjamin P. Brown

Publications and source records attributed to Benjamin P. Brown.

At least 37 records · Page 2Linked to original sources

arXiv2019

Entropy Rain: Dilution and Compression of Thermals in Stratified Domains

Large-scale convective flows called giant cells were once thought to transport the Sun's luminosity in the solar convection zone, but recent observations have called their existence into question. In place of large-scale flows, some authors have suggested the solar luminosity may instead be transported by small droplets of rapidly falling, low entropy fluid. This "entropy rain" could propagate as dense vortex rings, analogous to rising buoyant thermals in the Earth's atmosphere. In this work, we develop an analytical theory describing the evolution of dense, negatively buoyant thermals. We verify the theory with 2D cylindrical and 3D cartesian simulations of laminar, axisymmetric thermals in highly stratified atmospheres. Our results show that dense thermals fall in two categories: a stalling regime in which the droplets slow down and expand, and a falling regime in which the droplets accelerate and shrink as they propagate downwards. We estimate that solar downflows are in the falling regime and maintain their entropy perturbation against diffusion until they reach the base of the convection zone. This suggests that entropy rain may be an effective nonlocal mechanism for transporting the solar luminosity.

astro-ph.SR↗

arXiv2019

The "Sphered Cube": A New Method for the Solution of Partial Differential Equations in Cubical Geometry

A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere. By choosing to embed the cube inside of the sphere, one obtains a discretization that is free of any sharp edges or corners. Taking full advantage of the simple geometry of the sphere, spectral bases based on spin-weighted spherical harmonics and Jacobi polynomials, which properly capture the regularity of scalar, vector and tensor components in spherical coordinates, can be applied to obtain moderately efficient and accurate numerical solutions of partial differential equations in the cube. This technique demonstrates the advantages of these bases over other methods for solving PDEs in spherical coordinates. We present results for a test case of incompressible hydrodynamics in cubical geometry: Rayleigh-Bénard convection with fully Dirichlet boundary conditions. Analysis of the simulations provides what is, to our knowledge, the first result on the scaling of the heat flux with the thermal forcing for this type of convection in a cube in a sphere.

physics.comp-ph↗

arXiv2019

Breezing through the space environment of Barnard's Star b

A physically realistic stellar wind model based on Alfvén wave dissipation has been used to simulate the wind from Barnard's Star and to estimate the conditions at the location of its recently discovered planetary companion. Such models require knowledge of the stellar surface magnetic field that is currently unknown for Barnard's Star. We circumvent this by considering the observed field distributions of three different stars that constitute admissible magnetic proxies of this object. Under these considerations, Barnard's Star b experiences less intense wind pressure than the much more close-in planet Proxima~b and the planets of the TRAPPIST-1 system. The milder wind conditions are more a result of its much greater orbital distance rather than in differences in the surface magnetic field strengths of the host stars. The dynamic pressure experienced by the planet is comparable to present-day Earth values, but it can undergo variations by factors of several during current sheet crossings in each orbit. The magnetospause standoff distance would be $\sim$\,$20 - 40$\,\% smaller than that of the Earth for an equivalent planetary magnetic field strength.

astro-ph.SR↗

arXiv2019

Predicting the Rossby number in convective experiments

The Rossby number is a crucial parameter describing the degree of rotational constraint on the convective dynamics in stars and planets. However, it is not an input to computational models of convection but must be measured ex post facto. Here, we report the discovery of a new quantity, the Predictive Rossby number, which is both tightly correlated with the Rossby number and specified in terms of common inputs to numerical models. The Predictive Rossby number can be specified independent of Rayleigh number, allowing suites of numerical solutions to separate the degree of rotational constraint from the strength of the driving of convection. We examine the scaling of convective transport in terms of the Nusselt number and the degree of turbulence in terms of the Reynolds number of the flow, and we find scaling laws nearly identical to those in nonrotational convection at low Rossby number when the Predictive Rossby number is held constant. Finally, we describe the boundary layers as a function of increasing turbulence at constant Rossby number.

astro-ph.SR↗

arXiv2018

Accelerated evolution of convective simulations

High Peclet number, turbulent convection is a classic system with a large timescale separation between flow speeds and the thermal relaxation time. In this paper, we present a method of fast-forwarding through the long thermal relaxation of convective simulations, and we test the validity of this method. This accelerated evolution (AE) method involves measuring the dynamics of convection early in a simulation and using its characteristics to adjust the mean thermodynamic profile within the domain towards its evolved state. We study Rayleigh-Bénard convection as a test case for AE. Evolved flow properties of AE solutions are measured to be within a few percent of solutions which are reached through standard evolution (SE) over a full thermal timescale. At the highest values of the Rayleigh number at which we compare SE and AE, we find that AE solutions require roughly an order of magnitude fewer computing hours to evolve than SE solutions.

physics.flu-dyn↗

arXiv2018

Tensor calculus in spherical coordinates using Jacobi polynomials, Part-II: Implementation and Examples

We present a simulation code which can solve broad ranges of partial differential equations in a full sphere. The code expands tensorial variables in a spectral series of spin-weighted spherical harmonics in the angular directions and a scaled Jacobi polynomial basis in the radial direction, as described in Part-I. Nonlinear terms are calculated by transforming from the coefficients in the spectral series to the value of each quantity on the physical grid, where it is easy to calculate products and perform other local operations. The expansion makes it straightforward to solve equations in tensor form (i.e., without decomposition into scalars). We propose and study several unit tests which demonstrate the code can accurately solve linear problems, implement boundary conditions, and transform between spectral and physical space. We then run a series of benchmark problems proposed in Marti et al (2014), implementing the hydrodynamic and magnetohydrodynamic equations. We are able to calculate more accurate solutions than reported in Marti et al 2014 by running at higher spatial resolution and using a higher-order timestepping scheme. We find the rotating convection and convective dynamo benchmark problems depend sensitively on details of timestepping and data analysis. We also demonstrate that in low resolution simulations of the dynamo problem, small changes in a numerical scheme can lead to large changes in the solution. To aid future comparison to these benchmarks, we include the source code used to generate the data, as well as the data and analysis scripts used to generate the figures.

astro-ph.IM↗

arXiv2018

Convective dynamics and disequilibrium chemistry in the atmospheres of giant planets and brown dwarfs

Disequilibrium chemical processes have a large effect upon the spectra of substellar objects. To study these effects, dynamical disequilibrium has been parameterized using the quench and eddy diffusion approximations, but little work has been done to explore how these approximations perform under realistic planetary conditions in different dynamical regimes. As a first step in addressing this problem, we study the localized, small scale convective dynamics of planetary atmospheres by direct numerical simulation of fully compressible hydrodynamics with reactive tracers using the Dedalus code. Using polytropically-stratified, plane parallel atmospheres in 2- and 3-D, we explore the quenching behavior of different abstract chemical species as a function of the dynamical conditions of the atmosphere as parameterized by the Rayleigh number. We find that in both 2- and 3-D, chemical species quench deeper than would be predicted based on simple mixing length arguments. Instead, it is necessary to employ length scales based on the chemical equilibrium profile of the reacting species in order to predict quench points and perform chemical kinetics modeling in 1-D. Based on the results of our simulations, we provide a new length scale, derived from the chemical scale height, which can be used to perform these calculations. This length scale is simple to calculate from known chemical data and makes reasonable predictions for our dynamical simulations.

astro-ph.EP↗

arXiv2018

Perspectives on Reproducibility and Sustainability of Open-Source Scientific Software from Seven Years of the Dedalus Project

As the Science Mission Directorate contemplates establishing an open code policy, we consider it timely to share our experiences as the developers of the open-source partial differential equation solver Dedalus. Dedalus is a flexible framework for solving partial differential equations. Its development team primarily uses it for studying stellar and planetary astrophysics. Dedalus was developed originally for astrophysical fluid dynamics (AFD), though it has found a much broader user base, including applied mathematicians, plasma physicists, and oceanographers. Here, we will focus on issues related to open-source software from the perspective of AFD. We use the term AFD with the understanding that astrophysics simulations are inherently multi-physics: fluid dynamics coupled with some combination of gravitational dynamics, radiation transfer, relativity, and magnetic fields. In practice, a few well-known open-source simulation packages represent a large fraction of published work in the field. However, we will argue that an open-code policy should encompass not just these large simulation codes, but also the input files and analysis scripts. It is our interest that NASA adopt an open-code policy because without it, reproducibility in computational science is needlessly hampered.

astro-ph.IM↗

arXiv2017

Convective heat transport in stratified atmospheres at low and high Mach number

We study fully compressible convection in the context of plane-parallel, polytropically stratified atmospheres. We perform a suite of 2D and 3D simulations in which we vary the initial superadiabaticity ($ε$) and the Rayleigh number (Ra) while fixing the initial density stratification, aspect ratio, and Prandtl number. The evolved heat transport, quantified by the Nusselt number (Nu), follows scaling relationships similar to those found in the well-studied, incompressible Rayleigh-Bénard problem. This scaling holds up in both 2D and 3D and is not appreciably affected by the magnitude of $ε$.

physics.flu-dyn↗

arXiv2016

Turbulent Chemical Diffusion in Convectively Bounded Carbon Flames

It has been proposed that mixing induced by convective overshoot can disrupt the inward propagation of carbon deflagrations in super-asymptotic giant branch stars. To test this theory, we study an idealized model of convectively bounded carbon flames with 3D hydrodynamic simulations of the Boussinesq equations using the pseudospectral code Dedalus. Because the flame propagation timescale is much longer than the convection timescale, we approximate the flame as fixed in space, and only consider its effects on the buoyancy of the fluid. By evolving a passive scalar field, we derive a {\it turbulent} chemical diffusivity produced by the convection as a function of height, $D_{\rm t}(z)$. Convection can stall a flame if the chemical mixing timescale, set by the turbulent chemical diffusivity, $D_{\rm t}$, is shorter than the flame propagation timescale, set by the thermal diffusivity, $κ$, i.e., when $D_{\rm t}>κ$. However, we find $D_{\rm t}<κ$ for most of the flame because convective plumes are not dense enough to penetrate into the flame. Extrapolating to realistic stellar conditions, this implies that convective mixing cannot stall a carbon flame and that "hybrid carbon-oxygen-neon" white dwarfs are not a typical product of stellar evolution.

astro-ph.SR↗

arXiv2016

Tensor calculus in polar coordinates using Jacobi polynomials

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r=0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

math.NA↗

arXiv2016

M Dwarf Flare Continuum Variations on One-Second Timescales: Calibrating and Modeling of ULTRACAM Flare Color Indices

We present a large dataset of high cadence dMe flare light curves obtained with custom continuum filters on the triple-beam, high-speed camera system ULTRACAM. The measurements provide constraints for models of the NUV and optical continuum spectral evolution on timescales of ~1 second. We provide a robust interpretation of the flare emission in the ULTRACAM filters using simultaneously-obtained low-resolution spectra during two moderate-sized flares in the dM4.5e star YZ CMi. By avoiding the spectral complexity within the broadband Johnson filters, the ULTRACAM filters are shown to characterize bona-fide continuum emission in the NUV, blue, and red wavelength regimes. The NUV/blue flux ratio in flares is equivalent to a Balmer jump ratio, and the blue/red flux ratio provides an estimate for the color temperature of the optical continuum emission. We present a new "color-color" relationship for these continuum flux ratios at the peaks of the flares. Using the RADYN and RH codes, we interpret the ULTRACAM filter emission using the dominant emission processes from a radiative-hydrodynamic flare model with a high nonthermal electron beam flux, which explains a hot, T~10,000 K, color temperature at blue-to-red optical wavelengths and a small Balmer jump ratio as are observed in moderate-sized and large flares alike. We also discuss the high time-resolution, high signal-to-noise continuum color variations observed in YZ CMi during a giant flare, which increased the NUV flux from this star by over a factor of 100.

astro-ph.SR↗

arXiv2015

Numerical Simulations of Internal Wave Generation by Convection in Water

Water's density maximum at 4C makes it well suited to study internal gravity wave excitation by convection: an increasing temperature profile is unstable to convection below 4C, but stably stratified above 4C. We present numerical simulations of a water-like fluid near its density maximum in a two dimensional domain. We successfully model the damping of waves in the simulations using linear theory, provided we do not take the weak damping limit typically used in the literature. In order to isolate the physical mechanism exciting internal waves, we use the novel spectral code Dedalus to run several simplified model simulations of our more detailed simulation. We use data from the full simulation as source terms in two simplified models of internal wave excitation by convection: bulk excitation by convective Reynolds stresses, and interface forcing via the mechanical oscillator effect. We find excellent agreement between the waves generated in the full simulation and the simplified simulation implementing the bulk excitation mechanism. The interface forcing simulations over excite high frequency waves because they assume the excitation is by the "impulsive" penetration of plumes, which spreads energy to high frequencies. However, we find the real excitation is instead by the "sweeping" motion of plumes parallel to the interface. Our results imply that the bulk excitation mechanism is a very accurate heuristic for internal wave generation by convection.

astro-ph.SR↗

arXiv2014

Conduction in low Mach number flows: Part I Linear & weakly nonlinear regimes

Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier's law - the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion - is a well-known empirical model of thermal conduction. However, entropy diffusion has emerged as an alternative thermal conduction model, despite not ensuring the monotonicity of entropy. This paper investigates the differences between temperature and entropy diffusion for both linear internal gravity waves and weakly nonlinear convection. In addition to simulating the two thermal conduction models with the fully compressible Navier-Stokes equations, we also study their effects in the reduced, "sound-proof" anelastic and pseudo-incompressible equations. We find that in the linear and weakly nonlinear regimes, temperature and entropy diffusion give quantitatively similar results, although there are some larger errors in the pseudo-incompressible equations with temperature diffusion due to inaccuracies in the equation of state. Extrapolating our weakly nonlinear results, we speculate that differences between temperature and entropy diffusion might become more important for strongly turbulent convection.

astro-ph.SR↗

arXiv2013

Energy conservation and gravity waves in sound-proof treatments of stellar interiors: Part II Lagrangian constrained analysis

The speed of sound greatly exceeds typical flow velocities in many stellar and planetary interiors. To follow the slow evolution of subsonic motions, various sound-proof models attempt to remove fast acoustic waves whilst retaining stratified convection and buoyancy dynamics. In astrophysics, anelastic models typically receive the most attention in the class of sound-filtered stratified models. Generally, anelastic models remain valid in nearly adiabatically stratified regions like stellar convection zones, but may break down in strongly sub-adiabatic, stably stratified layers common in stellar radiative zones. However, studying stellar rotation, circulation, and dynamos requires understanding the complex coupling between convection and radiative zones, and this requires robust equations valid in both regimes. Here we extend the analysis of equation sets begun in Brown Vasil & Zweibel 2012, which studied anelastic models, to two types of pseudo-incompressible models. This class of models has received attention in atmospheric applications, and more recently in studies of white-dwarf supernovae progenitors. We demonstrate that one model conserves energy but the other does not. We use Lagrangian variational methods to extend the energy conserving model to a general equation of state, and dub the resulting equation set the Generalized Pseudo-Incompressible (GPI) model. We show that the GPI equations suitably capture low frequency phenomena in both convection and radiative zones in stars and other stratified systems, and we provide recommendations for converting low-Mach number codes to this equation set.

astro-ph.SR↗

arXiv2012

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much larger values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced.

astro-ph.SR↗

arXiv2012

Magnetic Wreaths and Cycles in Convective Dynamos

Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global 3D magnetohydrodynamic (MHD) simulations with the anelastic spherical harmonic (ASH) code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3$Ω_\odot$), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed.

astro-ph.SR↗

arXiv2012

Convective Babcock-Leighton Dynamo Models

We present the first global, three-dimensional simulations of solar/stellar convection that take into account the influence of magnetic flux emergence by means of the Babcock-Leighton (BL) mechanism. We have shown that the inclusion of a BL poloidal source term in a convection simulation can promote cyclic activity in an otherwise steady dynamo. Some cycle properties are reminiscent of solar observations, such as the equatorward propagation of toroidal flux near the base of the convection zone. However, the cycle period in this young sun (rotating three times faster than the solar rate) is very short ($\sim$ 6 months) and it is unclear whether much longer cycles may be achieved within this modeling framework, given the high efficiency of field generation and transport by the convection. Even so, the incorporation of mean-field parameterizations in 3D convection simulations to account for elusive processes such as flux emergence may well prove useful in the future modeling of solar and stellar activity cycles.

astro-ph.SR↗