The statistics of magnetised interstellar turbulence
Creators: name: Beattie, James
Publisher: name: The Australian National University
Year: 2024

description: Most of the baryonic matter in the Universe exists in a state of turbulence. On Earth, turbulence causes atmospheric pressure fluctuations that make stars twinkle, influences the chaotic movements of oceans and weather patterns, and poses challenges in engineering by dissipating energy from a plethora of different systems. Turbulence is so prevalent on Earth that it is not surprising that it plays a fundamental role on almost all scales of the Universe. At the scale of hundreds of light years, turbulence prevails in the dusty, multiphase plasma environment found in the discs of galaxies, known as the interstellar medium (ISM). Therefore, any model concerning the ISM of galaxies, such as gas structure, star formation paradigm, cosmic ray transport, mixing of metals, and chemistry, must consider the complex, nonlinear dynamics of turbulence. However, ISM turbulence differs from its terrestrial counterpart in several ways. Firstly, the multiphase ISM is, on average (by volume), trans-to-supersonic, meaning it is filled with supersonic shocks and gas density fluctuations. Secondly, galaxies have acquired magnetic fields through various mechanisms, which have grown in strength to the point that they act as a dynamically meaningful framework for the gas motions. This type of turbulence, compressible, and highly magnetised, is widespread in the Galaxy but lacks a well-developed theory. Many researchers in the ISM turbulence community still rely on results applicable only to specific incompressible turbulence regimes while neglecting the effects of compressibility. In my thesis, I present a comprehensive theoretical and numerical exploration of three main aspects of ISM turbulence: (1) the turbulent dynamo, (2) magnetised turbulent fluctuations in driven turbulence, and (3) the stationary turbulent energy cascade in supersonic, magnetised turbulence. Regarding the turbulent dynamo, I demonstrate that the long-term dynamics are universal for different initial magnetic field conditions. Furthermore, I develop numerous, detailed analytical, statistical models for various fluctuations in magnetohydrodynamic (MHD) turbulence, including compressibility and anisotropy effects. These models encompass gas density, ion Alfv\'en velocity, and magnetic field fluctuations over a broad range of turbulent parameters observed in the ISM, and are validated with hundreds of numerical experiments. The magnetic field fluctuations models have direct implications for the Davis-Chandrasekhar-Fermi methods used to probe magnetic field pseudo-vectors through dust polarisation measurements and are currently being employed in observational endeavours to measure the interstellar magnetic field amplitude. Furthermore, our gas density and ion Alfv\'en velocity fluctuations have significant implications for star formation theory in highly-intermittent non-lognormal media, and GeV cosmic ray transport through turbulent plasmas, including providing analytical models for the 1-point statistics of the ion Alfv\'en velocity that can be accessed via column density. Lastly, I present the world's largest compressible MHD turbulence simulation, which utilised over 80 million core-hours on 140,000 compute cores on grids of up to 10,080^3 and Reynolds number close to 10^6 to compute resolved turbulent energy spectra. Our kinetic energy spectra reveal a dichotomy of turbulent correlations separated by a transition scale between two cascades: (1) on large scales, we find Burgers-like turbulence - the turbulence of saw-tooth shocks - and on small scales, we find something akin to Boldyrev's aligned turbulence. We reveal power-law structure in the magnetic spectra only at the highest magnetic Reynolds numbers, which is not yet described by any (even asymptotic) magnetic spectra theories. This is the first calculation to demonstrate such a dichotomy in this regime, and holds significant implications not only for ISM turbulence, but also for fundamental plasma and fluid sciences.