arXiv subjects

Jeffrey B. Parker

Publications and source records attributed to Jeffrey B. Parker.

16 recordsLinked to original sources

arXiv2025

High-resolution simulations unravel intensification mechanisms of pyrocumulonimbus clouds

Pyrocumulonimbus (pyroCb) firestorms -- wildfire-generated thunderstorms -- can trigger rapid fire spread. However, the multi-physics nature of pyroCb has made their core mechanisms inaccessible to direct observation and previous simulation and prediction efforts. We introduce a new simulation capability with the first high-resolution, fully coupled simulations of a pyroCb, allowing us to unravel its life cycle governed by two opposing mechanisms. We show fuel moisture is an energy sink that attenuates fire intensity rather than fueling clouds, resolving a long-standing debate. Conversely, we identify the driver of rapid intensification: the Self-Amplifying Fire-Induced Recirculation (SAFIR) mechanism, where precipitation-induced downdrafts intensify the parent fire under weak winds. This work provides a new mechanistic framework for pyroCb prediction and demonstrates a transformative computational approach for previously intractable problems in environmental science.

physics.ao-ph↗

arXiv2024

DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of these systems exhibit ergodicity and an attractor: a compact and highly complex manifold, to which trajectories converge in finite-time, that supports an invariant measure, i.e., a probability distribution that is invariant under the action of the dynamics, which dictates the long-term statistical behavior of the system. In this work, we leverage this structure to propose a new framework that targets learning the invariant measure as well as the dynamics, in contrast with typical methods that only target the misfit between trajectories, which often leads to divergence as the trajectories' length increases. We use our framework to propose a tractable and sample efficient objective that can be used with any existing learning objectives. Our Dynamics Stable Learning by Invariant Measure (DySLIM) objective enables model training that achieves better point-wise tracking and long-term statistical accuracy relative to other learning objectives. By targeting the distribution with a scalable regularization term, we hope that this approach can be extended to more complex systems exhibiting slowly-variant distributions, such as weather and climate models.

cs.LG↗

arXiv2021

Topological phase in plasma physics

Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological phase can also be fruitfully applied to plasmas. Here, the theory of topological phase is introduced, including a discussion of Berry phase, Berry connection, Berry curvature, and Chern number. One of the clear physical manifestations of topological phase is the bulk-boundary correspondence, the existence of localized unidirectional modes at the interface between topologically distinct phases. These concepts are illustrated through examples, including the simple magnetized cold plasma. An outlook is provided for future theoretical developments and possible applications.

physics.plasm-ph↗

arXiv2021

Simulating nonnative cubic interactions on noisy quantum machines

As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates instead of a restricted set of standard gates. We demonstrate the general methodology by solving a cubic interaction problem, which appears in nonlinear optics, gauge theories, as well as plasma and fluid dynamics. To encode the nonnative Hamiltonian evolution, we decompose the Hilbert space into a direct sum of invariant subspaces in which the nonlinear problem is mapped to a finite-dimensional Hamiltonian simulation problem. In a three-states example, the resultant unitary evolution is realized by a product of ~20 standard gates, using which ~10 simulation steps can be carried out on state-of-the-art quantum hardware before results are corrupted by decoherence. In comparison, the simulation depth is improved by more than an order of magnitude when the unitary evolution is realized as a single cubic gate, which is compiled directly using optimal control. Alternatively, parametric gates may also be compiled by interpolating control pulses. Modular gates thus obtained provide high-fidelity building blocks for quantum Hamiltonian simulations.

quant-ph↗

arXiv2020

Nontrivial topology in the continuous spectrum of a magnetized plasma

Classification of matter through topological phases and topological edge states between distinct materials has been a subject of great interest recently. While lattices have been the main setting for these studies, a relatively unexplored realm for this physics is that of continuum fluids. In the typical case of a fluid model with a point spectrum, nontrivial topology and associated edge modes have been observed previously. However, another possibility is that a continuous spectrum can coexist with the point spectrum. Here we demonstrate that a fluid plasma model can harbor nontrivial topology within its continuous spectrum, and that there are boundary modes at the interface between topologically distinct regions. We consider the ideal magnetohydrodynamics (MHD) model. In the presence of magnetic shear, we find nontrivial topology in the Alfvén continuum. For strong shear, the Chern number is $\pm 1$, depending on the sign of the shear. If the magnetic shear changes sign within the plasma, a topological phase transition occurs, and bulk-boundary correspondence then suggests a mode localized to the layer of zero magnetic shear. We confirm the existence of this mode numerically. Moreover, this reversed-shear Alfvén eigenmode (RSAE) is well known within magnetic fusion as it has been observed in several tokamaks. In examining how the MHD model might be regularized at small scales, we also consider the electron limit of Hall MHD. We show that the whistler band, which plays an important role in planetary ionospheres, has nontrivial topology. More broadly, this work raises the possibility that fusion devices could be carefully tailored to produce other topological states with potentially useful behavior.

physics.plasm-ph↗

arXiv2020

Quantum phase estimation for a class of generalized eigenvalue problems

Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = λv$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to generalized eigenvalue problems $Av = λB v$, which arise in many areas of science and engineering. We answer this question affirmatively. A restricted class of generalized eigenvalue problems could be solved as efficiently as standard eigenvalue problems. A paradigmatic example is provided by Sturm--Liouville problems. Another example comes from linear ideal magnetohydrodynamics, where phase estimation could be used to determine the stability of magnetically confined plasmas in fusion reactors.

quant-ph↗

arXiv2020

Topological Gaseous Plasmon Polariton in Realistic Plasma

Nontrivial topology in bulk matter has been linked with the existence of topologically protected interfacial states. We show that a gaseous plasmon polariton (GPP), an electromagnetic surface wave existing at the boundary of magnetized plasma and vacuum, has a topological origin that arises from the nontrivial topology of magnetized plasma. Because a gaseous plasma cannot sustain a sharp interface with discontinuous density, one must consider a gradual density falloff with scale length comparable or longer than the wavelength of the wave. We show that the GPP may be found within a gapped spectrum in present-day laboratory devices, suggesting that platforms are currently available for experimental investigation of topological wave physics in plasmas.

physics.plasm-ph↗

arXiv2019

Magnetic eddy viscosity of mean shear flows in two-dimensional magnetohydrodynamics

Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than~1 has long been known to cause magnetic drag. Here, we show that when $\mathrm{Rm} \gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approximately $(B_p^2/2μ_0) τ_{\rm corr}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraro's law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains such as the interior of some gas giants.

physics.plasm-ph↗

arXiv2018

Magnetic suppression of zonal flows on a beta plane

Zonal flows in rotating systems have been previously shown to be suppressed by the imposition of a background magnetic field aligned with the direction of rotation. Understanding the physics behind the suppression may be important in systems found in astrophysical fluid dynamics, such as stellar interiors. However, the mechanism of suppression has not yet been explained. In the idealized setting of a magnetized beta plane, we provide a theoretical explanation that shows how magnetic fluctuations directly counteract the growth of weak zonal flows. Two distinct calculations yield consistent conclusions. The first, which is simpler and more physically transparent, extends the Kelvin-Orr shearing wave to include magnetic fields and shows that weak, long-wavelength shear flow organizes magnetic fluctuations to absorb energy from the mean flow. The second calculation, based on the quasilinear, statistical CE2 framework, is valid for arbitrary wavelength zonal flow and predicts a self-consistent growth rate of the zonal flow. We find that a background magnetic field suppresses zonal flow if the bare Alfven frequency is comparable to or larger than the bare Rossby frequency. However, suppression can occur for even smaller magnetic fields if the resistivity is sufficiently small enough to allow sizable magnetic fluctuations. Our calculations reproduce the $η/B_0^2 = \text{const.}$ scaling that describes the boundary of zonation, as found in previous work, and we explicitly link this scaling to the amplitude of magnetic fluctuations.

astro-ph.SR↗

arXiv2018

Investigation of a Multiple-Timescale Turbulence-Transport Coupling Method in the Presence of Random Fluctuations

One route to improved predictive modeling of magnetically confined fusion reactors is to couple transport solvers with direct numerical simulations (DNS) of turbulence, rather than with surrogate models. An additional challenge presented by coupling directly with DNS is that the inherent fluctuations in the turbulence, which limit the convergence achievable in the transport solver. In this article, we investigate the performance of one numerical coupling method in the presence of turbulent fluctuations. To test a particular numerical coupling method for the transport solver, we use an autoregressive-moving-average model to efficiently generate stochastic fluctuations with statistical properties resembling those of a gyrokinetic simulation. These fluctuations are then added to a simple, solvable problem, and we examine the behavior of the coupling method. We find that monitoring the residual as a proxy for the error can be misleading. From a pragmatic point of view, this study aids us in the full problem of transport coupled to DNS by predicting the amount of averaging required to reduce the fluctuation error and obtain a specific level of accuracy.

physics.plasm-ph↗

arXiv2018

Bringing global gyrokinetic turbulence simulations to the transport timescale using a multiscale approach

The vast separation dividing the characteristic times of energy confinement and turbulence in the core of toroidal plasmas makes first-principles prediction on long timescales extremely challenging. Here we report the demonstration of a multiple-timescale method that enables coupling global gyrokinetic simulations with a transport solver to calculate the evolution of the self-consistent temperature profile. This method, which exhibits resiliency to the intrinsic fluctuations arising in turbulence simulations, holds potential for integrating nonlocal gyrokinetic turbulence simulations into predictive, whole-device models.

physics.plasm-ph↗

arXiv2018

Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics

Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. We find that CE2-GO retains some similarities to QL. The partitioning of energy that resides in the zonal flow is in good quantitative agreement between CE2-GO and QL. On the other hand, the length scale of the zonal flow does not follow the same qualitative trend in the two models. Overall, these simulations indicate that CE2-GO provides a simpler and more tractable statistical paradigm than CE2, but CE2-GO is missing important physics.

physics.plasm-ph↗

arXiv2016

Dynamics of Zonal Flows: Failure of Wave-Kinetic Theory, and New Geometrical Optics Approximations

The self-organization of turbulence into regular zonal flows can be fruitfully investigated with quasilinear methods and statistical descriptions. A wave kinetic equation that assumes asymptotically large-scale zonal flows is pathological. From an exact description of quasilinear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.

physics.plasm-ph↗

arXiv2015

Zonal Flow as Pattern Formation

In this section, we examine the transition from statistically homogeneous turbulence to inhomogeneous turbulence with zonal flows. Statistical equations of motion can be derived from the quasilinear approximation to the Hasegawa-Mima equation. We review recent work that finds a bifurcation of these equations and shows that the emergence of zonal flows mathematically follows a standard type of pattern formation. We also show that the dispersion relation of modulational instability can be extracted from the statistical equations of motion in a certain limit. The statistical formulation can thus be thought to offer a more general perspective on growth of coherent structures, namely through instability of a full turbulent spectrum. Finally, we offer a physical perspective on the growth of large-scale structures.

physics.plasm-ph↗

arXiv2015

Zonal Flows and Turbulence in Fluids and Plasmas

In geophysical and plasma contexts, zonal flows are well known to arise out of turbulence. We elucidate the transition from statistically homogeneous turbulence without zonal flows to statistically inhomogeneous turbulence with steady zonal flows. Starting from the Hasegawa--Mima equation, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking `zonostrophic instability'. Zonostrophic instability can be understood in a very general way as the instability of some turbulent background spectrum to a zonally symmetric coherent mode. As a special case, the background spectrum can consist of only a single mode. We find that in this case the dispersion relation of zonostrophic instability from the CE2 formalism reduces exactly to that of the 4-mode truncation of generalized modulational instability. We then show that zonal flows constitute pattern formation amid a turbulent bath. Zonostrophic instability is an example of a Type I$_s$ instability of pattern-forming systems. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation, the real Ginzburg-Landau equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the zonal flow wavelength is not unique. In an idealized, infinite system, there is a continuous band of zonal flow wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors ...

physics.plasm-ph↗

arXiv2013

Zonal Flow as Pattern Formation

Zonal flows are well known to arise spontaneously out of turbulence. We show that for statistically averaged equations of the stochastically forced generalized Hasegawa-Mima model, steady-state zonal flows and inhomogeneous turbulence fit into the framework of pattern formation. There are many implications. First, the wavelength of the zonal flows is not unique. Indeed, in an idealized, infinite system, any wavelength within a certain continuous band corresponds to a solution. Second, of these wavelengths, only those within a smaller subband are linearly stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets.

physics.ao-ph↗