Fluid Dynamics

Modelling of dense stellar systems with central black holes

Supervisor(s): Anna Lisa Varri, Jacques Vanneste

Globular clusters are large, dense collections of tens of thousands, or millions, of stars, bound together by their mutual gravity. They are also one of the main candidates as hosts of intermediate-mass black holes (IMBH). As the name suggests, these are black holes with masses higher than those formed from the collapse of individual stars, called stellar-mass black holes (typically around 102 times the mass of the sun), but significantly smaller than the supermassive black holes which are typically found in the centres of galaxies (typically 106 times the mass of the sun). Until recently, there was no direct observational evidence of the existence of an IMBH, let alone one within a globular cluster. The recent signal GW190521, detected by the gravitational wave observatories LIGO and Virgo, is consistent with a merger of two stellar-mass black holes to leave a remnant with a mass of 150 solar masses, just within the mass range to be considered an IMBH. This is the first, and only, observation of an IMBH by direct means. With this general lack of direct observational evidence, indirect approaches using the motion of the stars within a globular cluster are important in the search for IMBHs. In these approaches, we use macroscopic properties of the star cluster to infer the presence of the gravity of a black hole, rather than “seeing” it directly. This strategy relies on having accurate dynamical models of a globular cluster, which is the focus of this thesis

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Examining the effects of magnetic fields in neutron star mergers through numerical simulations

Supervisor(s): Max Ruffert

Gamma ray bursts (GRBs) are flashes of gamma ray radiation, first observed in the late 1960s by a US military satellite program designed to monitor for gamma ray signatures of nuclear weapons testing. With only a handful of observations initially, the source of the bursts was poorly understood and dozens of different theories for their origin were proposed. Over the following decades, further observations by purpose-built gamma ray telescopes revealed that such events occur on a daily basis and that they originate from highly energetic events in other galaxies. This new information narrowed the range of likely theories and eventually a prominent theory emerged, which suggested that some GRBs could be produced by the collision of two neutron stars. In 2017, the observation of gravitational waves from a neutron star merger that coincided with a GRB [Abbott et al., 2017a] provided the first direct evidence in support of this, but the details of what conditions are required in a merger in order for it to produce a GRB are still not fully understood. Neutron star mergers involve extreme physical conditions that are far beyond what can be recreated in a laboratory, therefore in order to study them we use numerical simulations.

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Stochastic modelling and inference of ocean transport

Supervisor(s): Jacques Vanneste, James Maddison, Aretha Teckentrup

The motion of the ocean is notoriously difficult to observe. While satellites capture only the large-scale surface behaviour, a unique view is obtained from satellite-tracked drifting buoys known as drifters. These devices are released at sea and transported by ocean currents, experiencing the full complexity of ocean transport. The meandering trajectories that they follow can be studied to infer the statistics of ocean dynamics. This thesis is devoted to methods for carrying out this inference. A particular focus is on quantifying the uncertainty in our inferences. The distribution of drifters throughout the oceans is highly nonuniform, meaning that in some areas we have much less information than we need to make inferences with confidence.

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Bayesian inference for ocean transport and diffusivity fields from Lagrangian trajectory data

Supervisor(s): James Maddison, Jacques Vanneste

Calm as it seems, the ocean is never quiet. Scrutiny will reveal the abundance of eddies at all scales in the oceanic flows. The swirling and self-sustaining circular eddies transport heat and material around the globe, and in turn, regulate the climate. Modern computational capacity does not allow climate prediction models to fully resolve the turbulent motion of mesoscale eddies, living at the typical length scale of 10 km to 200 km, despite their significance redistributing heat. To overcome this technological constraint, a common approach is to decompose the turbulent ocean motion into a well-resolved mean and unresolved eddy component, with the latter modelled by a diffusion process. This leads to the notion of eddy diffusivity, which relates the rate of unresolved transport to resolved quantities.

Estimating the eddy diffusivity is however an outstanding challenge. In this thesis, we develop a Bayesian framework to infer the eddy diffusivity from the data of flow-following fluid parcels, with the vision to apply the method to the drifter data in the ocean. The Bayesian approach not only allows an estimation of the eddy diffusivity, but also the quantification of uncertainty

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Mathematics applied to the environment

Projects applying mathematics to environmental problems and supervised by James Maddison and Jacques Vanneste are available through the Edinburgh Earth, Ecology and Environment Doctoral Training Partnership.