Protoplanetary discs, composed of gas and dust, usually surround young stellar objects and serve two main purposes: they determine the accretion of matter onto the central object and also represent sites of planet formation. The accretion proceeds through the transport of angular momentum outwards allowing the disc matter to fall towards the centre. A mechanism responsible for the transport can be turbulence, waves or other coherent structures originating from various instabilities in discs that could, in addition, play a role in the planet formation process. For an understanding of these instabilities, it is necessary to study perturbation dynamics in differentially rotating, or sheared media. Thus, this thesis focuses on new aspects in the perturbation dynamics in non-magnetised protoplanetary discs that arise due to their self-gravity and velocity shear associated with the disc’s differential rotation. The analysis is carried out in the framework of the widely employed local shearing box approximation. We start with 2D discs and then move on to 3D ones. In 2D discs, there are two basic perturbation types/modes – spiral density waves and vortices – that are responsible for angular momentum transport and that can also contribute to accelerating planet formation. First, in the linear regime, we demonstrate that the vortical mode undergoes large growth due to self-gravity and in this process generates density waves via shear-induced linear mode coupling phenomenon. This is noteworthy, because commonly only density waves are considered in self-gravitating discs. Then we investigate vortex dynamics in the non-linear regime under the influence of self-gravity by means of numerical simulations. It is shown that vortices are no longer well-organised and long-lived structures, unlike those occurring in non-self-gravitating discs. They undergo recurring phases (lasting for a few disc rotation periods) of formation, growth and eventual destruction. We also discuss the dust trapping capability of such transient vortices. Perturbation dynamics in 3D vertically stratified discs is richer, as there are more mode types. We first consider non-axisymmetric modes in non-self-gravitating discs and then only axisymmetric modes in the more complicated case when self-gravity is present. Specifically, in non-self-gravitating discs with superadiabatic vertical stratification, motivated by the recent results on the transport properties of incompressible convection, we show that when compressibility is taken into account, the non-axisymmetric convective mode excites density waves via the same shear-induced linear mode coupling mechanism mentioned above. These generated density waves transport angular momentum outwards in the trailing phase, and we suggest that they may aid and enhance the transport due solely to convection in the non-linear regime, where the latter becomes outward. In the final part of the thesis, we carry out a linear analysis of axisymmetric vertical normal modes in stratified self-gravitating discs. Although axisymmetric modes do not display shear-induced couplings, their analysis provides insight into how gravitational instabilities develop in the 3D case and their onset criterion. We examine how the structure of dispersion curves and eigenfunctions of 3D modes are influenced by self-gravity, which mode first becomes gravitationally unstable and thus determines the onset criterion and nature of the gravitational instability in stratified discs. We also contrast the more exact instability criterion obtained with our 3D model with that of density waves in 2D discs. Based on these findings, we discuss the origin of 3D behaviour of perturbations involving noticeable disc surface distortions, as seen in some numerical simulations of self-gravitating discs.

Previous studies have shown that thermal feedback from protostars plays a key role in the process of low-mass star formation. In this thesis, we explore the effects of protostellar heating on the formation of stellar clusters. We describe new methods for modelling protostellar accretion luminosities and protostellar evolution in calculations of star formation. We then present results of a series of numerical simulations of stellar cluster formation which include these effects, and examine their impact. We begin by investigating the dependence of stellar properties on the initial density of molecular clouds. We find that the dependence of the median stellar mass on the initial density of the cloud is weaker than the dependence of the thermal Jeans mass when radiative effects are included. We suggest that including protostellar accretion luminosities and protostellar evolution may weaken this dependence further, and may account for the observed invariance of the median stellar mass in Galactic star-forming regions. Next, we investigate the effects of including accretion feedback from sink particles on the formation of small stellar groups. We find that including accretion feedback in calculations suppresses fragmentation even further than calculations that only include radiative transfer within the gas. Including feedback also produces a higher median stellar mass, which is insensitive to the sink particle accretion radius used. Finally, we compare calculations of small stellar clusters which model the evolution of protostars using a live stellar model with those which use a fixed stellar structure. We find that the dynamics of the clusters are primarily determined by the accretion luminosities of protostars, but that the relative effects of protostellar evolution depend on the accretion rate and advection of energy into the protostar. We also demonstrate how such calculations may be used to study the properties of young stellar populations.

Radio-loud active galactic nuclei (AGN) are one class of objects associated with accretion activity onto supermassive black holes in centers of massive galaxies. They are believed to be in a radiatively-inefficient accretion mode with low accretion rate. To understand this accretion mode, it is important to measure its radiative output at high energies (> 13.6eV), which can be traced through optical emission lines. However, little is known about their true radiative output. This is because no correlation between optical emission-line and radio luminosity has been found for the majority of low-luminosity radio AGN, which are often classified as low-excitation radio galaxies, or Fanaroff-Riley Class I (FR-I) radio galaxies. We demonstrate that most of the line emission found in these galaxies is not powered by the central AGN, but likely powered by some old stellar population. Only when this component is subtracted or otherwise taken into account can we estimate the true line emission associated with the AGN. These emissions may show interesting correlations with the radio luminosities in some cases.

This study proposes a method to enhance the anti-icing capabilities of superhydrophobic surfaces by utilizing vibration to further reduce contact time of an impacting droplet in addition to keeping the droplet in the Cassie-Baxter regime, where surface adhesion is lower than the opposing Wenzel regime. We tested this with two methods: by investigating the effects of vibration normal to the plane of a superhydrophobic surface being impacted by water droplets in a room temperature environment, with the surface horizontal in a room temperature environment and tiled in a subzero degree environment. The amplitude and frequency of the vibration were varied in our experiments. Our results show that the mean contact time of a 10µL droplet consistently decreased linearly as the vibration frequency increased, though the standard deviations drastically increased. The ice accretion in the second phase of the testing also had significant variance, which obfuscated any reliable trend from the introduction of vibration.

Historical change in the geomorphology, hydrodynamics, and surficial sediment of the tidal delta system of Tauranga Harbour are investigated with the general aim of analysing The general aims of this thesis are: firstly to analyse historical changes to inlet delta system geomorphology using historical hydrographic charts, secondly, to conduct hydrodynamic numerical modelling using historical bathymetries to access changes in peak spring flow and potential net tidal sediment transport, and thirdly, to analyse historical changes in surficial sediment and bedforms. Geomorphic change was investigated through plotting difference in bathymetry graphs and conducting cross sections taken from digisitied bathymetries obtained from historical hydrographic charts from 1852, 1879, 1901, 1927, 1954 and a modern bathymetry from 2006. Two-dimensional hydrodynamic numerical modelling was conducted to investigate the changes in peak tidal current flow and potential net sediment transport between 1852 and 2006. Changes in surficial sediment patterns were determined through completing a side scan sonar survey with associated sediment samples for ground truthing of grain size and underwater videography to gather surficial shell coverage information. This was used to produce a surficial sediment coverage map which was compared to historical studies Major geomorphological findings include that the shipping channel appears to have induced minor change in the geomorphology of the FTD but such changes are similar to those identified in the historical bathymetries of 1852, 1879, 1901, 1927, 1954 prior to dredging. Significant changes have occurred on the ETD, with the majority of the ETD showing scour of 1 m while the terminal lobe has extended seawards. This is associated with historical (since 1852) narrowing of the inlet from Panepane Point to Mt Maunganui by ~ 900 m. Hydrodynamic numerical modelling has shown a significant increase in potential net tidal sediment transport in the Cutter Channel due to dredging, while the Maunganui Roads Channel shows a reduction of net potential tidal sediment transport that is associated with the dredging of this channel. The area surrounding Panepane Point undergoes significant increases and decreases in net potential tidal sediment transport both before and after dredging Investigation of the surficial sediment patterns over the FTD and ETD from sidescan sonar and bottom samples show that between 1983 and 2007 there has been a northwards extension of the area of major shell (greater than 50 %) converge in the main ebb channel as well as reduction in major shell converge in flood tidal delta ebb shield region. The Maunganui Roads Channel changes from sitly sands to medium and fine sands.

Magnetorotational instability (MRI) is one of the most important and most common instabilities in astrophysics. Today it is widely accepted that it serves as a major source of turbulent viscosity in accretion disks, the most energy efficient objects in the universe. The importance of the MRI for astrophysics has been realized only in recent fifteen years. However, originally it was discovered much earlier, in 1959, in a very different context. Theoretical flow of a conducting liquid confined between differentially rotating cylinders in the presence of an external magnetic field was analyzed. The central conclusion is that the additional magnetic field parallel to the axis of rotation can destabilize otherwise stable flow. Theory of non-magnetized fluid motion between rotating cylinders has much longer history, though. It has been studied already in 1888 and today such setup is usually referred as a Taylor-Couette flow. To prove experimentally the existence of MRI in a magnetized Taylor-Couette flow is a demanding task and different MHD groups around the world try to achieve it. The main problem lies in the fact that laboratory liquid metals which are used in such experiments are characterized by small magnetic Prandtl number. Consequently rotation rates of the cylinders must be extremely large and vast amount of technical problems emerge. One of the most important difficulties is an influence of plates enclosing the cylinders in any experiment. For fast rotation the plates tend to dominate the whole flow and the MRI can not be observed. In this thesis we discuss a special helical configuration of the applied magnetic field which allows the critical rotation rates to be much smaller. If only the axial magnetic field is present, the cylinders must rotate with angular velocities corresponding to Reynolds numbers of order Re ≈ 10^6. With the helical field this number is dramatically reduced to Re ≈ 10^3. The azimuthal component of the magnetic field can be easily generated by letting an electric current through the axis of rotation, In a Taylor-Couette flow the (primary) instability manifests itself as Taylor vortices. The specific geometry of the helical magnetic field leads to a traveling wave solution and the vortices are drifting in a direction determined by rotation and the magnetic field. In an idealized study for infinitely long cylinders this is not a problem. However, if the cylinders have finite length and are bounded vertically by the plates the situation is different. In this dissertation it is shown, with use of numerical methods, that the traveling wave solution also exists for MHD Taylor-Couette flow at finite aspect ratio H/D, H being height of the cylinders, D width of the gap between them. The nonlinear simulations provide amplitudes of fluid velocity which are helpful in designing an experiment. Although the plates disturb the flow, parameters like the drift velocity indicate that the helical MRI operates in this case. The idea of the helical MRI was implemented in a very recent experiment PROMISE. The results provided, for the first time, an evidence that the (helical) MRI indeed exists. Nevertheless, the influence of the vertical endplates was evident and the experiment can be, in principle, improved. Exemplary methods of reduction of the end-effect are here proposed. Near the vertical boundaries develops an Ekman-Hartmann layer. Study of this layer for the MHD Taylor-Couette system as well as its impact on the global flow properties is presented. It is shown that the plates, especially if they are conducting, can disturb the flow far more then previously thought also for relatively slow rotation rates. / Die magnetische Scherinstabilitaet (engl. MRI) ist eine sehr häufig in der Astrophysik anzutreffende Instabilität. Es wird heute weithin angenommen, dass sie die Ursache für die turbulente Viskosität in Akkretionsscheiben ist, den Objekten mit der höchsten Energieeffizienz im Kosmos. Die Bedeutung der MRI ist erst in den letzten fünfzehn Jahren klargeworden. Entdeckt wurde sie jedoch schon viel früher, im Jahre 1959 in einem völlig anderen physikalischen Kontext. Die Strömung in einer leitfähigen Flüssigkeit zwischen differentiell rotierenden Zylindern unter dem Einfluss eines externen Magnetfeldes wurde theoretisch untersucht. Die Schlussfolgerung war, dass das zugesetzte Magnetfeld eine sonst stabile Strömung destabilisieren kann. Die Geschichte der Theorie von Strömungen zwischen Zylindern reicht bis ins Jahr 1888 zurück. Heute wird ein solcher Aufbau üblicherweise als Taylor-Couette-Strömung bezeichnet. Ein System rotierender Zylinder, zwischen denen sich flüssiges Metall befindet, war Gegenstand des kürzlich durchgeführten Experiments PROMISE. Die Ergebnisse belegen zum ersten Mal experimentell die Existenz der MRI. Um die notwendigen Drehzahlen gering zu halten, wurde ein spezielles, helikales Magnetfeld angelegt. Gegenstand dieser Dissertation ist die theoretische Behandlung der magnetohydrodynamischen Taylor-Couette-Strömung, ähnlich der des Experiments PROMISE. Insbesondere der Einfluss der vertikalen Ränder (Deckel) wird untersucht. Es wird gezeigt, dass die MRI auch in Zylindern mit endlicher Höhe und mit begrenzenden Deckeln einsetzt. In der Nähe der vertikalen Ränder bildet sich eine Ekman-Hartmann-Schicht. Die Untersuchung dieser Schicht im Zusammenhang mit dem MHD-Taylor-Couette-System sowie ihr Einfluss auf die globalen Strömungseigenschaften werden vorgestellt. Es wird gezeigt, dass die Deckel - insbesondere wenn sie elektrisch leitend sind - die Strömung stärker beeinflussen können als bisher angenommen, selbst bei den geringen Drehzahlen. Es werden Methoden zur Verringerung dieser unerwünschten Effekte vorgeschlagen.

Liniengetriebene Winde werden durch Impulsübertrag von Photonen auf ein Plasma bei Absorption oder Streuung in zahlreichen Spektrallinien beschleunigt. Dieser Prozess ist besonders effizient für ultraviolette Strahlung und Plasmatemperaturen zwischen 10^4 K und 10^5 K. Zu den astronomischen Objekten mit liniengetriebenen Winden gehören Sterne der Spektraltypen O, B und A, Wolf-Rayet-Sterne sowie Akkretionsscheiben verschiedenster Größenordnung, von Scheiben um junge Sterne und in kataklysmischen Veränderlichen bis zu Quasarscheiben. Es ist bislang nicht möglich, das vollständige Windproblem numerisch zu lösen, also die Hydrodynamik, den Strahlungstransport und das statistische Gleichgewicht dieser Strömungen gleichzeitig zu behandeln. Die Betonung liegt in dieser Arbeit auf der Windhydrodynamik, mit starken Vereinfachungen in den beiden anderen Gebieten. <br /> Wegen persönlicher Beteiligung betrachte ich drei Themen im Detail. <br /> 1. Windinstabilität durch Dopplerde-shadowing des Gases. Die Instabilität bewirkt, dass Windgas in dichte Schalen komprimiert wird, die von starken Stoßfronten begrenzt sind. Schnelle Wolken entstehen im Raum zwischen den Schalen und stoßen mit diesen zusammen. Dies erzeugt Röntgenflashes, die die beobachtete Röntgenstrahlung heißer Sterne erklären können. <br /> 2. Wind runway durch radiative Wellen. Der runaway zeigt, warum beobachtete liniengetriebene Winde schnelle, kritische Lösungen anstelle von Brisenlösungen (oder shallow solutions) annehmen. Unter bestimmten Bedingungen stabilisiert der Wind sich auf masseüberladenen Lösungen, mit einem breiten, abbremsenden Bereich und Knicken im Geschwindigkeitsfeld. <br /> 3. Magnetische Winde von Akkretionsscheiben um Sterne oder in aktiven Galaxienzentren. Die Linienbeschleunigung wird hier durch die Zentrifugalkraft entlang korotierender poloidaler Magnetfelder und die Lorentzkraft aufgrund von Gradienten im toroidalen Feld unterstützt. Ein Wirbelblatt, das am inneren Scheibenrand beginnt, kann zu stark erhöhten Massenverlustraten führen. / Line driven winds are accelerated by the momentum transfer from photons to a plasma, by absorption and scattering in numerous spectral lines. Line driving is most efficient for ultraviolet radiation, and at plasma temperatures from 10^4 K to 10^5 K. Astronomical objects which show line driven winds include stars of spectral type O, B, and A, Wolf-Rayet stars, and accretion disks over a wide range of scales, from disks in young stellar objects and cataclysmic variables to quasar disks. It is not yet possible to solve the full wind problem numerically, and treat the combined hydrodynamics, radiative transfer, and statistical equilibrium of these flows. The emphasis in the present writing is on wind hydrodynamics, with severe simplifications in the other two areas. <br /> I consider three topics in some detail, for reasons of personal involvement. <br /> 1. Wind instability, as caused by Doppler de-shadowing of gas parcels. The instability causes the wind gas to be compressed into dense shells enclosed by strong shocks. Fast clouds occur in the space between shells, and collide with the latter. This leads to X-ray flashes which may explain the observed X-ray emission from hot stars. <br /> 2. Wind runaway, as caused by a new type of radiative waves. The runaway may explain why observed line driven winds adopt fast, critical solutions instead of shallow (or breeze) solutions. Under certain conditions the wind settles on overloaded solutions, which show a broad deceleration region and kinks in their velocity law. <br /> 3. Magnetized winds, as launched from accretion disks around stars or in active galactic nuclei. Line driving is assisted by centrifugal forces along co-rotating poloidal magnetic field lines, and by Lorentz forces due to toroidal field gradients. A vortex sheet starting at the inner disk rim can lead to highly enhanced mass loss rates.

Motivated by recent successes in linking the kinetic power of relativistic jets in active galactic nuclei (AGN) to the low-frequency, isotropic lobe emission, I have re-examined the blazar and radio-loud AGN unification scheme through careful analysis of the four parameters we believe to be fundamental in producing a particular jet spectral energy distribution (SED): the kinetic power, accretion power, accretion mode, and orientation. In particular, I have compiled a multi-wavelength database for hundreds of jet SEDs in order to characterize the jet spectrum by the synchrotron peak output, and have conducted an analysis of the steep lobe emission in blazars in order to determine the intrinsic jet power. This study of the link between power and isotropic emission is likely to have a wider applicability to other types or relativistic jet phenomena, such as microquasars. Based on a well-characterized sample of over 200 sources, I suggest a new unification scheme for radio-loud AGN (Meyer et al. 2011) which compliments evidence that a transition in jet power at a few percent of the Eddington luminosity produces two types of relativistic jet (Ghisellini, et al., 2009). The `broken power sequence' addresses a series of recent findings severely at odds with the previous unification scheme. This scheme makes many testable predictions which will can be addressed with a larger body of data, including a way to determine whether the coupling between accretion and jet power is the currently presumed one-to-one correspondence, or whether accretion power forms an upper bound, as very recent observations suggest (Fernandes et al. 2011). This work is a first step toward a unified understanding of the relativistic jets found in radio-loud active galactic nuclei (AGN) and their connection to accretion onto the super-massive black holes from which they emanate.

Due to its adaptable nature in a broad range of problem domains, Smoothed Particle Hydrodynamics (SPH) is a popular numerical technique for computing solutions in astrophysics. This dissertation discusses the SPH technique and assesses its capabilities for reproducing steady-state spherically-symmetric accretion flow. The accretion scenario is of great interest for its applicability in a diverse array of astrophysical phenomena and, under certain assumptions, it also provides an accepted analytical solution against which the numerical method can be validated. After deriving the necessary equations from astrophysical fluid dynamics, giving a detailed review of solving the steady-state spherical accretion problem, and developing the SPH methodology, this work suggests solutions to the issues that must be overcome in order to successfully employ the SPH methodology to reproduce steady-state spherical accretion flow. Several techniques for setting initial data are addressed, resolution requirements are illustrated, inner and outer boundary conditions are discussed, and artificial dissipation parameters and methodologies are explored. / text

The Magnetorotational Instability (MRI) is believed to be the primary mechanism for angular momentum transfer in astrophysical accretion disks. This instability, which exists in ionized disks in the presence of weak magnetic fields, can either transfer angular momentum directly, or give rise to anomalous viscosity via non-linear turbulence. While many previous analytical treatments are concerned with the local theory of the MRI, when the length scale of rotation shear is comparable to the length scale of the most unstable modes, a global analysis is necessary. In this dissertation we investigate the global theory of the linear MRI. In particular, we show how rotation shear can localize global modes and how the global growth rates can differ signicantly from the local approximation in certain cases. Changes in the equilibrium density are considered. In addition, the effects of Hall Magnetohydrodynamics on the MRI are studied in both the local and global cases. / text