Statistical-dynamical analyses and modelling of multi-scale ocean variability

This thesis aims to provide a comprehensive analysis of multi-scale oceanic variabilities using various statistical and dynamical tools and explore the data-driven methods for correct statistical emulation of the oceans. We considered the classical, wind-driven, double-gyre ocean circulation model in quasi-geostrophic approximation and obtained its eddy-resolving solutions in terms of potential vorticity anomaly and geostrophic streamfunctions. The reference solutions possess two asymmetric gyres of opposite circulations and a strong meandering eastward jet separating them with rich eddy activities around it, such as the Gulf Stream in the North Atlantic and Kuroshio in the North Pacific. This thesis is divided into two parts. The first part discusses a novel scale-separation method based on the local spatial correlations, called correlation-based decomposition (CBD), and provides a comprehensive analysis of mesoscale eddy forcing. In particular, we analyse the instantaneous and time-lagged interactions between the diagnosed eddy forcing and the evolving large-scale PVA using the novel `product integral' characteristics. The product integral time series uncover robust causality between two drastically different yet interacting flow quantities, termed `eddy backscatter'. We also show data-driven augmentation of non-eddy-resolving ocean models by feeding them the eddy fields to restore the missing eddy-driven features, such as the merging western boundary currents, their eastward extension and low-frequency variabilities of gyres. In the second part, we present a systematic inter-comparison of Linear Regression (LR), stochastic and deep-learning methods to build low-cost reduced-order statistical emulators of the oceans. We obtain the forecasts on seasonal and centennial timescales and assess them for their skill, cost and complexity. We found that the multi-level linear stochastic model performs the best, followed by the ``hybrid stochastically-augmented deep learning models''. The superiority of these methods underscores the importance of incorporating core dynamics, memory effects and model errors for robust emulation of multi-scale dynamical systems, such as the oceans.Open Acces

THE AUTOMATIC CONTROL OF LARGE SHIPS IN CONFINED WATERS

The design and evaluation of a control system, which can be utilised for the automatic guidance of large ships in confined or restricted waters, is investigated. The vessel is assumed to be a multivariable system and it is demonstrated that a non-linear, time-varying mathematical model most accurately describes the motion of the hull, particularly in tight manoeuvres. A discrete optimal controller has been designed to control simultaneously track, heading and forward velocity. The system is most effective whilst operating under a dual-mode policy. It is shown that feedback matrix adaption is necessary to deal with changes in forward velocity and a form of gain scheduling is proposed. Active disturbance control is employed to counteract effects of wind and tide. An inertial navigation system, together with an optimal controller and filter, is installed on-board a car ferry model. Free-sailing tests show that the performance characteristics of the system are in accordance with theoretical predictions. The feasibility of implementation on a full-size vessel is considered.University College, Londo

On a Cartesian cut-cell methodology for simulating atmospheric ice accretion on aircraft

Atmospheric in-flight ice accretion has been a significant operational hazard in aviation for decades. Super-cooled water droplets impinge on exposed surfaces such as wings and rotor blades. These droplets may freeze on the surface thereby changing lift characteristics and disturb weight and aerodynamic balances. The multiple length scales involved prevent designing dynamically similar flows making traditional aeronautical engineering tools such as wind tunnel experiments not suitable. Therefore, computational fluid dynamics (CFD) methods have proved an attractive alternative to study atmospheric icing effects. However, most approaches are based on simple incompressible models and are only suited for small ice heights due to the difficulty of dynamically tracking the ice accretion. This thesis aims to develop novel mathematical models to capture more relevant phenomena and to improve the numerical methods to allow dynamic tracking of the air-ice interface. The initial chapter presents an augmented air and droplet model which tracks droplet temperatures thereby producing more accurate heat fluxes for the phase transition calculation. Firstly, we validate our novel model for common ice accretion test cases and find excellent agreement with literature. The advantage of the augmented system is demonstrated by applying it to an experimental setup that studies the heat exchange between water droplets and air for various flow conditions. We find excellent agreement between our model and the experiment for all presented cases whereas constant-temperature approaches match only for short interaction times. Finally, we apply the new system to study the droplet temperatures around various aerofoil and find significant temperature differences compared with conventional models. The following chapter studies the freezing process on the wing geometry. Presently, the most advanced model is based on lubrication theory, however, linear terms are truncated. We extend the series expansion to include first order terms and demonstrate that the additional order is necessary to accurately capture the thin film flow on a cylinder. Furthermore, we extend the lubrication-theory- based approach which was limited to simple geometries. The extended model is valid on arbitrary wing shapes making it more relevant for engineers studying real-world problems. The penultimate chapter combines the previous two to give a simulation of the full icing process. We integrate it with a Cartesian cut-cell method which can cope dynamically with moving interfaces. The robustness and performance of the cut-cell techniques allow us to simulate ice growth on real-world geometries. We demonstrate this capability by presenting results of the dynamic ice growth on a NACA 0012 aerofoil - making this the first such numerical experiment.EPSR

Mathematical modelling of tissue-engineering angiogenesis

We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay

Active Emulsions: Physicochemical Hydrodynamics and Collective Behavior

Active matter is a collection of constituent elements that constantly consume energy, convert it to mechanical work, and interact with their counterparts. These materials operate out of equilibrium and exhibit fascinating collective dynamics such as spontaneous pattern formation. Self-organization of bio-polymers within a cell, collective migration of bacteria in search of nutrition, and the bird flocks are paragons of active living matter and the primary source of our knowledge on it. To understand the overarching physical principles of active matter, it is desirable to build artificial systems that are capable of imitating living active matter while ruling out the biological complexities. The goal of this thesis is to study active micro-droplets as a paradigm for biomimetic artificial active particles, using fundamental principles of fluid dynamics and statistical physics. The Marangoni-driven motility in these droplets is reminiscent of the locomotion of some protozoal organisms, known as squirmers. The main scientific objectives of this research are to (i) investigate the potential biomimetic features of active droplets including compartmentalization, adaptability (e.g. multi-gait motility), and information processing (signaling and sensing) and (ii) study the implications of those features in the collective dynamics of active emulsions governed by hydrodynamic and autochemotactic interactions. These objectives are addressed experimentally using microfluidics and microscopy, integrated with quantitative image analysis. The quantitative experimental results are then compared with the predictions from theory or simulations. The findings of this thesis are presented in five chapters. First, we address the challenge of compartmentalizing active droplets. We use microfluidics to generate liquid shells (double emulsions). We propose and successfully prove the use of a nematic liquid crystal oil to stabilize the liquid shells, which are otherwise susceptible to break up during motility. We investigate the propulsion dynamics and use that insight to put forward routes to control shell motion via topology, chemical signaling, and topography. In the second results chapter, we establish the bimodal dynamics of chaotic motility in active droplets; a regime that emerges as a response to the increase of viscosity in the swimming medium. To establish the physical mechanism of this dynamical transition, we developed a novel technique to simultaneously visualize the hydrodynamic and chemical fields around the droplet. The results are rationalized by quantitative comparison to established advection-diffusion models. We further observe that the droplets undergo self-avoiding random walks as a result of interaction with the self-generated products of their activity, secreted in the environment. The third results chapter presents a review of the dynamics of chemotactic droplets in complex environments, highlighting the effects of self-generated chemical interactions on the droplet dynamics. In the fourth results chapter, we investigate how active droplets sense and react to the chemical gradients generated by their counterparts--- a behavior known as autochemotaxis. Then, we study the collective dynamics governed by these autochemotactic interactions, in two and three dimensions. For the first time, we report the observation of ‘history caging’, where swimmers are temporarily trapped in an evolving network of repulsive chemical trails. The caging results in a plateau in the mean squared displacement profiles as observed for dense colloidal systems near the glass transition. In the last results chapter, we investigate the collective dynamics in active emulsions, governed by hydrodynamic interactions. We report the emergence of spontaneously rotating clusters. We show that the rotational dynamics originates from a novel symmetry breaking mechanism for single isotropic droplets. By extending our understanding to the collective scale, we show how the stability and dynamics of the clusters can be controlled by droplet activity and cluster size. The experimental advancements and the findings presented in this thesis lay the groundwork for future investigations of emergent dynamics in active emulsions as a model system for active matter. In the outlook section, we present some of the new questions that have developed in the course of this research work and discuss a perspective on the future directions of the research on active droplets.2022-01-1

Active control of turbulence-induced helicopter vibration

Helicopter vibration signatures induced by severe atmospheric turbulence have been shown to differ considerably from nominal, still air vibration. The perturbations of the transmission frequency have significant implications for the design of passive and active vibration alleviation devices, which are generally tuned to the nominal vibration frequency. This thesis investigates the existence of the phenomena in several realistic atmospheric turbulence environments, generated using Computational Fluid Dynamic (CFD) engineering software and assimilated within a high-fidelity rotorcraft simulation, RASCAL. The RASCAL simulation is modified to calculate blade element sampling of the gust, enabling thorough, high frequency analyses of the rotor response. In a final modification, a numerical, integration-based inverse simulation algorithm, GENISA is incorporated and the augmented simulation is henceforth referred to as HISAT. Several implementation issues arise from the symbiosis, principally because of the modelling of variable rotorspeed and lead-lag motion. However, a novel technique for increasing the numerical stability margins is proposed and tested successfully. Two active vibration control schemes, higher harmonic control 'HHC' and individual blade control 'IBC', are then evaluated against a 'worst-case' sharp-edged gust field. The higher harmonic controller demonstrates a worrying lack of robustness, and actually begins to contribute to the vibration levels. Several intuitive modifications to the algorithm are proposed but only disturbance estimation is successful. A new simulation model of coupled blade motion is derived and implemented using MATLAB and is used to design a simple IBC compensator. Following bandwidth problems, a redesign is proposed using H theory which improves the controller performance. Disturbance prediction/estimation is attempted using artificial neural networks to limited success. Overall, the aims and objectives of the research are met

The role of acidity in tumour development

Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this thesis, we utilise mathematical modelling to examine the role of acidosis in the interaction between normal and tumour cell populations. In the first section we investigate the cell–microenvironmental interactions that mediate somatic evolution of cancer cells. The model predicts that selective forces in premalignant lesions act to favour cells whose metabolism is best suited to respond to local changes in oxygen, glucose and pH levels. In particular the emergent cellular phenotype, displaying increased acid production and resistance to acid-induced toxicity, has a significant proliferative advantage because it will consistently acidify the local environment in a way that is toxic to its competitors but harmless to itself. In the second section we analyse the role of acidity in tumour growth. Both vascular and avascular tumour dynamics are investigated, and a number of different behaviours are observed. Whilst an avascular tumour always proceeds to a benign steady state, a vascular tumour may display either benign or invasive dynamics, depending on the value of a critical parameter. Extensions of the model show that cellular quiescence, or non-proliferation, may provide an explanation for experimentally observed cycles of acidity within tumour tissue. Analysis of both models allows assessment of novel therapies directed towards changing the level of acidity within the tumour. Finally we undertake a comparison between experimental tumour pH images and the models of acid dynamics set out in previous chapters. This analysis will allow us to assess and verify the previous modelling work, giving the mathematics a firm biological foundation. Moreover, it provides a methodology of calculating important diagnostic parameters from pH images