Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 47-51). Also available in electronic version.

In many astrophysical problems magnetic reconnection plays a major role. Despite this reconnection theory remains incompletely understood, partly due to the strong non-linearity of the governing equations and the resulting difficulties in demonstrating analytical solutions. This thesis examines some fundamental aspects of reconnection theory: namely, the dynamics of driven and spontaneously reconnecting systems. We first consider the dynamics of a driven reconnecting system by numerically modelling a configuration consisting of two oppositely oriented flux systems with a variety of different boundary conditions and internal parameters. The results indicate that the rate of reconnection is chiefly dependent on the magnetic Reynolds number, but that the plasma flow is weakly dependent on this parameter, being more affected by the curvature of Incoming magnetic field. Scaling laws for the dimensions of the diffusion region are derived, and the existence of several reconnection regimes is shown. Using the same computer code we also simulate tearing modes in Cartesian geometry under different boundary conditions. By imposing a suitable perturbation a magnetic island is generated. The plasma flows show marked differences for the different boundary conditions implemented. Lastly, we examine some aspects of the coalescence instability. The usual flux function taken to represent a tearing node Island in the linear growth phase is shown to be erroneous, and we derive a correct expression. We show that under certain conditions there exists a threshold to coalescence that depends on the island wavenumbers and the associated perturbation.

This work assesses the importance of nonlinearity in the stability of flows over compliant and rigid walls, and comprises three main parts. The first part considers inviscid flow with a free surface over a flexible boundary. The dispersion relation is obtained, and the conditions for linear instability investigated. The linear dispersion relation is then used to show that the conditions for nonlinear three-wave resonance are often met. In some circumstances, the resonance may be of 'explosive' sort, involving waves of opposite energy sign; but non-explosive resonant configurations are most common. Next, the wave- amplitude evolution equations for three-wave resonance are derived, firstly by a 'direct' approach, and then via a variational (averaged Lagrangian) method. Results agree with those of Case & Chiu (1977) for capillary-gravity waves, and Craik & Adam (1979), for three-layer fluid flow, on taking the appropriate limits. We also consider a nonlinear model for the flexible boundary. In the second part, stability of Blasius flow over a compliant surface is studied. This extension of rigid-wall work of Craik (1971) and Hendriks (appendix to Usher & Craik 1975) determines the quadratic interaction coefficients of three-wave resonance, and complements the linear analysis of Carpenter & Garrad (1985, 1986) and others. First, the linear eigenvalue spectrum is investigated for various values of the wall parameters. Then, resonant triads are located and the quadratic interaction coefficients determined numerically. By way of introduction some rigid-wall results are also presented, extending those of Hendriks.

The buoyancy forcing of the Red Sea and its dynamical response are examined. Buoyancy transports through the Strait of Bab el Mandab, the major oceanic exchange point of the Red Sea with the open ocean, provide a strong constraint on the surface buoyancy fluxes. Hydrographic data and current records at the Strait require the annual mean surface heat flux to be −8 ± 2 W m⁻². For the annual mean freshwater fluxes the conservation of volume and salt give the net evaporation rate as 1.60 ± 0.35 m y⁻¹. The surface fluxes estimated from the heat and freshwater transports at the Strait are compared to the annual mean surface fluxes estimated from standard meteorological data sets and formulae used on a global scale as in the revised Comprehensive Ocean-Atmosphere Data Set (UWM/COADS). The difference between the surface heat fluxes and that implied by the exchange through the Strait is large and close to 100 W m⁻². A large portion of this difference is explained by the overestimated solar irradiance due to the neglect of spatial and seasonal variations of aerosol concentration, and misapplication of a standard formula for insolation. Another portion of the difference comes from the underestimated longwave radiation due to the use of a bulk formula which is adequate for the open ocean but inappropriate for the Red Sea. The evaporative losses are also found to be underestimated, probably because of underestimated wind speeds. The net evaporation is the main contributor to the annual mean buoyancy loss approximately of 2 × 10⁻⁸ m² s⁻3. The annual mean surface buoyancy flux, which is compatible with the oceanic buoyancy transport, is used with Phillips' similarity model to investigate the buoyancy driven flow of the upper 140m of the Red Sea. The observed stratification of the Red Sea can be achieved only with a very large eddy viscosity in the return flow. It is possible that this high vertical viscosity could be a proxy for processes neglected by this model such as bottom friction on the sloping boundaries. The effect of wind stress is small, but a southward wind combined with the bottom friction of a modified model with depth-dependent basin width could account for the viscous force required by a model. The effectiveness of the bottom friction in retarding the flow depends on the magnitude of the lateral diffusion of momentum. To explore the possibility of measuring the horizontal momentum fluxes above a sloping boundary in a channel, we performed an experiment in the Strait of Georgia with two Acoustic Doppler Current Profilers. Although further investigation of such measurements is required and several issues remain to be resolved, it is shown that an estimate of the horizontal eddy viscosity acting on the tidal currents is possible with this method and gives about 50 m² s⁻¹ . Overall, the dynamics of the Red Sea appears to be determined mainly by the surface buoyancy fluxes and internal and lateral frictional forces. Accurate modelling of the Red Sea requires improved knowledge of the forcing and of an appropriate parameterization of the friction. / Graduate

It is intended that this paper present an acceptable proof of the existence of a solution for the wave equation.

The effect of structuring, in the form of magnetic or density inhomogeneities, on the magnetohydrodynamic (mhd) waves of an infinite plasma is investigated. The appropriate dispersion formulae, in both Cartesian and cylindrical polar coordinate geometries, are derived. The main properties of the allowable modes in structured plasmas are described, particularly those featuring in a slender inhomogeneity. The inclusion of non-adiabatic effects is examined, specifically for a thermally dissipative, unstratified, finite structure and for a slender inhomogeneity in a stratified medium. The dissipative time scales of slender structures are shown to have a dependence on the Peclet number. Growth factors appropriate to these time scales for the overstable motions of a thermally dissipative, Boussinesq fluid are derived. For the linear analysis of a slender structure it is shown that the dispersive nature of the waves is deducible from the simplified one-dimensional equations. The analysis is extended, for slender structures, to nonlinear motions and the governing equation representing an effective balance between nonlinear, dispersive and dissipative effects, the Benjamin-Ono-Burgers equation, is established. The solutions of this equation are considered and, for weakly-dissipative systems, are shown to be slowly decaying solitons. The importance, in the context of group velocity, of the dispersive nature of waves in ducted structures is discussed and analogies are made with other ducted waves, for example, the Love waves of seismology. It is suggested that the behaviour of such waves, following an impulse, may account for the range of oscillatory behaviour, the quasi-periodic and short time scales, observed in both the solar corona and Earth's magnetosphere. Density variations across a structure and the structure's curvature, with possible applications to coronal loops, are also considered. Further suggestions for possibly identifying some of the theoretical results with observed behaviour in sunspots, chromospheric fibrils and spicules are also made.

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Doctor of Philosophy. Johannesburg, May 2017 / Shock{waves (shocks) exist in various shapes; restricted to two dimensions some examples are planar, cylindrical, parabolic and elliptical. However, most shock{wave research has been focussed mostly on plane shocks. In this research, the scope is expanded to cylindrical shock{wave segments where a plane shock can be viewed as a cylindrical shock segment (referred to as a cylindrical shock) with a large radius of curvature; with this view, the expectations are that cylindrical and plane shocks behave similarly although with quantitative di erences. Whereas plane shocks have constant orientation, constant strength and can be imagined to extend unbounded, cylindrical shock segments demand that both ends be bound; this leads to spatial constraints, shock strength varying with respect to radius and shock orientation being non-constant. Three shock phenomena were investigated: di raction, re ection and propagation in converging diverging nozzles. Shock{tube experiments were run for shocks with a radius of 165 mm and strength between Mach numbers 1.2 and 1.7. Complementing these were Computational Fluid Dynamics (CFD) and Geometric Shock Dynamics (GSD) simulations where GSD relies on Whitham's equations. On shock di raction, cylindrical shocks were shown to behave qualitatively like plane shocks. Upon encountering a sharp corner, expansion waves propagate along the shock. However, after re ecting o the opposite wall they become compression waves and form a 'Mach re ection (MR)' like con guration on the shock front. A method for calculating the locus of the expansion waves based on Whitham's theory is presented, which on comparison with CFD simulations gives good correlation. Comparisons of shock pro les calculated using Whitham's theory and CFD is also made; it showed good correspondence before the formation of MR like con gurations after which the pro les di er. The re ection of cylindrical shocks was investigated from both an experimental and numerical perspective. Shock{tube experiments were run for shocks propagating on concave cylindrical walls with radii of 100 mm, 180 mm, 140 mm and 82 mm, the range was expanded by use of CFD. An expression for calculating the locus of the MR that forms on iii the shock front was derived which generalises onto plane shocks. Two limits were recognised, one where shock radius is much greater than wall radius and another where shock radius is much smaller. The former corresponds to a cylindrical shock on a plane wall while the latter a plane shock on a cylindrical wall as illustrated by the data gathered. Cylindrical shock propagation in converging-diverging nozzles was also investigated. In this case, the phenomena at play are di raction, re ection and focusing, a combination which results in a complex evolution of the shock front. Two types of channels were investigated, one formed from a 3rd order polynomial and another from circular arcs. In both cases, wall signal were generated on either side of the shock which split the shock{front into three sections. The decreasing channel cross{section area causes the shock strength to increase resulting in very weak MR formation on the shock front. Channels from circular walls exhibit a single peak in the centre line shock strength while that from polynomial pro le walls results in a double peak. This was then related to type of wall disturbance generated. / MT 2017

Undulatory ribbon- n-based propulsion is an appealing propulsion mechanism due to its rich locomotor capabilities that can improve the propulsive performance and maneuverability of underwater vehicles. For instance, the swimming mechanics of weakly electric black ghost knife sh (Apteronotus albifrons) is of great interest to study because of their high swimming e ciency at low speeds and extraordinary agility such as rapid reversal swimming, hovering in presence of water disturbance, rolling and vertical swimming. In this thesis work, to facilitate our understanding on the exible undulatory ribbon n propulsion, we have four research motivations. The rst objective is to study how the use of exible rays and di erent n morphology can in uence the propulsive performance of ribbon- n propulsion. It is possible that natural swimmers using this locomotion method could take advantage of passive n motion based on the coupling of uid-structure interaction and the elasto-mechanical responses of the undulating n. Therefore, the second objective is to understand how an under-actuated undulating n can take advantage of natural dynamics of the uid-structure interaction for the propulsive force generation. In addition to the impressive propulsive performance of the undulatory n propulsion, the exceptional maneuverability of knife sh is also a key motivation that drives this thesis work. Thus, we dedicate to investigate how traveling wave shapes and actuation parameters (frequency, wavelength) can manipulate the maneuvering behaviors of a swimmer propelled by an undulating ribbon n. Lastly, we aim to uncover the e ect of varying traveling wave amplitudes and pectoral ns on its maneuvering performances. Two robotic devices were developed to study the propulsive performance of both fullyactuated and under-actuated ribbon n propulsion and investigate the maneuver control of a free-swimming underwater robot propelled by an undulatory n. For the rst research aim, we study the e ect of exible rays and di erent n morphology on the propulsive performance of ribbon- n propulsion. A physical model composed of fteen rays interconnected with an elastic membrane was used to test four di erent ray exural sti ness and four aspect ratios. Our results show that exible rays can improve the propulsive e ciency compared to a rigid counterpart. In addition, the morphology of the ribbon n a ects its propulsive performance as well, and there could exist an optimal n morphology. To understand how an underactuated undulating n can modify its active and passive n motion to e ectively control the hydrodynamic force and propulsive e ciency. We did a series of experiments using the same robotic n model but with some structural modi cations and we measured n kinematics, net surge force and power consumption. We nd that the under-actuated n can keep the equivalent propulsive e ciency as the fully-actuated counterpart within our experimental parameter range. Moreover, our results demonstrate that the thrust force and power consumption of an under-actuated n follow the same scaling laws as the fully-actuated n. To conduct the free-swimming maneuver study, we developed a self-contained, free-swimming robot propelled by an undulatory n, which is able to perform the following maneuvers: forward, reversed swimming and hovering motion. We also performed V3V PIV experiments to capture the ow structures generated by the robotic device. Our results show that the robot can reach higher swimming e ciency at low frequencies. As the number of traveling waves increases, the robot swims more stably in roll, pitch and yaw motions. For cases with varying wave amplitudes, traveling wave with incremental wave amplitude can achieve free-swimming velocity higher than that of decremental wave amplitude. However, the latter case can generate higher pitch angles. For the robot with slightly negative-pitched pectoral ns, it can perform slow diving maneuvers. These ndings demonstrate that we can take advantage of the undulating ribbon n propulsion to achieve high maneuverability for the future underwater vehicles in complex environment. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

The aim of this project is to identify the effect of wind on near-shore breaking waves. A breaking wave was created using a simulated beach slope configuration. Testing was done on two different beach slope configurations. The effect of offshore winds of varying speeds was considered. Waves of various frequencies and heights were considered. A parametric study was carried out. The experiments took place in the Hydrodynamics lab at FAU Boca Raton campus. The experimental data validates the knowledge we currently know about breaking waves. Offshore winds effect is known to increase the breaking height of a plunging wave, while also decreasing the breaking water depth, causing the wave to break further inland. Offshore winds cause spilling waves to react more like plunging waves, therefore increasing the height of the spilling wave while consequently decreasing the breaking water depth. / by Faydra Schaffer. / Thesis (M.S.C.S.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

Scale model tests are conducted of a Surface Effect Ship in a near-shore developing sea. A beach is built and installed in a wave tank, and a wavemaker is built and installed in the same wave tank. This arrangement is used to simulate developing sea conditions and a 1:30 scale model SES is used for a series of experiments. Pitch and heave measurements are used to investigate the seakeaping response of the vessel in developing seas. The air-cushion pressure and the vessel speed are varied, and the seakeeping results are compared as functions of these two parameters. The experiment results show a distinct correlation between the air-cushion pressure and the response amplitude of both pitch and heave. The results of these experiments are compared against results of a computer model of a Surface Effect Ship (SES). / by Michael Kindel. / Thesis (M.S.C.S.)--Florida Atlantic University, 2012. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web. / Mode of access: World Wide Web. / System requirements: Adobe Reader.