Session E05: Astrophysical Fluid Dynamics (3:10pm - 3:55pm CST)

Penetration of a cooling convective layer into a stably-stratified composition gradient: entrainment at low Prandtl number

We study the formation and evolution of a convective layer when a stably-stratified fluid with a composition gradient is cooled from above. We perform a series of 2D simulations using the Bousinessq approximation with Prandtl number ranging from Pr = 0.1 to 7, extending previous work on salty water to low Pr. We show that the evolution of the convection zone is well-described by an entrainment prescription in which a fixed fraction of the kinetic energy of convective motions is used to mix fluid at the interface with the stable layer. We measure the entrainment efficiency and find that it grows with decreasing Prandtl number or increased applied heat flux. The kinetic energy flux that determines the entrainment rate is a small fraction of the total convective luminosity. In this time-dependent situation, the density ratio at the interface is driven to a narrow range that depends on the value of Pr, and with low enough values that advection dominates the interfacial transport. We characterize the interfacial flux ratio and how it depends on the interface stability. We present an analytic model that accounts for the growth of the convective layer with two parameters, the entrainment efficiency and the interfacial heat transport, both of which can be measure from the simulations.   

Identification of a novel non-axisymmetric mode in the Princeton Magnetorotational Instability Experiment

We report a new kind of magneto-hydrodynamic (MHD) instability in a modified Taylor-Couette experiment using Galinstan as the working fluid. In the experiment, the inner cylinder, outer cylinder and upper (lower) endcaps corotate independently at a fixed angular speed ratio of $W_{\mathrm{1}}$:$W_{\mathrm{2}}$:$W_{\mathrm{3}}=$1:0.19:0.58. A uniform magnetic field $B_{\mathrm{z}}$ is applied along the central axis. Using high-precision Hall probes installed at the inner cylinder surface, we obtain the radial magnetic field $B_{\mathrm{r}}$ at various azimuths and the new MHD instability is identified from its time series. The new instability is non-axisymmetric having an azimuthal mode number $m=$1 and a moderate frequency between $W_{\mathrm{1}}$-$W_{\mathrm{3}}$ and $W_{\mathrm{1}}$-$W_{\mathrm{2}}$. It only exists at sufficiently large $W_{\mathrm{1}}$ and moderate $B_{\mathrm{z}}$, consistent with typical requirements for the magnetorotational instability (MRI), and detailed quantitative comparisons are underway with theoretical analysis and numerical simulations. Further analysis shows it is not the Rayleigh instability or the Shercliff layer instability. Our results therefore shed light on the direction for finding a non-axisymmetric MRI.   

Tides and turbulent convection: a new frequency dependence

The interaction of tidal flows and convection within a star or giant planet plays an important role in the spin and orbital evolution of close binary systems. It is thought to act as an effective (turbulent) viscosity ($\nu_E$) in dampening the large-scale tidal flow. However, there exists a debate in the efficiency of this mechanism when the tidal frequency ($\omega$) exceeds the relevant convective frequency ($\omega_c$). Zahn (1966) proposed that $\nu_E \sim \omega^{-1}$ while Goldreich and Nicholson (1977) proposed $\nu_E \sim \omega^{-2}$. We use hydrodynamical simulations in a local Cartesian domain to investigate the dissipation of the large-scale tidal flow as a result of its interaction with convection. We use the well-studied Rayleigh-Bénard equations for convection along with an oscillatory background shear flow which represents our tidal-like flow. We will present results of an extensive parameter survey which explores the frequency dependence of the effective viscosity. The key result is a new scaling law which has not been predicted or observed previously. This result will then be related to the inherent nature of the turbulent convection in the absence of shear and as such gives a hint as to the physical mechanism responsible for this scaling.   

Bennu & Ryugu: Diamonds in the sky

Rapidly spinning and loosely aggregated asteroids appear to take on diamond-shaped profiles, with elevated poles as well as equators. Yet simulations show that such “rubble pile” asteroids should tend to evolve into flattened ellipsoids. We derive an analytic expression for shapes of rapidly spinning rubble piles based on the principle that as rubble is deposited it assumes a critical angle of repose. We show that this expression correctly reproduces diamond shapes in simulations provided that the simulations include deposition. This implies that the shapes of such asteroids were produced during their early evolution, and were not a result of later reshaping.   

Generation of coherent magnetic fields in periodic (closed) and non-periodic (open) domains

The origin of large-scale magnetic fields in most astrophysical systems like the Sun, stars and galaxies remains a challenging open problem. Dynamo action in the underlying turbulent fluid is thought to be responsible for the emergence of coherent magnetic fields. Due to the enormity of magnetic Reynolds numbers in these astrophysical systems, current theoretical models of the turbulent dynamo struggle to generate large-scale field on fast dynamic timescales. The conservation properties of magnetic helicity can constrain the nonlinear evolution of the dynamo. We have performed direct numerical simulations of the turbulent dynamo to investigate if employing open boundaries relaxes the constraint imposed by magnetic helicity conservation. We find that in the open systems a net magnetic flux (or system-scale fields) of significant strength arises. However, the type of open boundary we employ does not alleviate the magnetic Reynolds number (in the range explored) dependence in the nonlinear evolution of the large-scale fields. Finally, simulations performed across different magnetic Prandtl numbers indicate that the behavior of the magnetic helicity evolution is affected by flow properties as well.   

Lattice Boltzmann approach to radiative transport in numerical astrophysics

Radiative Transfer expresses how energy is carried by electromagnetic waves through media while being affected by absorption, emission and scattering. It is described by the Radiative Transfer Equation (RTE), which can be obtained building on the kinetic equations describing the evolution of gasses composed of massless particles like photons or neutrinos. Analytical solutions for this equation are available only for a small number of cases, and therefore numerical methods are needed for the study of physically interesting processes. In this talk, we present a novel approach for the simulation of the RTE which builds on the Boltzmann-like nature of the governing equations and is inspired by Lattice Boltzmann methods (LBM), commonly used in many different areas of fluid-dynamics. Our approach retains several advantages of LBM, including outstanding efficiency in parallel computations. We test our numerical methods against several benchmark cases and present results of the coupling of this LBM approach to a hydrodynamic solver for the simulation of a relativistic jet, which is an astrophysical phenomenon that plays a role in the evolution of neutron stars.   

MHD turbulence subject to global rotation and a misaligned background magnetic field

Astrophysical plasmas are often subject to both rotation and large-scale background magnetic fields. Individually, each is known to two-dimensionalize the flow perpendicular to the direction of interest. In realistic flows, both of these effects are simultaneously present and, importantly, need not be aligned. In this work, we numerically investigate forced MHD turbulence subject to the competing effects of global rotation and a background magnetic field, when the global rotation vector and the magnetic field are perpendicular. We find rich behavior in the parameter space of rotation rate and field strength. In the case of a strong background field, increasing the rotation rate from zero produces significant changes in the structure of the turbulent flow. Starting from a two-dimensional inverse cascade scenario at zero rotation, the flow transitions to a forward cascade of kinetic energy, then a shear-layer dominated regime, and finally a second shear-layer regime where the kinetic energy flux is strongly suppressed and the energy transfer is purely mediated by the induced magnetic field. Furthermore, we find that, when considering the limit of strong rotation and strong magnetic field, the order in which those limits are taken matters.   

Secondary instability of forced baroclinic critical layers

Baroclinic critical levels arise as a singularities in the inviscid linear theory of waves propagating through stratified fluid with horizontally sheared flow. For a steady wave forcing, disturbances grow secularly over the criticial layers surrounding these levels, generating a jet-like defect in the mean flow. We use a matched asymptotic expansion to furnish a reduced model of the nonlinear dynamics of such defects. By solving the linear initial-value problem for small perturbations to the defect, we establish that secondary instabilities appear at later times. Although a conventional normal-mode analysis does not strictly apply to the evolving defect, it does successfully predict the occurrence of the secondary instability, but with quantitatively inaccurate results. Notably, the model becomes ill-posed at late times, with the mode with shortest wavelength growing most vigorously, unless dissipation is included. Numerical computations with the reduced nonlinear model demonstrate that the secondary instability prompts the roll up of the defect's vorticity into vortices.   

Simultaneous Measurements of velocity and density in the Blast-Driven Instability

The presented work focuses on implementation of Planar Laser Induced Fluorescence (PLIF) to study the Blast-Driven Instability (BDI) in the Georgia Tech Blast Wave Facility. Using detonators to generate blast waves, a gaseous, membraneless interface is subjected to the combined Richtmyer-Meshkov (RMI) and Rayleigh-Taylor Instabilities (RTI) --comprising the BDI. PLIF diagnostics are added to the currently functional particle image velocimetry (PIV) diagnostic in a synchronized manner. Simultaneous velocity fields (from PIV) and density fields (from PLIF) are recorded to observe turbulence cross statistics of the BDI for the first time. Further, the cylindrical geometry provides an important platform to collect data for validation in predictive models in flows subjected to Bell-Plesset effects in polar geometries. The aim is estimating various velocity-density cross statistics, and tuning the coefficients in RANS models that are used for predicting flows involving variable density mixing effects (such as BHR model). Ensembles of high-resolution simultaneous data are compared with high-speed data previously acquired to further study the evolution of the instability.   

Predicting Magnetic Constraint in MHD Convective Simulations

Strong background magnetic fields inhibit fluid flow in convective regions, as seen in sunspot generation and phenomena such as flux separation. Understanding the nature of this convection is crucial to the developing theory of magnetoconvection and its effects on astrophysical systems. In this work, we study MHD Rayleigh-Bernard convection under the Boussinesq approximation using the Dedalus pseudospectral framework. We perform a suite of 2D simulations in which we vary the strength of the strong background magnetic field and the strength of convective driving (quantified by the Chandrasekhar number and the Rayleigh number, respectively) by many orders of magnitude. We measure \& report the scaling of the magnitude of the evolved vertical magnetic field as well as the heat transport in terms of the Nusselt number. Using these measurements, we develop a predictive parameter that predicts \textit{a priori} the degree of magnetic constraint felt by the nonlinear convective solution. This parameter will enable numericists to run targeted simulations in specific regimes of magnetic constraint in order to understand convection in sunspots and other magnetised natural environments.   

Dynamics in the Ball: Surprising Single-Hemisphere Dynamos in Fully Convective M-dwarf Simulations

M-dwarf stars are smaller and less luminous than our Sun; unlike our Sun, M-dwarf stars below a certain mass are convective from their cores to their photospheres. These fully convective objects are extremely numerous, very magnetically active, and the likely hosts of many exoplanets. This ball-like interior geometry is unique among all the stars on the main-sequence, and studying dynamics in the ball requires new computational techniques. Here we study, for the first time, dynamo action in simulations of stratified, rotating fully convective M-dwarf stars. We do this using the novel spherical Dedalus pseudospectral framework to capture the coordinate singularity at the center ($r=0$), as well as the north and south pole. We find that surprising single-hemisphere dynamo states are achieved, with most of the global-scale fields located in a single (northern or southern) hemisphere. These dynamos undergo cyclic reversals and exist over a broad range of the parameter space studied so far.   

Shock-producing Convection in Hot Jupiter Atmospheres

Observations and models suggest that Hot Jupiters have supersonic jets which produce shocks in their upper atmospheres. Models also predict that there is a high Mach number convection zone deep in the atmospheres of these planets. In this work, we study stratified, high Mach number convection in conditions appropriate for the deep atmospheres of hot Jupiters. We use the Dedalus pseudospectral framework to study a set of fully compressible convection simulations at high Mach number. At sufficiently high levels of turbulence, we observe shocks launching from convective downflow lanes. We identify the conditions where shocks occur in our simulations, discuss what effects they have on atmospheric dynamics, and how our model atmospheres can be extrapolated out to more realistic models.   

Magnetic reconnection as mechanism for inverse energy transfer in nonhelical magnetic turbulence

Recently, it has been shown numerically that there exists an inverse transfer of magnetic energy in decaying, nonhelical, magnetically dominated, magnetohydrodynamic turbulence in 3-dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the two-dimensional (2D) case, the inverse transfer is easily inferred to be due to smaller magnetic structures merging to form larger ones via reconnection. The scaling behaviour is found to be similar between the 2D and the 3D cases, i.e., the magnetic energy evolves as $t^{-1}$, and the magnetic power spectrum follows a slope of $k^{-2}$. We show that the reconnection timescale is the relevant timescale governing the dynamics. We constantly compare the 2D and the 3D cases, also via studies of the conserved quantities in the system and the energy transfer functions, to make the case that the dynamics in 3D could be approximately explained by what we understand in 2D.