arXiv subjects

Keaton J. Burns

Publications and source records attributed to Keaton J. Burns.

At least 19 recordsLinked to original sources

arXiv2026

High-level, efficient ocean modeling at all scales with Oceananigans

We describe the user interface, governing equations, and numerical methods underpinning the ocean modeling software called "Oceananigans". Oceananigans development has been led by the Climate Modeling Alliance as part of a larger effort to build a trainable climate model with quantifiable uncertainty. Notably, Oceananigans is written in the Julia programming language, is optimized for GPUs, and can efficiently simulate all scales of ocean motion ranging from millimeter-scale turbulence in a small box to planetary-scale ocean circulation. We argue that this combination of capabilities is enabled by a design that combines a basic, easy-to-optimize, GPU-friendly structured finite volume algorithm exposed behind a high-level, programmable user interface. This design negotiates a dual mandate for highest-possible performance (to support state-of-the-art applications) and enhanced accessibility (to facilitate adoption and development). The dual mandate aims ultimately to accelerate the progress of Earth system science.

physics.ao-ph↗

arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗

arXiv2026

Emergent universal statistics in nonequilibrium systems with dynamical scale selection

Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their far-from-equilibrium dynamics and statistics poses major conceptual and practical challenges due to the absence of energy and momentum conservation laws. Here, we experimentally and theoretically investigate the statistics of prototypical nonequilibrium systems in which inherent length-scale selection confines the dynamics near a mean energy hypersurface. Guided by spectral analysis of the field modes and scaling arguments, we derive a universal nonequilibrium distribution for kinetic field observables. We confirm the predicted energy distributions in experimental observations of Faraday surface waves, and in random scattering and active turbulence simulations. Our results indicate that pattern dynamics and transport in driven physical and biological matter can often be described through monochromatic random fields, suggesting a path towards a unified statistical field theory of nonequilibrium systems with length-scale selection.

cond-mat.stat-mech↗

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

Instability triggered by mixed convection in a thin fluid layer

We investigate the convective stability of a thin, infinite fluid layer with a rectangular cross-section, subject to imposed heat fluxes at the top and bottom and fixed temperature along the vertical sides. The instability threshold depends on the Prandtl number as well as the normalized flux difference ($f$) and decreases with the aspect ratio ($ε$), following a $εf^{-1}$ power law. Using 3D initial value and 2D eigenvalue calculations, we identify a dominant 3D mode characterized by two transverse standing waves attached to the domain edges. We characterize the dominant mode's frequency and transverse wave number as functions of the Rayleigh number and aspect ratio. An analytical asymptotic solution for the base state in the bulk is obtained, valid over most of the domain and increasingly accurate for lower aspect ratios. A local stability analysis, based on the analytical base state, reveals oscillatory transverse instabilities consistent with the global instability characteristics. The source term for this most unstable mode appears to be interactions between vertical shear and horizontal temperature gradients.

physics.flu-dyn↗

arXiv2025

Rapidly Rotating Wall-Mode Convection

In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode convection is a multiscale phenomenon where the dynamics of the bulk interior diagnostically determine the small-scale dynamics within Stewartson boundary layers at the sidewalls. The sidewall boundary layers feedback on the interior via a nonlinear lateral heat-flux boundary condition, providing a closed system. Outside the asymptotically thin boundary layer, the convective modes connect to a dynamical interior that maintains scales set by the domain geometry. In many ways, the final system of equations resembles boundary-forced planetary geostrophic baroclinic dynamics coupled with barotropic quasi-geostrophic vorticity. The reduced system contains the results from previous linear instability theory but captured in an elementary fashion, providing a new avenue for investigating wall-mode convection in the strongly nonlinear regime. We also derive the dominant Ekman-flux correction to the onset Rayleigh number for large Taylor number, $\textit{Ra} \approx 31.8 \,\textit{Ta}^{1/2} - 4.43 \,\textit{Ta}^{5/12} + \mathcal{O}(\textit{Ta}^{1/3})$ for no-slip boundaries. However, we find that the linear onset in a finite cylinder differs noticeably compared to a Cartesian channel. We demonstrate some of the reduced model's nonlinear dynamics with numerical simulations in a cylindrical container.

physics.flu-dyn↗

arXiv2025

Fast automated adjoints for spectral PDE solvers

We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic differentiation to symbolic graph representations of PDEs, efficiently constructing adjoint solvers that retain the speed and memory efficiency of this important class of modern numerical methods. This approach enables users to compute gradients and perform optimization for a wide range of time-dependent and nonlinear systems without writing additional code. The framework supports a broad class of equations, geometries, and boundary conditions, and runs efficiently in parallel using MPI. We demonstrate the flexibility and capabilities of this system using canonical problems from the literature, showing both strong performance and practical utility for a wide variety of inverse problems. By integrating automatic adjoints into a flexible high-level solver, our approach enables researchers to perform gradient-based optimization and sensitivity analyses in spectral simulations with ease and efficiency.

math.NA↗

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↗

arXiv2024

Corner cases of the tau method: symmetrically imposing boundary conditions on hypercubes

Polynomial spectral methods produce fast, accurate, and flexible solvers for broad ranges of PDEs with one bounded dimension, where the incorporation of general boundary conditions is well understood. However, automating extensions to domains with multiple bounded dimensions is challenging because of difficulties in imposing boundary conditions at shared edges and corners. Past work has included various workarounds, such as the anisotropic inclusion of partial boundary data at shared edges or approaches that only work for specific boundary conditions. Here we present a general system for imposing boundary conditions for elliptic equations on hypercubes. We take an approach based on the generalized tau method, which allows for a wide range of boundary conditions for many different spectral schemes. The generalized tau method has the distinct advantage that the specified polynomial residual determines the exact algebraic solution; afterwards, any stable numerical scheme will find the same result. We can, therefore, provide one-to-one comparisons to traditional collocation and Galerkin methods within the tau framework. As an essential requirement, we add specific tau corrections to the boundary conditions, in addition to the bulk PDE, which produce a unique set of compatible boundary data at shared subsurfaces. Our approach works with general boundary conditions that commute on intersecting subsurfaces, including Dirichlet, Neumann, Robin, and any combination of these on all boundaries. The boundary tau corrections can be made hyperoctahedrally symmetric and easily incorporated into existing solvers. We present the method explicitly for the Poisson equation in two and three dimensions and describe its extension to arbitrary elliptic equations (e.g. biharmonic) in any dimension.

math.NA↗

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↗

arXiv2023

Vortex line entanglement in active Beltrami flows

Over the last decade, substantial progress has been made in understanding the topology of quasi-2D non-equilibrium fluid flows driven by ATP-powered microtubules and microorganisms. By contrast, the topology of 3D active fluid flows still poses interesting open questions. Here, we study the topology of a spherically confined active flow using 3D direct numerical simulations of generalized Navier-Stokes (GNS) equations at the scale of typical microfluidic experiments. Consistent with earlier results for unbounded periodic domains, our simulations confirm the formation of Beltrami-like bulk flows with spontaneously broken chiral symmetry in this model. Furthermore, by leveraging fast methods to compute linking numbers, we explicitly connect this chiral symmetry breaking to the entanglement statistics of vortex lines. We observe that the mean of linking number distribution converges to the global helicity, consistent with the asymptotic result by Arnold. Additionally, we characterize the rate of convergence of this measure with respect to the number and length of observed vortex lines, and examine higher moments of the distribution. We find that the full distribution is well described by a k-Gamma distribution, in agreement with an entropic argument. Beyond active suspensions, the tools for the topological characterization of 3D vector fields developed here are applicable to any solenoidal field whose curl is tangent to or cancels at the boundaries in a simply connected domain.

physics.flu-dyn↗

arXiv2023

Dynamics, scaling behavior, and control of nuclear wrinkling

The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. Here, we combine live-imaging experiments, theory, and simulations to characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly, Drosophila melanogaster, when nurse cell nuclei increase in size and display stereotypical wrinkling behavior. A spectral analysis of three-dimensional high-resolution data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing mechanical properties of the nuclear envelope. Our findings advance the biophysical understanding of nuclear membrane fluctuations during early multicellular development.

physics.bio-ph↗

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

The Puzzling Structure of Solar Convection: Window into the Dynamo

The operation of the solar dynamo, with all of its remarkable spatio-temporal ordering, remains an outstanding problem of modern solar physics. A number of mechanisms that might plausibly contribute to its operation have been proposed, but the relative role played by each remains unclear. This uncertainty stems from continuing questions concerning the speed and structure of deep-seated convective flows. Those flows are in-turn thought to sustain both the Sun's turbulent EMF and the large-scale flows of differential rotation and meridional circulation suspected of influencing the dynamo's organization and timing. Continued progress in this area is complicated by (i) inconsistencies between helioseismic measurements of convective and meridional flow made with different techniques and instruments, and (ii) a lack of high-latitude data for convection, differential rotation, and meridional flow. We suggest that the path forward to resolving these difficulties is twofold. First, the acquisition of long-term helioseismic and emissivity measurements obtained from a polar vantage point is vital to complete our picture of the Sun's outer convection zone. Second, sustained and expanded investment in theory-oriented and combined theory/observational research initiatives will be crucial to fully exploit these new observations and to resolve inconsistencies between existing measurements.

astro-ph.SR↗

arXiv2022

Transport and emergent stratification in the equilibrated Eady model: the vortex gas scaling regime

We numerically and theoretically investigate the Boussinesq Eady model, where a rapidly rotating density-stratified layer of fluid is subject to a meridional temperature gradient in thermal wind balance with a uniform vertically sheared zonal flow. Through a suite of numerical simulations, we show that the transport properties of the resulting turbulent flow are governed by quasi-geostrophic (QG) dynamics in the rapidly rotating strongly stratified regime. The 'vortex gas' scaling predictions put forward in the context of the two-layer QG model carry over to this fully 3D system: the functional dependence of the meridional flux on the control parameters is the same, the two ajustable parameters entering the theory taking slightly different values. In line with the QG prediction, the meridional buoyancy flux is depth-independent. The vertical buoyancy flux is such that turbulence transports buoyancy along isopycnals, except in narrow layers near the the top and bottom boundaries, the thickness of which decreases as the diffusivities go to zero. The emergent (re)stratification is set by a simple balance between the vertical buoyancy flux and diffusion along the vertical direction. Overall, this study demonstrates how the vortex-gas scaling theory can be adapted to quantitatively predict the magnitude and vertical structure of the meridional and vertical buoyancy fluxes, and of the emergent stratification, without additional fitting parameters.

physics.flu-dyn↗

arXiv2022

Effective drag in rotating, poorly conducting plasma turbulence

Despite the increasing sophistication of numerical models of hot Jupiter atmospheres, the large time-scale separation required in simulating the wide range in electrical conductivity between the dayside and nightside has made it difficult to run fully consistent magnetohydrodynamic (MHD) models. This has led to many studies that resort to drag parametrizations of MHD. In this study, we revisit the question of the Lorentz force as an effective drag by running a series of direct numerical simulations of a weakly rotating, poorly conducting flow in the presence of a misaligned, strong background magnetic field. We find that the drag parametrization fails once the time-scale associated with the Lorentz force becomes shorter than the dynamical time-scale in the system, beyond which the effective drag coefficient remains roughly constant, despite orders-of-magnitude variation in the Lorentz (magnetic) time-scale. We offer an improvement to the drag parametrization by considering the relevant asymptotic limit of low conductivity and strong background magnetic field, known as the quasi-static MHD approximation of the Lorentz force. This approximation removes the fast time-scale associated with magnetic diffusion, but retains a more complex version of the Lorentz force, which could be utilized in future numerical models of hot Jupiter atmospheric circulation.

physics.flu-dyn↗

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

Direct Statistical Simulation of the Busse Annulus

We consider direct statistical simulation (DSS) of a paradigm system of convection interacting with mean flows. In the Busse Annulus model zonal jets are generated through the interaction of convectively driven turbulence and rotation; non-trivial dynamics including the emergence of multiple jets and bursting `predator-prey' type dynamics can be found. We formulate the DSS by expanding around the mean flow in terms of equal-time cumulants and arrive at a closed set of equations of motion for the cumulants. Here, we present results using an expansion terminated at the second cumulant (CE2); it is fundamentally a quasi-linear theory. We focus on particular cases including bursting and bistable multiple jets and demonstrate that CE2 can reproduce the results of direct numerical simulation if particular attention is given to symmetry considerations.

physics.flu-dyn↗