2018 GTP Abstracts

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Jonathan Aurnou, UCLA

Title: On the reinterpretation of magnetostrophic balance in dynamo systems

Abstract: Planetary magnetic field generation has long been argued to be the result of magnetostrophic dynamo action, in which the leading order forces are due to the Coriolis, Lorentz and pressure terms. A number of recent dynamo models claim to be operating in this purported ultimate dynamo regime. Here I will argue that these simulations are more likely in leading order quasi-geostrophic (QG) balance, with magnetostrophic effects occurring only at higher orders. Thus, presenting these simulations as examples of leading order magnetostrophy is a reinterpretation of the very definition of this regime. Simple scaling arguments will be presented that imply that turbulent planetary dynamos and dynamo models most likely operate in the QG dynamo regime. Whether or not leading order magnetostrophic dynamo action can occur in planetary settings remains an open, unanswered question.

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Amitava Bhattacharjee, Princeton University

Title: The magnetic shear current effect: implications for the accretion disk and the solar dynamo

Abstract: Recently, there has been a significant advance in our theoretical understanding of the turbulent dynamo /1/. Known as the magnetic shear current effect, it has been demonstrated that in the presence of background sheared flows, a turbulent system shows spontaneous growth of the large-scale magnetic field from a small-scale dynamo (which carries magnetic energy but no net flux). We will report on further developments of the theory, applying it to stratified accretion disks and the solar convection zone. 1. J. Squire and A. Bhattacharjee, Physical Review Letters 115,175003 (2015)

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Eric Blackman, University of Rochester

Title: Toward connecting fundamental mean field electrodynamics to practical observational models

Abstract: Mean field electrodynamics (MFE) facilitates practical modeling of secular, large scale properties of magnetohydrodynamic or plasma systems with fluctuations. But there are conceptual gaps between work focused on fundamental principles of mean field theory in idealized systems and the practical use of mean field theory to compare to observations. I will address multiple aspects of this issue. First, even the concept of “large scale” can mean different things in different contexts. Second, in the context of large scale dynamo theory, practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. But real systems do not exhibit such scale separation. This raises questions of how to generalize the equations of MFE in the presence of mesoscale fluctuations and how precise are theoretical predictions from MFE in general? The latter quantifies the resolution of predictive power of the theory and is important when comparing to observations, as will be exemplified for galactic dynamos and accretion disks. And in the context of accretion disks, there have been decades of simulations of accretion type flows, but little feedback from lessons learned into improvements in practical disk models models used to compare to observations. Given evidence from both simulations and observations that large scale transport is important, there is a specific need and opportunity to augment mean field accretion disk theory to better accommodate this non-local transport.

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Eberhard Bodenschatz, Max Planck Institute for Dynamics and Self-Organization

Title: Streaming instability in protoplanetary discs [Holly L. Capelo, Jan Molacek, Michiel Lambrechts, John Lawson , Anders Johansen, Jürgen Blum, Eberhard Bodenschatz, Haitao Xu]

Abstract: How planetary precursors (planetesimals) from out of the primordial dust grains present in gaseous protoplanetary discs remains an open question. While grain adhesion forces bind solids at small scales (micrometers-decimeters) and gravity on large scales (kilometers), bridging these extremes across growth barriers in the meter size range requires an additional solid-concentration mechanism, usually assumed to derive from collective gas-particle interaction. I present the results from ground-based experiments designed to test the most well-accepted theory of particle concentration due to 'streaming instability' (SI) in protoplanetary discs. The experimental data demonstrate spontaneous concentration of spherical dust-particle analogues via fluid instability. The conditions involve a very dilute, low Reynold's number flow (Re

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Guido Boffetta, University of Torino

Title: Rotating Rayleigh-Taylor turbulence

Abstract: The statistics of Rayleigh-Taylor turbulence in presence of rotation is studied by means of direct numerical simulations within the Oberbeck- Boussinesq approximation. On the basis of theoretical arguments, supported by simulations, it is shown that the Rossby number decreases in time, and therefore the Coriolis force becomes more important as the system evolves and produces several effects. Rotation reduces the intensity of turbulent velocity fluctuations and therefore the growth rate of the temperature mixing layer. As a consequence of the Taylor-Proudman bidimensionalization of the velocity field, the integral scale based on velocity fluctuations decouples from the integral scale associated to temperature fluctuations. The conversion of potential energy into turbulent kinetic energy is found to be less effective in the presence of rotation and the efficiency of the heat transfer is reduced for any value of rotation.

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Axel Brandenburg, NORDITA & University of Colorado

Title: The turbulent chiral-magnetic cascade in the early universe

Abstract: The presence of asymmetry between fermions of opposite handedness in plasmas of relativistic particles can lead to exponential growth of a helical magnetic field via a small-scale chiral dynamo instability known as the chiral magnetic effect. Here, we show, using dimensional arguments and numerical simulations, that this process produces through the Lorentz force chiral magnetically driven turbulence. A k^{-2} magnetic energy spectrum emerges via inverse transfer over a certain range of wavenumbers k. The total chirality (magnetic helicity plus normalized chiral chemical potential) is conserved in this system. Therefore, as the helical magnetic field grows, most of the total chirality gets transferred into magnetic helicity until the chiral magnetic effect terminates. Quantitative results for height, slope, and extent of the spectrum are obtained. Consequences of this effect for cosmic magnetic fields are discussed.

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Benjamin Brown, University of Colorado

Title: Overshoot in low-Mach number, rotating, stellar convection

Abstract: In natural systems, regions of convection are often bounded by regions of stable-stratification, where convective motions stop and wave motions dominate. In stars like the Sun, this occurs at the bottom of the convection zone, while in the cores of massive stars this occurs at the top of the convection zone. In all cases, it is crucially important to understand how far nonlinear motions extend beyond the nominal convective boundary, and what sets the location of that boundary. Here, using the Dedalus framework, we study the degree of overshoot in rotating stratified systems. We explore the difference between systems where the convective/stable boundary is externally imposed and those systems where that boundary is self-consistently achieved by balances between sources of internal heating and thermal diffusion coefficients that vary in response to the evolved thermodynamics of the flows.

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Nicholas Brummell, University of California, Santa Cruz

Title: Transport of large-scale magnetic fields in the solar interior

Abstract: Numerous mechanisms for the transport of magnetic field are available in the solar interior. For example, magnetic buoyancy is usually cited as the major upward transport of large but concentrated magnetic field to create emergence at the photosphere, whereas magnetic and gyroscopic pumping are often invoked for the confinement of large-scale diffuse magnetic field. This talk will examine some aspects of these matters.

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Michael Calkins, University of Colorado

Title: Asymptotic models for rapidly rotating magnetohydrodynamics

Abstract: The majority of planets and stars possess global-scale magnetic fields that are generated by the motion of electrically-conducting fluid. Rotation plays a fundamental role in the generation process, but studying these systems with direct numerical simulation (DNS) remains difficult due to the vast range of spatiotemporal scales that characterize them. Asymptotic models represent an alternative to DNS that can access more extreme parameter regimes, and therefore help improve our understanding of natural dynamos. I will discuss several interesting results from numerical simulations of convection-driven asymptotic magnetohydrodynamic models, including the influence of electromagnetic fields on heat transfer and large-scale, turbulent flows. A comparison between the asymptotic models and DNS will also be presented.

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Herman Clercx, Eindhoven University of Technology, The Netherlands

Title: Rotating Rayleigh-Bénard convection: probing the transition to the rotation-dominated regime

Abstract: (Rudie Kunnen & Herman Clercx) Most geo- and astrophysical flows are driven by strong thermal forcing and affected by high rotation. In these systems, direct measurements of the physical quantities are not possible due to their large scales, remoteness and complexity. A model containing the main physical constituents is rather beneficial. This approach is given by the problem of rotating Rayleigh-Bénard convection (RRBC): a rotating fluid layer heated from below and cooled from above. For large-scale systems, the governing parameters of RRBC take extreme values, leading to a regime of geostrophic turbulence. Background rotation causes different flow structures and heat transfer efficiencies in Rayleigh-Bénard convection. Three main regimes are known: rotation-unaffected (regime I), rotation-affected (regime II) and rotation-dominated (regime III). Regimes I and II are easily accessible with experiments and numerical simulations, thus they have been extensively studied, see for a recent review [1]. On the other hand, access to regime III is more troublesome. Thus, regime III and the transition to this regime are less explored. Approaching the geostrophic regime of rotating convection, where the flow is highly turbulent and at the same time dominated by the Coriolis force, typically requires dedicated setups with either extreme dimensions or troublesome working fluids (e.g., cryogenic helium). In this study, we explore the possibilities of entering the geostrophic regime of rotating convection with classical experimental tools: a table-top conventional convection cell with a height of 0.2 m and water as the working fluid [2]. In order to examine our experimental measurements, we compare the spatial vorticity autocorrelations with the statistics from simulations of geostrophic convection reported earlier [3]. Our findings show that we have indeed access to the geostrophic convection regime and can observe the signatures of the typical flow features reported in the aforementioned simulations. As a next step we explored the role of coherent flow structures on the transition to regime III in RRBC. There are two main hypotheses proposed for the driving mechanisms of the transition to regime III one of them directly related to flow coherency. These hypotheses are usually examined through different parameters such as viscous and thermal boundary layers thicknesses and heat transfer efficiency [4,5]. In this work, we study regime III and these hypotheses from a new perspective: Lagrangian velocity and acceleration fluctuations and autocorrelations of tracers from experiments. We have found that the transition to regime III coincides with three phenomena; the vertical motions are suppressed, the vortical plumes penetrate further into the bulk and the vortical plumes interact less with their surroundings. These findings allow us to evaluate the available hypotheses and to understand more about regime III [6]. Finally, and if time allows, we will discuss some first results from a dedicated setup designed to study the unexplored parts of the geostrophic convection regime in detail. [1] R.J.A.M. Stevens, H.J.H. Clercx and D. Lohse, Eur. J. Mech. B/Fluids 40, 41-49 (2013). [2] D. Nieves, A.M. Rubio and K. Julien, Phys. Fluids 26, 086602 (2014). [3] H. Rajaei, R.P.J. Kunnen and H.J.H. Clercx, Phys. Fluids 29, 045105 (2017). [4] E.M. King, S. Stellmach, J. Noir, U. Hansen and J.M. Aurnou, Nature 457, 301-304 (2009). [5] K. Julien, E. Knobloch, A.M. Rubio and G.M. Vasil, Phys. Rev. Lett. 109, 254503 (2012). [6] H. Rajaei, K.M.J. Alards, R.P.J. Kunnen and H.J.H. Clercx, submitted (2017)

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Steven Cranmer, University of Colorado

Title: Corotating streams in solar and stellar winds

Abstract: All stars are believed to possess expanding outer atmospheres known as stellar winds. These outflows serve as a unique "plasma laboratory" not only because they help us better understand some fundamental physical processes, but also because the winds themselves have significant impacts on nearby planets and the interstellar medium. Stars also rotate, so their winds tend to be influenced by a combination of centrifugal/Coriolis forces, magnetohydrodynamics (MHD), and radiative transfer. This talk will review what we know about the ways stellar winds generate structured corotating flows. The local solar wind is comprised of small-scale MHD turbulence that flows through larger-scale corotating interaction regions (CIRs). CIRs are generated by the complex solar magnetic field (which is in turn driven by the Sun's convection zone) and they can be a source of potentially dangerous space weather. Recent multi-scale simulations include both turbulence and CIR evolution, and they successfully predict many properties of the observed solar wind. The signatures of CIRs are also seen in the vicinity of massive stars that do not have subsurface convection. In these cases, the corotating streams are believed to be driven by either global pulsations or bright starspots. The insights gained from decades of studying solar CIRs continue to guide the study of variable outflows from a wide range of other stars.

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Mausumi Dikpati, NCAR/HAO

Title: Role of tachocline nonlinear oscillations (TNOs) in producing "solar seasons"

Abstract: Recent observations indicate that solar cycle variability consists of short-term quasi-periodic bursts of magnetic activity, called ``solar seasons''. Burst periods are 6-18 months. Using a nonlinear MHD shallow water tachocline model we show that a back-and-forth exchange of energy between tachocline latitudinal differential rotation and Rossby waves occurs with a periodicity of 2-20 months, for a wide range of effective gravities, differential rotation amplitude, latitude location of toroidal magnetic bands and their peak field strength. These Tachocline Nonlinear Oscillations (TNOs) can cause enhanced activity bursts when the Rossby wave energy grows to its maximum, because the tachocline top surface is maximally deformed then. Hence, nearly 'frozen-in' toroidal fields can enter the convection zone from the tachocline, starting their buoyant rise to the surface to erupt as active regions. The bursty phase is followed by a relatively quiet phase, during which the differential rotation gets restored by extracting energy from Rossby waves and top surface deformations subside. TNOs involve periodic reversals in energy-flow among six reservoirs by means of eight different energy conversion processes. TNO periods decrease with the increase of differential rotation amplitude, the effective gravity, the field strength and the latitude location of toroidal magnetic band. We also find that the TNO period increases with the decrease in rotation rate, implying that the younger Sun had more frequent seasons.

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Keren Duer, Weizmann Institute of Science

Title: The interaction between the flow and the magnetic field in atmospheres of gas-giants

Abstract: The nature of Jupiter's deep flow, as well as other gas giants, is still largely unknown. The recent gravity measurements from the Juno spacecraft, currently orbiting Jupiter, have led to significant progress, revealing that the depth of the observed zonal jets, as they appear at the cloud-level, extend to depths of about 3000 km. This depth is also where the electrical conductivity is high enough so that the magnetic field affects the flow and visa-versa. This unique interaction between the flow field and the magnetic field in the semi-conductive region might hold the answer for the specific depth of the winds. In regions where the Lorentz force plays an important role, geostrophic balance breaks and a magnetostrophic balance must be applied. Here, we analyze this interaction using a general circulation model that includes the MHD effects, focusing on the interaction between the interior and the atmospheric flows by applying constant background magnetic field and an induced one created from the conductive flows. We also show how further constraints on Jupiter's flow can be obtained by combining the Juno gravity and magnetic field independent measurements.

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Yuhong Fan, NCAR/HAO

Title: Magnetic flux emergence in the solar convective envelope

Abstract: It remains uncertain whether emerging flux responsible for the formation of solar active regions rises from the overshoot region at the bottom of the solar convection zone or is generated in the bulk of the convection zone. We present 3D MHD simulations of the convective dynamo in the rotating solar convective envelope, which produces a large-scale mean magnetic field that show irregular cyclic behavior and the emergence of super-equipartition toroidal flux bundles that exhibit properties similar to emerging solar active regions. We compare the properties of such emerging flux produced by the convective dynamo with those resulting from the buoyant rise of isolated, highly super-equipartition toroidal flux tubes from the overshoot region at the bottom of the convection zone based on thin flux tube simulations.

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Nicholas Featherstone, University of Colorado

Title: The planetary stellar dynamo

Abstract: While the details may differ, the fundamental building blocks of a dynamo are the same whether that dynamo originates within a planetary or stellar interior. Heat emanating from within the core of such an object is transported outward, across some fraction of the interior, by the bulk motion of an electrically-conducting fluid. In planets, this fluid might be a liquid metal, as with iron in the Earth's core. In stellar interiors, this fluid is a dense plasma, consisting primarily of ionized hydrogen and helium. In either instance, the convective motion of this fluid, sustained through the steady release of heat in the interior, gives rise to electrical currents that induce an associated magnetic field. The fundamental difference between planetary and stellar dynamos has long been assumed to be one of timescales. Planets are thought to possess convective overturnings that occur on timescales much longer than their rotation periods. In stars, particularly the Sun, these timescales have historically been assumed to be more similar in magnitude. Recent progress in helioseismology and numerical modeling suggests that solar convective flows may be 10-100 times slower than originally thought, calling into question the meaning of "slowly-rotating" and "rapidly-rotating" in the stellar context. In this talk, I will discuss the implications of these results for stellar dynamo theory and describe how numerical models might be used to further constrain convective flow speeds in the Sun and other stars.

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Federico Gasperini, HAO

Title: A whole-atmospheric perspective on connections between intra-seasonal variations in the troposphere and thermosphere

Abstract: In the last decade evidence demonstrated that terrestrial weather greatly impacts the dynamics and mean state of the thermosphere via small-scale gravity waves and global-scale solar tidal propagation and dissipation effects. While observations have shown significant intra-seasonal variability in the upper mesospheric mean winds, relatively little is known about this variability at satellite altitudes (∼250–400 km). Using cross-track wind measurements from the Challenging Minisatellite Payload (CHAMP) and Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellites, winds from a Modern-Era Retrospective Analysis for Research and Applications/Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model (MERRA/TIME-GCM) simulation, and Outgoing Longwave Radiation (OLR) data, strong coupling between the troposphere and the thermosphere is found to occur on intra-seasonal timescales.

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Andrew Gilbert, University of Exeter

Title: Geometric generalised Lagrangian mean theories

Abstract: Many fluctuation-driven phenomena in fluids can be analysed effectively using the generalised Lagrangian mean (GLM) theory of Andrews & McIntyre (1978). This finite amplitude theory relies on particle-following averaging to incorporate the constraints imposed by the material conservation of certain quantities in inviscid regimes. Its original formulation, in terms of Cartesian coordinates, relies implicitly on an assumed Euclidean structure; as a result, it does not have a geometrically intrinsic, coordinate-free interpretation on curved manifolds, and suffers from undesirable features. Motivated by this, we develop a geometric generalisation of GLM that we formulate intrinsically, using coordinate-free notation. One benefit is that the theory applies to arbitrary Riemannian manifolds; another is that it establishes a clear distinction between results that stem directly from geometric consistency and those that depend on particular choices. Starting from a decomposition of an ensemble of flow maps into mean and perturbation, we define the Lagrangian-mean momentum as the average of the pull-back of the momentum one-form by the perturbation flow maps. We show that it obeys a simple equation which guarantees the conservation of Kelvin's circulation, irrespective of the specific definition of the mean flow map. The Lagrangian-mean momentum is the integrand in Kelvin's circulation and distinct from the mean velocity (the time derivative of the mean flow map) which advects the contour of integration. A pseudomomentum consistent with GLM's can then be defined by subtracting the Lagrangian-mean momentum from the one-form obtained from the mean velocity using the manifold's metric. We mostly focus on the Euler equations for incompressible inviscid fluids but sketch out extensions to the rotating {stratified Boussinesq, compressible Euler, and magnetohydrodynamic equations.

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Laurent Gizon, Max-Plank Institute for Solar System Research

Title: Observations of large-scale equatorial Rossby waves in the solar interior

Abstract: I will report on observations of waves of vertical vorticity in maps of surface and subsurface solar flows. These waves have amplitudes that peak at the equator and propagate in the retrograde direction with the dispersion relation of textbook Rossby waves.

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Ian Grooms, University of Colorado

Title: Stochastic subgrid-scale parameterizations in geophysical turbulence applied to large-scale ocean modeling

Abstract: Stochastic parameterizations in geophysical turbulence are broadly reviewed, followed by specific discussion of a recent approach developed for large-scale ocean models. The approach begins by making a random-field model of the unresolved subgrid scales that can be sampled efficiently. Samples from this model are then used to generate the subgrid-scale feedback terms in a numerical model. The approach is described in the context of non-eddying global ocean models.

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Lee Gunderson, Princeton Plasma Physics Laboratory

Title: A model of solar equilibrium

Abstract: Helioseismology has revealed the internal density and rotation profile of the Sun. Yet, knowledge of its magnetic fields and meridional circulation is confined much closer to the surface, and mean entropy gradients at the surface are below detectable limits. Numerical simulations can offer insight into the interior dynamics, and help identify which ingredients are necessary to produce particular features. However, several gross features of the Sun can be understood from an equilibrium perspective, for example the 1-D density profile arising from steady-state energy transport from the core to the surface, or the tilting of isorotation contours in the convection zone due to baroclinic forcing. To help answer the question of which features can be qualitatively explained by equilibrium, we propose analyzing stationary axisymmetric ideal MHD flows in the solar regime. By choosing an appropriate latitudinal entropy profile, we recover a hydrodynamic rotation profile that reasonably matches observations in the bulk of the convection zone. By including the effects of poloidal flow, we develop a feature reminiscent of the near surface shear layer. Although, no tachocline-like feature is seen in hydrodynamic equilibrium, the model naturally incorporates magnetic fields, allowing for a natural extension to the magnetized interior. The transition between the a flow-dominated convection zone and a magnetic-dominated regime leads to a critical Alfven surface, and we are currently investigating if this layer can produce a tachocline-like feature.

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Lia Hankla, University of Colorado

Title: Dependence of the nonhelical dynamo on shear: numerical exploration of the magnetic shear-current and stochastic-alpha effects

Abstract: This project tests two models of the nonhelical dynamo: the stochastic-alpha effect and the magnetic shear-current effect. The former relies on random fluctuations of the alpha coefficient of mean-field theory, whereas the latter suggests that an off-diagonal resistive term can be negative, acting as a reverse diffusion of the magnetic field. Using unstratified shearing boxes, we explore the influence of these two models by varying the local shear. We find an as-yet unexplained jump in certain volume-averaged quantities (such as the ratio of Maxwell stress to magnetic energy) around a critical shearing parameter of q=1.2 which is only found in “tall” boxes whose length in the vertical direction is at least twice as long as the radial length. By analyzing the dynamo transport coefficients, a similar jump is found in the magnetic shear-current’s flagship coefficient, indicating the importance of the magnetic shear-current effect. However, inspecting the dependence of the dynamo growth rate reveals the presence of the stochastic-alpha effect as well. More work is needed to disentangle the two models in this setting.

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John Hawley, University of Virginia

Title: Tilted disks around black holes: elucidating the alignment mechanism

Abstract: When matter orbits around a black hole obliquely with respect to the hole’s spin axis, a relativistic torque causes the orbits to precess at a rate declining sharply with radius. Astrophysicists have long expected that in an orbiting accretion disk, the orbital angular momentum at small radii should align with the mass's spin. The location of the alignment front should be determined by a balance between the torque, the resulting differential precession, and warp-induced inward mixing of misaligned angular momentum from the outer to the inner disk. We are investigating the physics of this process through MHD simulations of mis-aligned disks. Our approach has been to use a semi-Newtonian method, in which the only relativistic effect retained is the lowest-order post-Newtonian term describing the torque. Through this approach, we have demonstrated a sound-speed dependence on the location of the alignment front, and the relative independence of the process from degree of black hole tilt.

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Susanne Horn, UCLA

Title: Flow morphologies in low Prandtl number rotating magneto-convection

Abstract: Many geophysical fluid dynamical systems, notably planetary cores, are characterised by a low Prandtl number Pr, i.e. the thermal diffusivity is greater than the kinematic viscosity. Unlike in moderate Pr ≥ 1 fluids, as used in most current day dynamo models, in low Pr fluids rotating convection can also occur in the form of thermal inertial oscillatory modes. We will present direct numerical simulations of the idealised problem of rotating Rayleigh-Bénard convection with and without mag-netic field in a cylindrical geometry. Depending on the strength of the thermal forcing, the magnetic field and the rotation rate, the flow becomes susceptible to several different instability mechanism, resulting generally in a highly multi-modal flow. We use the Dynamic Mode Decomposition (DMD) to extract and identify the flow structures that govern the dynamics, as well as their corresponding frequencies.

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Keith Julien, University of Colorado

Title: Reduced quasi-geostrophic dynamics and the impact of domain anisotropy on the inverse cascade

Abstract: TBD

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Yohai Kaspi, Weizmann Institute of Science

Title: Evidence from the Juno mission that Jupiter’s zonal jets extend down to the depth of magnetic dissipation

Abstract: The depth to which Jupiter's observed east-west jet-streams extend has been a long-standing question. Resolving this puzzle has been a primary goal of NASA's Juno mission to Jupiter, which has been in orbit around the gas giant since July 2016. Juno's gravitational measurements have improved the known accuracy of Jupiter’s gravity field by two orders of magnitude, and revealed that Jupiter's gravitational field is north-south asymmetric, which is a signature of atmospheric and interior flows within the planet. Using this asymmetry (measured gravity harmonics J3, J5, J7 and J9), we show that the observed jet-streams, as they appear at the cloud-level, extend down to depths of thousands of kilometers beneath the cloud-level, to the region of magnetic dissipation at a depth of about 3000 km. At these depths the Lorentz force acts to dissipate the flow and truncate the jets. Inverting the measured gravity values into a wind field, we provide the most likely vertical profile of the deep atmospheric and interior flow, and the latitudinal dependence of its depth. Furthermore, the even gravity harmonics (J8 and J10) resulting from this flow profile match the measurement as well, when taking into account the contribution of the interior structure. These results indicate that the mass of the dynamical atmosphere is about one percent of Jupiter's total mass. In this talk we will present the results from the Juno mission, the interpretation regarding the depth of the flows and model simulations focusing on the interaction between the flow and the magnetic field.

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Hubert Klahr, Max-Planck-Institute for Astronomy

Title: Radially and vertically stratified disks: stability and structure formation

Abstract: Radial buoyancy and vertical shear are both ingredients that can destabilise disks around young stars. Convective overstability and vertical shear instability are two candidates to efficiently create vortices, zonal flows and provide turbulent mixing and Reynolds stresses. Dust opacities are vital in mapping out regions that will undergo instability because optical depth determines both thermal structure and thermal relaxation. Here we show how the stabilities depend on parameters like stellar mass and luminosity, disk mass and opacity of the dust grains. We also report on the latest findings of numerical experiments discussing the formation and longevity of giant vortices.

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Daniel Lathrop, University of Maryland

Title: Waves, turbulence, and magnetic field predictability in spherical Couette flow

Abstract: The spherical Couette geometry is natural for examining planetary fluid flows. Rotation, shear, zonal flows, and the associated angular momentum fluxes are all naturally represented. In addition, by using a conducting fluid one can study the conditions of planetary cores and magnetic field / fluid interactions. Using a series of experiments, of increasing size and increasing power input (now a three-meter diameter system), we have examined liquid sodium spherical Couette flows to understand planetary cores. We have uncovered precessional flows, inertial waves, turbulent bi-stability, many turbulent states, magnetic field gain by the Omega effect, and most recently magnetic field gain in the axial dipole. In addition, we are exploring how machine-learning tools can be used to do short-term prediction of the time evolution of our laboratory magnetic fields variation.

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Michael Le Bars, CNRS, Aix-Marseille Univ, IRPHE, Marseille, France for Benjamin Favier, CNRS/IRPHE

Title: Inertial instabilities in rotating fluids: local models and wave turbulence

Abstract: This talk will focus on instabilities and resonances in rotating or stratified fluids driven by mechanical forcing. For example, when a moon orbits around a planet, the rotation of the induced tidal bulge drives a homogeneous, periodic, large-scale flow. The combination of such an excitation with the rotating motion of the planet has been shown to drive parametric resonance of a pair of inertial waves in a mechanism called the elliptical instability. Geophysical fluid layers can also be stratified: this is the case for instance of the Earth's oceans and, as suggested by several studies, of the upper part of the Earth's liquid outer core. We thus investigate the stability of a rotating and stratified layer undergoing tidal distortion in the limit where either rotation or stratification is dominant. We show that the periodic tidal flow drives a parametric subharmonic resonance of inertial (resp. internal) waves in the rotating (resp. stratified) case. The instability saturates into a wave turbulence pervading the whole fluid layer. In such a state, the instability mechanism conveys the tidal energy from the large scale tidal flow to the resonant modes, which then feed a succession of triadic resonances also generating small spatial scales. In addition to revealing an instability driving homogeneous turbulence in geophysical fluid layers, our approach is also an efficient numerical tool to investigate the possibly universal properties of wave turbulence in a geophysical context.

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Daniel Lecoanet, Princeton University

Title: Mean flow interaction with convectively generated internal waves

Abstract: We present a series of simulations of convective fluid underlying a stably stratified fluid (similar to the Earth's atmosphere or the interiors of massive stars). The convection excites internal gravity waves in the stably stratified layer. These waves undergo weak nonlinear interactions, and produce a coherent mean flow, which reverses on long time scales. The mean-flow oscillations are reminiscent of the quasi-biennial oscillation of winds in the equatorial stratosphere. We describe several reduced models of wave--mean-flow interaction which produce similar oscillations, but bypass the need to simulate the convective flow. These reduced models suggest that the intermittency and variability of the waves self-consistently generated by convection plays an important role in determining the features (period, amplitude) of the mean flow oscillations.

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Geoffroy Lesur, IPAG/Université Grenoble Alpes

Title: Winds and magnetic self-organisation in protoplanetary discs

Abstract: The planet-forming region of protoplanetary disks is cold, dense, and therefore weakly ionized. For this reason, MHD turbulence is thought to be mostly absent, and another mechanism has to be found to explain gas accretion. It has been proposed that magnetized winds, launched from the ionized disk surface, could drive accretion in the presence of a large-scale magnetic field. The efficiency and the impact of these surface winds on the disk structure is still highly uncertain. In this talk, I will present global simulations of a weakly ionized disk which exhibits large-scale magnetized winds and accretion. These magnetised accretion-ejection scenarios are prone to a large scale instability leading to self-organised ring-like structures. I will discuss the origin of this self-organisation and detail its potential observational implication.

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Philip Marcus, University of California at Berkeley

Title: The zombie and other instabilities in stratified, rotating, shearing flows & their roles in star and planet formation

Abstract: Without instabilities, gas around a forming protostar remains in orbit, and the final star cannot form; dust grains cannot accumulate to form planets; and the compositions of meteorites cannot be explained. Unfortunately, the Keplerian motion within a protoplanetary disk is assumed by most astrophysicists to be stable to purely hydrodynamic instabilities by Rayleigh’s theorem because the angular momentum of the disk increases with increasing radius, and the gas is too cool to ionize and allow magneto-rotational instabilities. Here we discuss the zombie and other instabilities that can grow and modify the rotating, stratified, shearing environments of protoplanetary disks. We present recent numerical results and discuss how dissipation, such as viscosity, thermal diffusivity, Newton cooling, and radiative transfer affect (and in the case of realistic dissipations in a protoplanetary disk, do NOT affect) the instabilities and their subsequent evolutions. We also compare our results with recent laboratory experiments in stratified plane Couette flows.

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Hiroake Matsui, UC Davis

Title: Dynamic sub-grid scale (SGS) modeling for dynamo simulations in a rotating spherical shell modeled on the Earth's outer core

Abstract: The flow in the Earth's outer core is expected to have vast length scale from the geometry of the outer core to the thickness of the boundary layer. Because of the limitation of the spatial resolution in the numerical simulations, sub-grid scale (SGS) modeling is required to model the effects of the unresolved field on the large-scale fields. We model the effects of sub-grid scale flow and magnetic field using a dynamic scale similarity model. Four terms are introduced for the momentum flux, heat flux, Lorentz force and magnetic induction. The model was previously used in the convection-driven dynamo in a rotating plane layer and spherical shell using the Finite Element Methods. In the present study, we perform large eddy simulations (LES) using the dynamic scale similarity model. The scale similarity model is implement in Calypso, which is a numerical dynamo model using spherical harmonics expansion. To obtain the SGS terms, the spatial filtering in the horizontal directions is done by taking the convolution of a Gaussian filter expressed in terms of a spherical harmonic expansion, following Jekeli (1981). A Gaussian field is also applied in the radial direction. In the present study, we perform a fully resolved direct numerical simulation (DNS) with the truncation of the spherical harmonics $L = 255$ as a reference. And, we perform unresolved DNS and LES with SGS model on coarser resolution ($L =$ 127, 84, and 63) using the same control parameter as the resolved DNS. In $l_{max} = 127$ case, SGS model improves the kinetic energy comparing with the resolved and unresolved DNS, but the improvement is not enough. Consequently, there is no improvements in the magnetic energy by the present SGS model. In $l_{max} = 84$ case, however, large kinetic energy is observed near the truncation both in the LES and unresolved DNS cases. We conclude that the present SGS model does not work properly because the assumption of the scale similarity is not satisfied at the truncation level.

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Scott McIntosh, NCAR/HAO

Title: 140 years of the “extended” solar cycle: predictability, expectations for SUNSPOT cycle 25 and what is to follow

Abstract: Starting with 22 years of contemporary observations of the solar corona we readily see bands of activity- long-lived patterns that mark out the 22-year solar magnetic activity cycle. The modulation of these bands can explain the landmarks of the sunspot cycle – that only occurs over about half of the magnetic cycle span. Exploiting routine observations of the green-line corona that go back to the late 1930s and of solar filaments that go back to the dawn of H-alpha photography in the late 1870s we demonstrate that the 22-year magnetic cycle is extremely robust and is predictable through this continuous observational record. Using this record we explore the ”climatology” of the system and the root drivers of solar variability and activity. Given the apparent predictability in the system we look at sunspot cycle 25, how it has evolved since first appearing in 2012/2014, what it may yield in terms of activity, and also what may follow…..

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Charles Meneveau, Johns Hopkins University

Title: Intermittency modeling based on the Lagrangian evolution of the velocity gradient tensor

Abstract: Non-Gaussianity and rapid growth of intermittency of small-scale motions is a ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem, even in non-rotating non-stratified turbulence. We review recent efforts to derive models for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. Unlike previous phenomenological intermittency models of turbulence, in the proposed new model the dynamics driving the growth of intermittency due to gradient self-stretching and rotation are derived directly from the Navier-Stokes equations. Numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen-directions of the strain-rate. We also explore how to implement similar models into predictive computational tools such as Large Eddy Simulations. This research was performed with Perry Johnson and had support from the National Science Foundation.

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Åke Nordlund, University of Copenhagen

Title: Global modeling of the solar convection zone with the DISPATCH code framework

Abstract: We have recently introduce a high-performance simulation framework, which allows semi-independent, task-based updates of a collection of `patches' in space-time. A hybrid MPI/OpenMP execution model is adopted, where work tasks are controlled by a rank-local `dispatcher' which selects that are ready for updating, from a set of tasks generally much larger than the number of hardware threads. Tasks may use either Cartesian or orthogonal curvilinear meshes, and patches may be stationary or moving. Mesh refinement can be static or dynamic. A feature of decisive importance for the overall performance of the framework is that time steps are determined and applied locally; this allows potentially large reductions in the total number of updates required in cases when the signal speed varies greatly across the computational domain, and therefore a corresponding reduction in computing time. Here we report results from modeling the entire solar convection zone, using a curvilinear coordinate system inspired by the 18 patches outlined on a volleyball. Each of the 18 main patches are again split into a large number of subdomains. This allows the use of patches that appear to be essentially Cartesian from the point of view of domain decomposition, thus avoiding the difficulties associated with spherical coordinates or other coordinate systems used in the past.

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Arakel Petrosyan, Space Research Institute of the Russian Academy of Sciences

Title: Nonlinear interactions in shallow water magnetohydrodynamics of rotating astrophysical plasma

Abstract: This work discusses nonlinear effects in rotating astrophysical plasma in the magnetohydrodynamic shallow water approximation. The well-known shallow water approximation is generalized to the case of an external vertical magnetic field and to the case of compressible magnetohydrodynamic flows. Linear theory in this approximation includes magneto-Poincare waves, magnetostrophic waves in the presence of slow rotation and Rossby waves in the presence of rapid rotation on beta-plane. The theory of three-wave interactions of magneto-Poincare waves and magnetostrophic waves and the theory of three-wave interactions for Rossby waves are developed. It is shown that there are various types of parametric instabilities. It is shown that it is the presence of an external vertical magnetic field that provides three-wave interactions of magneto-Poincare waves and magnetostrophic waves. In the absence of an external magnetic field, the theory of four-wave interactions of such waves is developed, an amplitude equation is obtained, and its exact solution is found. The influence of compressibility on the astrophysical plasma flows in the shallow-water approximation is discussed.

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Annick Pouquet, LASP & NCAR/CISL

Title: Vertical drafts and mixing in stratified turbulence: sharp transition with Froude number

Abstract: We investigate the large-scale intermittency of vertical velocity and temperature, and the mixing properties of stably stratified turbulent flows using both Lagrangian and Eulerian fields from direct numerical simulations, in a parameter space relevant for the atmosphere and the oceans. Over a range of Froude numbers of geophysical interest (≈ 0.05 − 0.3) we observe very large fluctuations of the vertical velocity w, localized in space and time, with a sharp transition leading to non-Gaussian wings of the probability distribution functions of w. This behavior is captured by a simple model representing the competition between gravity waves on a fast time scale and nonlinear steepening on a slower time-scale. The existence of a resonant regime characterized by enhanced large-scale intermittency, as understood within the framework of the proposed model, is then linked to the emergence of structures in the velocity and potential temperature fields, localized overturning and mixing. Finally, in the same regime we observe a linear scaling of the mixing efficiency with the Froude number and an increase of its value of roughly one order of magnitude.

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Annick Pouquet, LASP & NCAR/CISL

Title: Turbulence and waves in geophysical flows: a few examples, advances and questions

Abstract: In magnetohydrodynamic turbulence, the velocity field is coupled to the magnetic field, whereas in the Boussinesq framework, velocity couples to density fluctuations. Both systems support waves (Alfvén, or inertia-gravity in the presence of rotation), with anisotropic dispersion relations. What kind of turbulence regimes result from the interactions between nonlinear eddies and waves in such flows? And what is delimiting these regimes? Two specific examples will be analyzed below: strength (i) of energy cascades, and (ii) of energy dissipation. Results have emerged recently using numerical simulations for two-dimensional (2D) and 3D MHD and for RST (rotating stratified turbulence). They show that a dual scascade of energy can be observed, towards both small and large scales and in both cases with constant fluxes. The scaling of the strength of the inverse relative to the direct constant energy fluxes is obtained through a simple modeling of wave-eddy interactions that relies on the efficiency of the cascade to small scales. For RST*, using β as the effective rate of kinetic energy dissipation compared to its dimensional estimate, we find β ~Fr, where Fr is the Froude number, that is the ratio of the gravity wave period to the eddy turn-over time [1,2]. This defines an intermediate regime bridging the gap between the strong-wave and the strong-eddy regimes in such flows. Finally, I shall sketch the phenomenological framework for RST within which one is led to similar scaling laws in terms of Froude number for the flux Richardson number and for related expressions measuring the relative roles of the buoyancy flux due to the waves, and of the measured kinetic and potential energy dissipation rates. They all are found to vary as power laws of Fr that differ for the three regimes [2]; this corroborates results from other numerical data sets, as well as from atmospheric and oceanic observations. * NCAR/NSF ASD allocation for a large parametric study of RST, on grids of 5123, 10243 and 20483 points. [1] R. Marino, AP & D. Rosenberg, Resolving the paradox of oceanic large-scale balance and small-scale mixing. Physical Review Letters 114, 114504, 2015. [2] AP, D. Rosenberg, R. Marino & C. Herbert, Scaling laws for mixing and dissipation in unforced rotating stratified turbulence. Submitted to J. Fluid Mechanics, under revision. See ArXiv Physics.flu-dyn/1708.07146v1, 2017.

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Ralph Pudritz, McMaster University

Title: The formation of filamentary molecular clouds in magnetized galaxies

Abstract: The origin of giant molecular clouds (GMCs) in galaxies remains one of the central problems of ISM and star formation physics. Observations reveal that clouds are highly filamentary, and that large scale galactic fields are often perpendicular to these dense filaments. How do these structures form? Moreover, how can structures which form from the initially magnetically dominated, diffuse ISM end up being gravitationally dominated GMCs? I will discuss recent global galactic scale simulations of magnetized galaxies that we have performed that reveal the crucial role of Parker instabilities - long thought to be important - in producing filamentary GMCs that appear to match the observations.

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Mark Rast, Department of Astrophysical and Planetary Sciences, University of Colorado

Title: Modeling transport using turbulent flow statistics

Abstract: We examine single particle dispersion in simulations of both three-dimensional isotropic and stratified turbulence. In both cases Lagrangian displacements share behaviors similar to ones we have previously identified in a simple point-vortex analog flow, and the statistical model developed in that later context can be applied to theses more realistic flows. In particular, we show that single particle dispersion can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. We discuss extension of this transport model to vector fields, focusing on the induction equation, and indicate its possible role in formulating a subgird description.

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Matthias Rempel, NCAR/HAO

Title: Simulations of quiet Sun magnetism: on the role of deep and shallow recirculation in small-scale dynamo simulations

Abstract: Observations suggest that small-scale magnetic field in the solar photosphere is mostly independent from the strength of nearby network field as well as independent of the solar cycle. This supports the view that the origin of small-scale magnetism is due to a small-scale dynamo that operates independently from the large-scale dynamo responsible for the solar cycle. The saturation field strength and structure of the resulting magnetic field in the photosphere depends critically on the contributions from deep and shallow recirculation within the strongly stratified convection zone. We analyze recent high resolution photospheric small-scale dynamo simulations that were computed with the MURaM radiative MHD code. We focus the analysis on newly forming downflow lanes in exploding granules since they show how the most weakly magnetized regions in the photosphere (center of granules) evolve into the most strongly magnetized regions (downflow lanes). We find that newly formed downflow lanes exhibit initially mostly a laminar converging flow that amplifies the vertical magnetic field embedded in the granule from initially a few 10 G to field strengths of up to 1 kG on a time scale of about 2 minutes. This results in extended magnetic sheets that have a length comparable to granular scales. Field amplification by turbulent shear happens first a few 100 km beneath the visible layers of the photosphere. Shallow recirculation transports the resulting turbulent field into the photosphere within minutes, after which the newly formed downflow lane shows a mix of strong magnetic sheets and turbulent field components. In all the analyzed cases we find that the turbulent field appears only on one side of the downflow lane, which suggests asymmetric horizontal vorticity that is also evident in the emergent intensity at the edges of the nearby granule. We discuss the potential of these findings for further constraining small-scale dynamo models through high resolution observations. We stress in particular the role of shallow and deep recirculation for the organization and strength of magnetic field in the photosphere.

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Michel Rieutord, Institut de Recherche en Astrophysique et Planétologie

Title: Inertial and gravito-inertial modes in a spherical shell - Applications to stars and planets

Abstract: Stars and planets all hold layers whose shape is close to a spherical shell. The knowledge of the oscillations of these layers is therefore crucial to understand the oscillation spectrum of stars and planets. But the low-frequency spectrum, where inertial and gravity modes coexist, is however particular since it is associated with an ill-posed problem when diffusive effects are neglected. This is best illustrated by the Poincaré equation in its most fundamental form. In this talk I will present the latest results that we obtained on the questions raised by inertial modes in a spherical shell, either when these modes are alone, or influenced by various effects like a differential rotation or a stable stratification, or both.

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Rick Salmon, University of California, San Diego

Title: Turbulent structures predicted by a spectral closure theory

Abstract: Spectral closure theories predict the Fourier amplitudes—but not the phases—of two-dimensional turbulence. However, the phases contain most of the information about structure. The eddy-damped quasi-normal Markovian approximation is a spectral closure theory whose closure hypothesis can be recast as a statistical constraint on the phases. Exploration of this constraint yields predictions of structure.

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Adam Showman, University of Arizona

Title: Atmospheric dynamics of giant planets and brown dwarfs

Abstract: The giant planets and brown dwarfs, broadly defined, exhibit a diverse range of behaviors that continue challenge our understanding. In many ways, giant planets are less well understood than either stars or terrestrial planets, which bound giant planets on the high- and low-mass ends, respectively. Here, I will review recent observations and theoretical advances that address the "grand challenge" of dynamically understanding these fascinating objects. Major observational advances are occurring simultaneously on three main fronts, comprising, respectively, the "local" giant planets of our solar system; the highly irradiated hot Jupiters; and brown dwarfs and directly imaged giant planets. Our solar system giant planets have atmospheric circulations dominated by numerous east-west (zonal) jet streams, cloud bands, and vortices; major effort is currently being spent to understand the structure and mechanisms driving these circulations. Brown dwarfs and directly imaged giant planets show extensive evidence of dynamics via their cloud layers, surface patchiness, chemical disequilibrium, and other signatures. These observations raise numerous puzzles about the nature of the circulation on brown dwarfs and its relationship to that of Jupiter and Saturn. Finally, for the hot Jupiters, a wealth of observations constrain the day-night temperature differences, vertical temperature structure, circulation, and cloudiness. The presumed tidal locking of close-in planets implies a novel--and still poorly understood--climate regime of permanent dayside heating and nightside cooling. Collectively, these diverse objects span over four orders of magnitude in intrinsic heat flux and incident stellar flux, and two orders of magnitude in gravity and rotation rate--thereby placing strong constraints on how the circulation of giant planets (broadly defined) depend on these parameters. I will review the specific theoretical puzzles and advances in each of these fields, and attempt to highlight aspects where dynamical unity emerges, as well as aspects where the diverse conditions lead to divergent outcomes.

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Jacob Simon, University of Colorado

Title: What drives accretion in protoplanetary disks?

Abstract: It is still uncertain what exactly is responsible for driving angular momentum transport in protoplanetary disks, thus setting the environment in which planets are born. This transport may find its origin in turbulence driven by the magnetorotational instability (MRI), magnetically driven winds that remove angular momentum vertically, or some combination of both. Recent disagreement between predicted signatures of turbulence from numerical simulations and observational constraints made by ALMA of the outer regions of protoplanetary disks have brought into question the turbulent origin of angular momentum transport, suggesting instead that angular momentum transport is primarily driven by a magnetically launched wind at large distances from the star. Here, I present recent numerical simulations that demonstrate that even for a wind-dominated accretion flow, significant turbulence is induced by highly localized regions of active MRI. These results suggest that in the outer disk, both weak magnetic fields and very low ionization levels are necessary in order to be consistent with the low turbulence values inferred from observations. To interpret these findings, I describe a new model in which a large scale magnetic field, confined to the inner disk, blocks ionizing radiation from reaching large radial distances. I conclude with some predictions made by this new model to be tested with future ALMA observations.

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Krista Soderlund, University of Texas at Austin, Institute for Geophysics

Title: Dynamos of ice giant planets

Abstract: Uranus and Neptune are relatively unexplored, yet critical for understanding the physical and chemical processes that control the behavior and evolution of giant planets. Because their multipolar magnetic fields, three-jet zonal winds, and extreme energy balances are distinct from other planets in our Solar System, the ice giants provide a unique opportunity to test hypotheses for internal dynamics and magnetic field generation. While it is generally agreed that dynamo action in the ionic ocean generates their magnetic fields, the mechanisms that control the morphology, strength, and evolution of the dynamos - which are likely distinct from those in the gas giants and terrestrial planets - are not well understood. We hypothesize that the dynamos and zonal winds are dynamically coupled and argue that their characteristics are a consequence of quasi-three-dimensional turbulence in their interiors. Here, we will present new dynamo simulations with an inner electrically conducting region and outer electrically insulating layer to self-consistently couple the ionic oceans and molecular envelopes of these planets. The resulting magnetic field morphology and amplitude, zonal flow profile, and internal heat flux pattern will be compared against corresponding observations of Uranus and Neptune.

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Frank Stefani, Helmholtz-Zentrum Dresden-Rossendorf

Title: The DRESDYN project: liquid metal experiments on dynamo action and magnetorotational instability

Abstract: The dynamo effect in moving electrically conducting fluids is at the root of magnetic field generation in planets and stars. Yet, cosmic magnetic fields play also an active role in the formation of central objects, such as protostars and black holes, by destabilizing accretion disks that would be hydrodynamically stable. While often studied separately, dynamo action and magnetically triggered instabilities may also occur together in such highly non-linear processes as the MRI dynamo or the Tayler-Spruit dynamo. The DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) serves as a platform for continuing the liquid metal experiments of the last two decades which were related to dynamo action and magnetically triggered flow instabilities. After a short survey of the dynamo experiments in Riga, Karlsruhe and Cadarache, and the various MRI experiments at the PROMISE facility at HZDR, I discuss the preparatory status of a large-scale precession experiment and a Taylor-Couette experiment for investigating various forms of the MRI and their combinations with the Tayler instability. Special focus will be laid on the numerical predictions of both experiments, as well as on some recent findings concerning the relation of non-modal growth in rotating flows with dissipation-induced instabilities, such as helical and azimuthal MRI for negative and positive shear.

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Glen Stewart, University of Colorado

Title: Detecting subcritical nonlinear instabilities in rotating fluids using Hamiltonian methods

Abstract: Differentially rotating fluids with radial stratification can sometimes exhibit nonlinear instabilities even though they are formally stable in the linear approximation. The differential rotation can produce large transient growth of initially small perturbations, which allows the system to enter the nonlinear instability quite easily in numerical simulations. These “subcritical” instabilities are difficult to detect analytically because the large-scale radial stratification complicates the usual modal analysis. Rotating, stratified fluid-dynamical systems often have an underlying noncanonical Hamiltonian structure that can be used to detect these nonlinear instabilities. The essential difficulty is that the noncanonical Poisson bracket is often state-dependent, which complicates the development of Hamiltonian perturbation methods. Fortunately, Morrison and Vanneste (Annals of Physics 368 (2016) 117-147) have discovered approximate transformations of the dependent variables that systematically remove the state-dependence of the Poisson brackets, which in turn simplifies the stability analysis of the transformed Hamiltonian. An analysis of the subcritical baroclinic instability in a radially stratified circumstellar disk will be used to illustrate the theory.

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Peter Sullivan, NCAR

Title: Upper ocean mixing driven by Langmuir turbulence and submesoscale density filaments

Abstract: The spatial and temporal state of the upper ocean boundary layer is determined by a set of poorly understood complex interactions between submesoscale turbulence, (e.g., fronts, dense filaments and coherent vortices) and small-scale boundary-layer turbulence. Of particular interest here is the life-cycle of a cold dense filament undergoing frontogenesis in the presence of wind-wave generated Langmuir turbulence. Cold filaments generate secondary circulations that are frontogenetic with super-exponential sharpening of the cross-filament buoyancy and horizontal velocity gradients. Within less than a day, the frontogenesis is arrested at a very small width, less than 100 m, primarily by boundary layer turbulence, with a subsequent slow decay by further turbulent mixing. This phenomenon is examined in Large-Eddy Simulations (LESs) with resolved turbulent motions in large-horizontal domains using 10^9 gridpoints. Winds and waves are oriented in directions both perpendicular and parallel to the cold filaments in the LES. The LES solutions show that the boundary layer turbulence is strikingly inhomogeneous in relation to the submesoscale filamentary currents and density stratification, and there is large horizontal transport of cold water at the base of the mixed layer. Also, the spatial and temporal evolution of frontogenesis is dependent on the orientation of the winds and waves, and for some wind-wave combinations the sharp filament exhibits an unexpected submesoscale lateral shear instability that facilitates the frontogenetic arrest.

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Steven Tobias, University of Leeds

Title: Interaction of turbulence and mean flows and fields in rotating systems

Abstract: In many systems, whether convectively driven, or driven by the instability of a large-scale flow or magnetic field, systematic mean flows interact with turbulence in a non-trivial manner. The presence of rotation engenders correlations in the turbulence that have significant effects on their interaction with the mean flows/fields. In this talk I will describe some model problems and how statistical descriptions can be made efficient via the use of model reduction.

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Juri Toomre, JILA and Dept Astrophysical & Planetary Sciences, University of Colorado

Title: Tiny stars with fierce fields: exploring the origin of intense magnetism in M stars

Abstract: The M-type stars are becoming dominant targets in searches for Earth-like planets that could occupy their habitable zones. The low masses and luminosities of M-dwarf central stars make them very attractive for such exoplanetary hunts. The habitable zone of M dwarfs is close to the star due to their low luminosity. Thus possibly habitable planets will have short orbital periods, making their detection feasible both with the transit method (used by Kepler, K2 and soon with TESS) and with the radial velocity approaches. Yet habitability on a planet likely requires both solid surfaces and atmospheres, but also a favorable radiation environment. It is here that the M-dwarf central stars raise major theoretical puzzles, for many of them exhibit remarkably intense and frequent flaring, despite their modest intrinsic luminosities. The super-flares release their energy both in white light and in X-rays, and can be thousands of times brighter than the strongest solar flares. M-type stars are distinctive in becoming fully convective with decreasing mass at about M3.5 in spectral type (or about 0.35 solar masses). At this transition, a steep rise in the fraction of magnetically active stars is observed that is accompanied by an increasing rotational velocity. We have been using 3-D MHD simulations with both the ASH and Rayleigh codes to study the coupling of turbulent convection, rotation, and magnetism within full spherical domains such as the interior of an M dwarf. This permits the exploration of the magnetic dynamos that must be responsible for the evolving magnetism and intense activity of many M dwarfs. We concentrate on the manner in which dynamos operating in fully convective M dwarf interiors beyond the transition may be able to achieve very strong magnetic fields, and how field strengths and apparent magnetic activity increases with rotation rate as suggested by observations.

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Santiago Triana, Royal Observatory of Belgium

Title: The coupling between Earth's inertial and rotational eigenmodes

Abstract: The Earth is a rapidly rotating body. The centrifugal pull makes its shape resemble a flattened ellipsoid. Coriolis forces are also of great importance, not only in the fluid dynamics of the oceans and atmosphere but also in the dynamics of the fluid outer core. The restoring action of the Coriolis force can support waves, known as inertial waves. A familiar example are Rossby waves in the atmosphere. In the molten core of the Earth, these waves can lead to global oscillations of the fluid. Periodic variations of the Earth’s rotation axis (nutations) can exchange angular momentum with the fluid core and excite these inertial modes. In addition to viscous torques that exist regardless of the shape of the boundaries, the small flattening of the core-mantle boundary (CMB) allows inertial modes to exert torques on the mantle (topographical torques). This interaction effectively couples the rigid-body dynamics of the Earth with the fluid dynamics of the molten core. Here we present the first high resolution numerical model that solves simultaneously the rigid body dynamics of the mantle and the Navier-Stokes equation for the molten core. This method takes naturally into account dissipative processes in the fluid that are ignored in current nutation models.

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Joseph Tribbia, NCAR

Title: Climate predictability: a case of ‘almost intransitivity’?

Abstract: This study will examine the impact of nonlinear surface friction on driven barotropic turbulence comparing the impact in both the non-divergent barotropic vorticity equation and the shallow water system. Specifically, we will examine the impact of the nonlinearity of the surface drag on the inverse cascade of energy to large scales and the consequent loss of planetary scale predictability. As it is well known that the inverse cascade is quite sensitive to the magnitude of linear drag in two-dimensional driven turbulence, investigations of the comparable sensitivity to the potentially self-regulating nonlinear friction will be undertaken to quantify the changes in planetary scale predictability.

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Jeffrey Weiss, University of Colorado

Title: Spatio-temporal oscillations and nonequilibrium fluctuations

Abstract: The natural variability of complex multi-scale turbulent fluids self-organizes into coherent spatio-temporal oscillations. In the climate system these take the form of well-known phenomena such as the El-Niño Southern Oscillation, the Madden-Julien Oscillation, the Atlantic Multidecadal Oscillation, and the Pacific Decadal Oscillation. Each oscillation has its own spatio-temporal scales and involves different dynamical mechanisms. The climate system is approximately a system in a non-equilibrium steady-state. Apart from anthropogenic forcing and intermittent perturbations such as volcanoes, the climate system is in a statistically steady-state forced by short-wave radiation from the Sun and damped by outgoing long-wave radiation to space. Such nonequilibrium steady-states have the property that their fluctuations are determined by phase space currents. We apply the techniques of non equilibrium physics to climate oscillations and propose a new diagnostic based on the phase space currents for quantifying climate oscillations allowing inter-comparisons between models and observations. We expect this diagnostic to be a useful way of quantifying spatio-temporal oscillations in rotating magnetic fluids in addition to the climate system.

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Rakesh Yadav, Harvard University

Title: Applications of low viscosity and rapidly-rotating dynamos to planets and stars

Abstract: Fluid dynamics of rapidly rotating fluids with low viscosity plays a governing role in setting the magnetic field properties of many planets and stars. The classical non-dimensional parameters, Ekman number and Rossby number, quantify the ratio of Coriolis, viscous, and the convection time scales. A small value of both represents the low viscosity and rapidly-rotating fluid dynamics regime. In this talk, I will discuss how direct numerical simulations of low Rossby and low Ekman number thermal convection in spherical shells can be used to better understand intriguing magnetic field observations in planets and stars. In particular, I will show how detailed analysis of force balance in simulations helps us to approach a more realistic dynamo regime similar to Earth like planets, and how several fundamental properties of magnetic fields in M-stars can be spontaneously generated in a dynamo simulation.

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Ron Yellin, Tel Aviv University

Title: Understanding vertical shear instability in protoplanetary accretion disks as a symmetric slantwise convection [Ron Yellin-Bergovoy*, Eyal Heifetz and Orkan M. Umurhan]

Abstract: Vertical shear instability is an axi-symmetric instability that is suggested to be active in the ``dead zones'' of protoplanetary accretion discs. Here we examine its physical mechanism in a minimal model and shows that its essence is similar to the slantwise convective symmetric instability in the mid-latitude Earth atmosphere, in the presence of vertical shear of the baroclinic jet stream. We show that in order to obtain instability the fluid parcels' slope should exceed the slope of the mean absolute momentum in the disk radial-vertical plane. We provide a detailed physical explanation for the instability, both in terms of the interplay between the radial and azimuthal vorticity components and in terms of the energetic Goldreich-Schubert-Fricke generalized Rayleigh condition. Furthermore, we explain why anelastic dynamics yields oscillatory unstable modes and isolate the oscillation mechanism from the instability one.

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Teimuraz Zaqarashvili, Space Research Institute of Austrian Academy of Sciences, Graz, Austria

Title: Equatorial MHD shallow water waves and solar activity variations

Abstract: The influence of toroidal magnetic field on the dynamics of shallow water waves in the solar tachocline is studied. Sub-adiabatic temperature gradient in the upper overshoot layer of the tachocline causes significant reduction of surface gravity speed, which leads to the trapping of the waves near the equator. Dispersion relations of all equatorial MHD shallow water waves are obtained in the upper tachocline conditions and solved analytically and numerically. It is found that the toroidal magnetic field splits equatorial Rossby waves into fast and slow magneto-Rossby waves. The solutions are confined around the equator between ±30 − 40 latitudes coinciding with sunspot activity belts. For reasonable value of reduced gravity, global equatorial MHD shallow water waves in the upper overshoot tachocline capture all time scales of observed variations in solar activity, but detailed analytical and numerical studies are necessary to make firm conclusion towards the connection of the waves to the solar/stellar dynamo.