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Zero-carbon flight represents arguably the biggest challenge of the green revolution. A variety of novel flight concepts have been proposed in response to emissions targets set by the International Air Transport Association (IATA). The common theme to enabling these innovative technologies is efficient, reliable, low-weight solutions to the control of airflow: from controlling aircraft aerodynamics to heat transfer in gas turbines. Active flow control represents a family of such solutions, and is based on the idea of harnessing the natural amplification provided by nonlinearities in fluid mechanics to bring about large-scale system change with only a small energy input. Fluidic devices are a highly-reliable means of controlling high-speed flows and have a small response time. A analytical, dynamic model of an attached jet, the canonical form of all fluidic devices, is developed from first principles. The jet is excited acoustically, which is modelled as a time-varying component of additional entrainment. The core component of the model is a novel, unsteady jet curvature equation, which finally removes the need for the quasi-steady jet assumption. An accompanying experimental validation is performed, and a strategy for inverting system nonlinearities is presented. The model is linearised so that magnitude and phase frequency responses can be compared with the validation data. Good agreement is found for one roll-off in the data, and explanations for a second, unmodelled roll-off are given. A closed-loop controller is designed and implemented for an acoustically-driven fluidic amplifier in which the flow is continuously modulated. The attached-jet model provides good agreement with experimentally-identified frequency responses, and a black-box identification is used for control purposes. The performance of the resulting LQG controller is evaluated in several experiments, and is shown either to match or outperform its open-loop counterpart in every respect. However, closed-loop bandwidth is limited by turbulent noise in the region of the system dynamics, and a means of overcoming this fundamental challenge is discussed. The response of a jet shear layer to a modulated perturbation is explored from a signal processing perspective. The well-known shear layer demodulation property is identified specifically as an envelope detector because of its phase insensitivity. A novel input over-modulation technique is proposed that halves the required actuator bandwidth while suffering only a 2.7 dB reduction in response magnitude. It is further hypothesised that the shear layer response includes a sampler, and an analogy with the Nyquist sampling theorem is made. Early experiments appear to invalidate the analogy, although the experiments are somewhat inconclusive. If the Nyquist theorem does not hold, interesting implications are raised about the current paradigm of the response of shear layers to modulated perturbations.

In this thesis we accomplish four main results related to Jacobians of curves. Firstly, we find a large number of hyperelliptic curves of genus 2, 3 and 4 whose Jacobians have torsion points of large order. The genus 2 case is particularly well-studied in the literature, and we provide a new example of a geometrically simple Jacobian of a genus 2 curve with a point of order 25, an order which was not previously known. For geometrically simple Jacobians of curves of genus 3 and 4, we extend the known orders of points, increasing the largest known order in both cases to 91 and 88, respectively. Secondly, we find an explicit embedding of the Kummer variety of a genus 3 superelliptic curve into projective space. This is a natural extension of the embeddings that are already known for the Kummer varieties of hyperelliptic curves of genus 2 and 3. Thirdly, we classify the genus 2 curves whose Jacobians admit a (4,4)- isogeny. We find an infinite family of genus 2 curves for which the elements of the kernel of the (4,4)-isogeny are defined over the ground field, and make partial progress on classifying the genus 2 curves with this property. We also extend Flynn's example of a genus 2 curve whose Jacobian admits a (5, 5)-isogeny to infinitely many geometrically nonisomorphic curves. Finally, we extend Schaefer's algorithm for computing the Selmer group of a Jacobian to carry out a (4, 4)-descent on Jacobians of curves that admit a (4, 4)-isogeny.