# 2022 PDG seminars

## Statistical methods for analyzing turbulent flows

Turbulent flows are represented by complex multi-scale phenomena and chaotic motions. Despite its complexity, we can find some more elementary components referred to as coherent or quasi-coherent structures. These structures are challenging to define precisely and are usually identified by flow visualization, conditional sampling techniques, or other methodologies. In the past decades, different methodologies were extensively applied for better understanding and modeling the chaotic motion of turbulent flows. This presentation will review classical and modern statistical tools for extracting information from turbulent flows. First, some classical tools to quantify the state of turbulence will be presented, such as two-point correlation, multidimensional correlation maps, space-time correlations, and turbulence anisotropy maps. Finally, we will discuss modern flow decomposition methods such as orthogonal decomposition (POD), spectral proper orthogonal decomposition (SPOD), and momentum potential theory, focusing on how those methods can help us to analyze coherent structures and build reduced-order models.

## Phase mixing in partially ionised plasmas

Effective plasma heating requires short transversal scales. Phase mixing is one of the most promising mechanisms for explaining the heating of the upper solar atmosphere by producing small transversal scales in the presence of large transversal gradients in the Alfvén speed, here we take that to mean a gradient in the equilibrium magnetic field. Such transversal gradients in the equilibrium magnetic field are abundant in the solar atmosphere.

Using a single fluid approximation of a partially ionised chromospheric plasma we study the effectiveness of the damping of phase mixed shear Alfvén waves and investigate the effect of varying the ionisation degree on the dissipation of waves.

Our results show that the dissipation length of shear Alfvén waves strongly depends on the ionisation degree of the plasma, but more importantly, in a partially ionised plasma the damping length of shear Alfvén waves is several orders of magnitude shorter than in the case a fully ionised plasma, providing further evidence that phase mixing is a large contributor to heating the solar corona. The effectiveness of phase mixing is investigated for various ionisation degrees, ranging from fully neutral to fully ionised plasmas.

## Twisted magnetic flux tubes and its stability

We construct a magnetohydrostatic (MHS) equilibrium model of a vertical axisymmetric flux tube with a twisted magnetic field that expands as it spans from the photosphere to the transition region in a stratified solar atmosphere under the influence of solar gravity. Using a self-similar formulation and a quadratic flux function for the poloidal current and gas pressure, expressed as a second-order polynomial of the flux function for the magnetic shape function, we solve the Grad-Shafranov equation (GSE) semi-analytically. Incorporating the appropriate boundary conditions we have built a closed field configuration of the flux tube. Using the input parameter space which is consistent with the observations, we calculate the magnetic and thermodynamic structure of the flux tube. We also study the stability analysis of the flux tube configuration using the variational method to find the minima of the constrained energy to obtain the region of stability for the flux tube models. We find that the estimated configurations are in reasonable agreement with the observations for magnetic bright points (MBPs). The obtained closed field model can be used for the construction of a realistic structure like a magnetic canopy.

## On measures of dependence between solar wind parameters and fluxes of relativistic electrons at GEO

The identification of the external parameters that govern complex systems is a central problem in the analysis of system dynamics. Data-driven approaches often rely on classical measures of dependence to identify the input parameters, such as linear correlation, error reduction ratio, mutual information, and maximal correlation. All of the above, with the exception of linear correlation, capture nonlinear dependencies in the dynamical system but lack scalability and require non-trivial parameter selection to tune the analysis. While measures of dependence provide quantitative estimates of the dependence between the variables in the data, only maximal correlation describes the structure of the dependence in terms of the best linear regressor under quadratic penalty. We review the properties of different measures and provide operational insight into the estimates provided by different measures. We use the nonlinear dependence measures to study what solar wind parameters govern the evolution of fluxes of electrons in the energy range 1.8-3.5 MeV at the geostationary orbit. Data from Los Alamos National Laboratory (LANL) geosynchronous energetic particle instrument Energetic Sensor for Particles (ESP) [Reeves et al. 2011] is used in this investigation. The results obtained are discussed in relation to the relative importance of the solar wind density and the solar wind velocity as control parameters for fluxes of relativistic electrons at GEO.

Bio Dr Iñaki Esnaola is the fire marshal for the D Floor of the Amy Johnson Building. He is also a senior lecturer at UoS ACSE working at the intersection of information theory, random processes, and high-dimensional statistics with application to estimation, communication, and cybersecurity problems. He is also currently a visiting researcher at the Department of Electrical and Computer Engineering, Princeton University, USA, working on a joint project on information-theoretic security approaches to the smart grid. Since 2018 he is the Power Systems and Cyber Security Subject Editor for the IET Smart Grid Journal and was the Cybersecurity and Privacy Symposium Co-Chair for the 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids.

## Methods in Machine Learning for solar spectroscopy

Solar spectropolarimetry is entering the realm of big data. Current and future telescopes will produce data at a rate that will make it hard to store in a single machine and even harder to operate on the data. Thankfully, in the last decade, machine learning has experienced an enormous advance, thanks to the open possibility of training very deep and complex neural networks. In this contribution I show options to explore to deal with the big data problem and also how deep learning can be used to efficiently solve difficult problems in Solar Physics. I will focus on how differentiable programming (aka deep learning) is helping us to have access to velocity fields in the solar atmosphere, correct for the atmospheric degradation of spectropolarimetric data and carry out fast 3D inversions of the Stokes parameters to get physical information of the solar atmosphere.

## Complexity of intermittent magnetic field turbulence within reconnection exhausts in the solar wind at 1 AU

We apply the Jensen-Shannon (J-S) complexity-entropy index to magnetic field data of four reconnection exhausts detected in the solar wind at 1 AU. Three events are related to the passage of an interplanetary coronal mass ejection, and one event is related to a rope-rope magnetic reconnection event. The interplanetary magnetic field is projected into the LMN coordinates by applying the hybrid minimum variance analysis. The J-S index indicates that the three components of the magnetic field display entropy and complexity values similar to stochastic fluctuations. However, we show that a high degree of intermittency within the inertial subrange is related to a lower degree of entropy and a higher degree of complexity. We also show that, for all four events, the L component of the magnetic field displays lower entropy and higher complexity than the M and N components. These results suggest that coherent structures can be responsible for decreasing entropy and increasing complexity within reconnection exhausts in the interplanetary magnetic-field turbulence.

## The First AI Simulation of a Black Holes

In this pilot study, we investigate the use of a deep learning (DL) model to temporally evolve the dynamics of gas accreting onto a black hole in the form of a radiatively inefficient accretion flow (RIAF). We have trained a machine to forecast such a spatiotemporally chaotic system -- i.e. black hole weather forecasting -- using a convolutional neural network (CNN) and a training dataset which consists of numerical solutions of the hydrodynamical equations, for a range of initial conditions. We find that deep neural networks seem to learn well black hole accretion physics and evolve the accretion flow orders of magnitude faster than traditional numerical solvers, while maintaining a reasonable accuracy for a long time. For instance, CNNs predict well the temporal evolution of a RIAF over a long duration of 8e4 GM/c³ which corresponds to 80 dynamical times at r = 100 GM/c². The DL model is able to evolve flows from initial conditions not present in the training dataset with good accuracy. Our approach thus seems to generalize well. Once trained, the DL model evolves a turbulent RIAF on a single GPU four orders of magnitude faster than usual fluid dynamics integrators running in parallel on 200 CPU cores. We speculate that a data-driven machine learning approach should be very promising for accelerating not only fluid dynamics simulations, but also general relativistic magnetohydrodynamic ones.

## On the scientific capabilities of SO/PHI

The Polarimetric and Helioseismic Imager (PHI) is one of the six remote sensing instruments on board the Solar Orbiter Satellite (SO). It is a spectropolarimetric imager which provides maps of the photospheric magnetic field with a spatial resolution of 200 km at perihelion (0.3 AU). In this talk, I will introduce the SO/PHI instrument and show its proven capabilities tested during the commissioning and cruise phase of the Solar Orbiter. Cross-calibration of the SO/PHI data products with other NEO satellites like SDO will be presented as well. Intercalibration of the SO/PHI high resolution magnetograms with the EUV images of the Extreme Ultraviolet Imager (EUI) on-board SO allowed for studying the magnetic component of the small-scale EUV brightenings detected by EUI and termed campfires. I will present the results of this study and show how the next higher resolution SO/PHI data taken near perihelion at 0.3 AU from the Sun will help improve our understanding of the magnetic origin of these campfires.

Mr Abdulaziz Alharbi

The University of Sheffield

10 March 2022

## Waves in Partially Ionised Multi-Fluid Solar Atmospheric Plasmas

The solar atmospheric plasma is a complex environment, where the plasma changes with height from being controlled by pressure forces to a regime where dynamics is driven by magnetic forces, but also where the plasma changes from being partially ionised to fully ionised. In this talk, I will give an overview of the research I have undertaken throughout my PhD studies on this topic where I discuss results on waves and their properties in strongly and weakly partially ionised plasma using a multi-fluid framework.

## Simulation, visualization, and analysis of the world's most powerful thunderstorms

Supercell thunderstorms are recognized as the one of the earth's most powerful atmospheric phenomena, producing heavy rain, hail, and tornadoes that sometimes result in catastrophic devastation and loss of life. Accurately predicting supercell behavior in order to alert the public remains a top priority for federal forecasters, and much work remains to be done to achieve this goal. Part of the difficulty of forecasting the behavior of these storms stems from our poor understanding of processes that occur within supercells that result in violent tornadoes. In this talk, I will first provide a brief background that includes the mathematical equations and numerical model used in the study, and describe my own specific code development involving I/O and lossy floating point compreSimulation, visualization, and analysis of the world's most powerful thunderstormsssion. I will then present results from tornado-resolving large eddy supercell thunderstorm simulations conducted on some of the world's most powerful research supercomputers, focusing on processes that are associated with tornado formation and maintenance. I will also present recent research that focuses on the tops of the thunderstorms (what is visible to orbiting meteorological satellites) exploring the behavior of simulated cloud-top features that are associated with the most severe thunderstorms.

More presentations

Simulating and visualizing the most devastating thunderstorms [SC14]

## Properties of MHD waves in non-uniform equilibria

In this talk I will give an overview of the research I have undertaken throughout my PhD journey. I will introduce a numerical eigensolver that is capable of finding the permissible wave solutions in any symmetrically non-uniform equilibrium relevant to the solar atmosphere, in both a Cartesian and cylindrical geometry. Results of the numerical approach are compared with known analytical solutions which are then extended to investigate a number of non-uniform case studies including (i) non-uniform plasma density in a magnetic slab (ii) non-uniform plasma flow in a coronal slab (iii) non-uniform plasma density in a magnetic flux tube (iv) non-uniform plasma flow in a coronal flux tube (v) linear and non-linear rotational plasma flow in a magnetic flux tube. For a number of case studies, both 2D and 3D visualisations of the resulting propagating MHD modes are shown. Implications of the results for observations and seismological purposes are discussed.