Evan Anders

• Doctor of Philosophy
• Postdoctoral Scholar at University of California, Santa Barbara

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...

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 semiconvective staircase, i.e., multiple convective layers separated by dif...

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 re...

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...

One-dimensional stellar evolution calculations produce uncertain predictions for quantities like the age, core mass, core compactness, and nucleosynthetic 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 s...

Convection and strong magnetic fields interact in the Sun's envelope and produce many magnetic features. In sunspots, the most intense of these structures, magnetic fields are strong enough to inhibit convection. In this work, we study simulations of magnetohydrodynamic Rayleigh-Bénard convection (RBC) using the Dedalus pseudospectral framework. We...

Massive stars die in catastrophic explosions that 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...

To comprehensively understand saturation of two-dimensional ($2$D) magnetized Kelvin-Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and m...

To comprehensively understand the saturation of two-dimensional (2D) magnetized Kelvin–Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and...

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...

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 observatio...

We investigate heat transport associated with compositionally driven convection driven by crystallization at the ocean–crust interface in accreting neutron stars, or growth of the solid core in cooling white dwarfs. We study the effect of thermal diffusion and rapid rotation on the convective heat transport, using both mixing length theory and nume...

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...

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 c...

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 c...

We investigate heat transport associated with compositionally-driven convection driven by crystallization at the ocean-crust interface in accreting neutron stars, or growth of the solid core in cooling white dwarfs. We study the effect of thermal diffusion and rapid rotation on the convective heat transport, using both mixing length theory and nume...

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 p...

In one-dimensional (1D) evolution models of gas giant planets, an outer convection zone advances into the interior as the surface cools, and multiple convective layers form beneath that convective front. To study layer formation below an outer convection zone in a similar scenario, we investigate the evolution of a stably stratified fluid with a li...

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...

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...

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 that emerge from the application of mixing length theory. We first define each quantity in terms familiar to both the 1D stellar ev...

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 e...

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 that causes it remain uncertain. Recently, Anders et al. developed a theory of convective penetration and calibrated it with 3D numerical hydrodynamics simulations....

It is theorized that in gas giants, an outer convection zone advances into the interior as the surface cools, and multiple convective layers form beneath that convective front. To study layer formation below an outer convection zone in a similar scenario, we investigate the evolution of a stably-stratified fluid with a linear composition gradient t...

Observations show an almost ubiquitous presence of extra mixing in low-mass upper giant branch stars. The most commonly invoked explanation for this is the thermohaline instability. One dimensional stellar evolution models include prescriptions for thermohaline mixing, but our ability to make direct comparisons between models and observations has t...

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 convecti...

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 simul...

Stellar evolution models calculate convective boundaries using either the Schwarzschild or Ledoux criterion, but confusion remains regarding which criterion to use. Here we present a 3D hydrodynamical simulation of a convection zone and adjacent radiative zone, including both thermal and compositional buoyancy forces. As expected, regions which are...

Stellar evolution models calculate convective boundaries using either the Schwarzschild or Ledoux criterion, but confusion remains regarding which criterion to use. Here we present a 3D hydrodynamical simulation of a convection zone and adjacent radiative zone, including both thermal and compositional buoyancy forces. As expected, regions that are...

Convective motions extend beyond the nominal boundaries of a convection zone. These motions mix fluid through multiple mechanisms collectively called “convective boundary mixing.” In this note, we discuss three distinct fluid dynamical processes: convective overshoot, entrainment, and penetrative convection. We describe the structure of a convectiv...

Convection is efficient when advection matters much more than thermal diffusion. Despite this conceptually simple definition, there are several different measures of convective efficiency which are not quite equivalent. Here we recall the definitions of these measures and examine how they are related in different limits.

Most stars host convection zones in which heat is transported directly by fluid motion, but the behavior of convective boundaries is not well-understood. Here, we present 3D numerical simulations that exhibit penetration zones: regions where the entire luminosity could be carried by radiation, but where the temperature gradient is approximately adi...

Subsurface convection zones are ubiquitous in early-type stars. Driven by narrow opacity peaks, these thin convective regions transport little heat but play an important role in setting the magnetic properties and surface variability of stars. Here we demonstrate that these convection zones are not present in as wide a range of stars as previously...

Subsurface convection zones are ubiquitous in early-type stars. Driven by narrow opacity peaks, these thin convective regions transport little heat but play an important role in setting the magnetic properties and surface variability of stars. Here we demonstrate that these convection zones are \emph{not} present in as wide a range of stars as prev...

Most stars host convection zones in which heat is transported directly by fluid motion. Parameterizations like mixing length theory adequately describe convective flows in the bulk of these regions, but the behavior of convective boundaries is not well understood. Here we present 3D numerical simulations which exhibit penetration zones: regions whe...

Recent photometric observations of massive stars show ubiquitous low-frequency ‘red noise’ variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red noise. Theoretical calculations using linear wave theory by Shiode...

Natural convection exhibits turbulent flows which are difficult or impossible to resolve in direct numerical simulations. In this work we investigate a quasilinear form of the Rayleigh-Bénard problem which describes the bulk one-dimensional properties of convection without resolving the turbulent dynamics. We represent perturbations away from the m...

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-B\'enard problem by representing the perturbations in terms of marginally-stable eigenmodes. The amplitude of each eige...

Recent photometric observations of massive stars show ubiquitous low-frequency "red-noise" variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red-noise. On the other hand, theoretical calculations by Shiode et al...

Light curves produced by the Kepler mission demonstrate stochastic brightness fluctuations (or flicker ) of stellar origin which contribute to the noise floor, limiting the sensitivity of exoplanet detection and characterization methods. In stars with surface convection, the primary driver of these variations on short (sub-eight-hour) timescales is...

Light curves produced by the Kepler mission demonstrate stochastic brightness fluctuations (or "flicker") of stellar origin which contribute to the noise floor, limiting the sensitivity of exoplanet detection and characterization methods. In stars with surface convection, the primary driver of these variations on short (sub-eight-hour) timescales i...

Astrophysical simulations of convection frequently impose different thermal boundary conditions at the top and the bottom of the domain in an effort to more accurately model natural systems. In this work, we study Rayleigh-Bénard convection (RBC) under the Boussinesq approximation. We examine simulations with mixed temperature boundary conditions i...

Astrophysical simulations of convection frequently impose different thermal boundary conditions at the top and the bottom of the domain in an effort to more accurately reflect the natural system being modeled. In this work, we study Rayleigh-B\'enard convection (RBC) with mixed (``FT'') temperature boundary conditions. We aim to understand how FT b...

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-entr...

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 entr...

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...

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...

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 invol...

High Peclet number, turbulent convection is a classic system with a large timescale separation between flow speeds and equilibration time. In this paper, we present a method of achieving Accelerated Evolution (AE) of convective simulations which fast-forwards through the long thermal evolution of these systems, and we test the validity of this meth...

Convection in astrophysical systems is stratified and often occurs at high Rayleigh number (Ra) and low Mach number (Ma). Here we study stratified convection in the context of plane-parallel, polytropically stratified atmospheres. We hold the density stratification ($n_{\rho}$) and Prandtl number (Pr) constant while varying Ma and Ra to determine t...

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 ($\epsilon$) and the Rayleigh number (Ra) while fixing the initial density stratification, aspect ratio, and Prandtl number. The evolved heat trans...