Christopher John Wareing

We compare the efficiency and ease-of-use of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) framework in recovering the relevant governing equations and boundary conditions from data generated by direct numerical simulations (DNS) of turbulent convective flows. In the former case, a weak-form implementation pySINDy is used. Time-dependent data for two- (2D) and three-dimensional (3D) DNS simulation of Rayleigh-Benard convection and convective plane Couette flow is generated using the Dedalus PDE framework for spectrally solving differential equations. Using pySINDy we are able to recover the governing equations of 2D models of Rayleigh-Benard convection at Rayleigh numbers, R, from laminar, through transitional to moderately turbulent flow conditions, albeit with increasing difficulty with larger Rayleigh number, especially in recovery of the diffusive terms (with coefficient magnitude proportional to 1/R^0.5). SPIDER requires a much smaller library of terms and we are able to recover more easily the governing equations for a wider range of R in 2D and 3D convection and plane flow models and go on to recover constraints (the incompressibility condition) and boundary conditions, demonstrating the benefits and capabilities of SPIDER to go beyond pySINDy for these fluid problems governed by second-order PDEs. [We] demonstrat[e] the potential of machine-learning methods to validate numerical solvers and solutions for such flow problems. We also find that properties of the flow, specifically the correlation time and spatial scales, should inform the initial selection of spatiotemporal subdomain sizes [abbreviated]

Using the adaptive mesh refinement code mg, we perform 3D hydrodynamic simulations of a supernova-cloud interaction in the ‘large cloud regime’. The cloud is initially atomic and evolving due to the thermal instability (TI) and gravity. We study interactions in a ‘pre-TI’ and ‘post-TI’ stage when cold and dense clumps are present, and compare these results to idealised shock-cloud scenarios in the ‘small cloud regime’, and a scenario without shocks. On aggregate, the supernova disruption is significantly weaker than that from an idealised shock due to the supernova impact being instantaneous, and not continuous. In both supernova-cloud interactions, we observe two shocks impact the cloud, followed by the development of a weak 10 km s⁻¹ upstream flow on the cloud interface, and a global ambient pressure drop. When the cloud is still atomic, it expands due to this drop. Additionally, the TI is triggered at the front of the cloud, causing the formation of a cap-like structure with clumps embedded inside. The upstream flow converges in this region, resulting in a lobe-like cloud morphology. When the cloud is molecular, the transmitted shock disrupts the inter-clump material and causes the clumps’ outer envelopes to expand slightly and form tail-like morphologies. These effects are less pronounced than those in our shock-cloud scenarios, and more pronounced that those in our un-shocked scenario. After ∼ 3.5 Myrs, the effects from the supernova decay and the cloud returns to an almost indistinguishable state from an un-shocked cloud, in spite of the global ambient pressure drop. In neither supernova-cloud scenario do we see any local gravitational collapse.

Stellar winds are one of several ways that massive stars can affect the star formation process on local and galactic scales. In this paper, we investigate the numerical resolution needed to inflate an energy-driven stellar wind bubble in an external medium. We find that the radius of the wind injection region, r_inj, must be below a maximum value, r_inj,max, in order for a bubble to be produced, but must be significantly below this value if the bubble properties are to closely agree with analytical predictions. The final bubble momentum is within 25 per cent of the value from a higher resolution reference model if χ = r_inj/r_inj,max = 0.1. Our work has significance for the amount of radial momentum that a wind-blown bubble can impart to the ambient medium in simulations, and thus on the relative importance of stellar wind feedback.

Using the adaptive mesh refinement code mg, we perform hydrodynamic simulations of the interaction of a shock with a molecular cloud evolving due to thermal instability (TI) and gravity. To explore the relative importance of these processes, three case studies are presented. The first follows the formation of a molecular cloud out of an initially quiescent atomic medium due to the effects of TI and gravity. The second case introduces a shock whilst the cloud is still in the warm atomic phase, and the third scenario introduces a shock once the molecular cloud has formed. The shocks accelerate the global collapse of the clouds with both experiencing local gravitational collapse prior to this. When the cloud is still atomic, the evolution is shock dominated and structures form due to dynamical instabilities within a radiatively cooled shell. While the transmitted shock can potentially trigger the TI, this is prevented as material is shocked multiple times on the order of a cloud-crushing time-scale. When the cloud is molecular, the post-shock flow is directed via the pre-existing structure through low-density regions in the inter-clump medium. The clumps are accelerated and deformed as the flow induces clump–clump collisions and mergers that collapse under gravity. For a limited period, both shocked cases show a mixture of Kolmogorov and Burgers turbulence-like velocity and logarithmic density power spectra, and strongly varying density spectra. The clouds presented in this work provide realistic conditions that will be used in future feedback studies.

The MHD version of the adaptive mesh refinement (AMR) code, MG, has been employed to study the interaction of thermal instability, magnetic fields, and gravity through 3D simulations of the formation of collapsing cold clumps on the scale of a few parsecs, inside a larger molecular cloud. The diffuse atomic initial condition consists of a stationary, thermally unstable, spherical cloud in pressure equilibrium with lower density surroundings and threaded by a uniform magnetic field. This cloud was seeded with 10 per cent density perturbations at the finest initial grid level around n = 1.1 cm−3 and evolved with self-gravity included from the outset. Several cloud diameters were considered (100, 200, and 400 pc) equating to several cloud masses (17 000, 136 000, and 1.1 × 106 M⊙). Low-density magnetic-field-aligned striations were observed as the clouds collapse along the field lines into disc-like structures. The induced flow along field lines leads to oscillations of the sheet about the gravitational minimum and an integral-shaped appearance. When magnetically supercritical, the clouds then collapse and generate hourglass magnetic field configurations with strongly intensified magnetic fields, reproducing observational behaviour. Resimulation of a region of the highest mass cloud at higher resolution forms gravitationally bound collapsing clumps within the sheet that contain clump-frame supersonic (M ∼ 5) and super-Alfvénic (MA ∼ 4) velocities. Observationally realistic density and velocity power spectra of the cloud and densest clump are obtained. Future work will use these realistic initial conditions to study individual star and cluster feedback.

The MHD version of the adaptive mesh refinement (AMR) code, MG, has been employed to study the interaction of thermal instability, magnetic fields and gravity through 3D simulations of the formation of collapsing cold clumps on the scale of a few parsecs, inside a larger molecular cloud. The diffuse atomic initial condition consists of a stationary, thermally unstable, spherical cloud in pressure equilibrium with lower density surroundings and threaded by a uniform magnetic field. This cloud was seeded with 10% density perturbations at the finest initial grid level around n=1.1 cm^{-3} and evolved with self-gravity included from the outset. Several cloud diameters were considered (100 pc, 200 pc and 400 pc) equating to several cloud masses (17,000 Msun, 136,000 Msun and 1.1x10^6 Msun). Low-density magnetic-field-aligned striations were observed as the clouds collapse along the field lines into disc-like structures. The induced flow along field lines leads to oscillations of the sheet about the gravitational minimum and an integral-shaped appearance. When magnetically supercritical, the clouds then collapse and generate hourglass magnetic field configurations with strongly intensified magnetic fields, reproducing observational behaviour. Resimulation of a region of the highest mass cloud at higher resolution forms gravitationally-bound collapsing clumps within the sheet that contain clump-frame supersonic (M~5) and super-Alfvenic (M_A~4) velocities. Observationally realistic density and velocity power spectra of the cloud and densest clump are obtained. Future work will use these realistic initial conditions to study individual star and cluster feedback.

Field’s linear analysis of thermal instability is repeated using methods related to Whitham’s theory of wave hierarchies, which brings out the physically relevant parameters in a much clearer way than in the original analysis. It is also used for the stability of non-equilibrium states and we show that for gas cooling behind a shock, the usual analysis is only quantitatively valid for shocks that are just able to trigger a transition to the cold phase. A magnetic field can readily be included and we show that this does not change the stability criteria. By considering steady shock solutions, we show that almost all plausible initial conditions lead to a magnetically dominated state on the unstable part of the equilibrium curve. These results are used to analyse numerical calculations of perturbed steady shock solutions and of shocks interacting with a warm cloud.