Tsunami are a very dangerous natural hazard, as highlighted in recent years by the Indian Ocean Tsunami of 2004 and the Japan Tsunami of 2011. In the last decade, tsunami have claimed hundreds of thousands of lives, and caused billions of dollars in damage around the world. The hazard posed to coastal communities by tsunami is expected to increase in the future, due to population growth, intensification of coastal development and sea level rise due to climate change. Tsunami may be generated by a number of different source mechanisms. One such source mechanism is a submarine landslide, which can occur in a number of marine environments containing significant sediment accumulation on a sloping seafloor. The high amplitudes and rapid celerities of landslide-generated tsunami make them very dangerous to communities in the vicinity of the landslide, although these waves do not possess the potential for transoceanic devastation. The objectives of this research project are to carry out a series of two-dimensional physical experiments investigating the waves generated by a rigid block landslide moving along a horizontal boundary. The use of a horizontal boundary has the advantage that waves propagating in the offshore and onshore directions may be measured (unlike previous studies using sloping boundaries). The landslide motion is provided by a mechanical system, allowing testing of a broad range of motion, and isolation of the wavemaking properties of different phases of landslide motion. Experiments are carried out in a 14.66 m long flume, with width 0.25 m and working depth 0.50 m. A false floor installed in the flume provides the sliding surface for the landslide motion, and houses the mechanical system. A series of preliminary particle tracking velocimetry experiments confirm the ability of the mechanical system to achieve its velocity targets to within 5% or better, depending on the parameters of the landslide motion. Full spatial and temporal resolution of the wave field is achieved using a laser-induced fluorescence technique to identify the air-water interface to sub-pixel accuracy. The measurements obtained using laser-induced fluorescence are validated against measurements from a resistance wave gauge, with sub-millimetre agreement. In an additional experiment, the particle tracking velocimetry technique provides measurements of the subsurface velocity field. The landslide motion during all experiments consists of an initial period of constant acceleration, followed by a period of constant velocity, followed by a deceleration to rest (at the same rate as the initial acceleration). The landslide acceleration generates two dispersive packets of waves, travelling in the offshore and onshore directions. The offshore-propagating wave packet contains a leading crest and the onshore-propagating wave packet contains a leading trough, with both waves approaching the shallow water limit. A free surface depression forms above the landslide during its constant-velocity motion, and its amplitude may be predicted to within approximately 20% using standard hydraulic theory (considering a frame of reference moving with the landslide). The offshore-propagating waves passing over the landslide cause the amplitude of this depression to fluctuate over time. The deceleration of the landslide generates two additional packets of waves with the opposite polarity to the waves generated by the landslide acceleration. The full spatial and temporal resolution of the generated wave field allows the calculation of the potential energy within the wave field. Additionally, the energy (and mass) within the onshore- and offshore-propagating wave packets may be estimated by calculating these quantities within the onshore and offshore regions of the experimental domain. The wave packets generated by the initial landslide acceleration transport positive mass in the offshore direction, and negative mass in the onshore direction. This mass transport is balanced by the waves generated during the deceleration of the landslide. The nondimensional landslide acceleration, landslide Froude number and submergence depth are varied during the physical experiments. The landslide Froude number has the greatest effect on the behaviour of the generated wave field. At low Froude numbers, the wave field is dominated by the waves generated by the acceleration and deceleration of the landslide. As the Froude number increases, the onshore-propagating waves become negligible in amplitude compared to the offshore-propagating waves. Additionally, the free surface depression increases in amplitude and a group of short-wavelength waves become trapped behind the landslide. These waves exhibit highly nonlinear behaviour at landslide Froude numbers greater than 0.5. The simple experimental geometry allows comparison between the measured wave fields with the predictions of three mathematical models. Two inviscid-irrotational models, differing in their treatment of the bottom boundary condition, provide comparisons over the entire parameter space. These models under-predict the amplitudes of the generated waves, and fail to correctly predict the ongoing interaction between the landslide and the offshore-propagating waves. The inclusion of bottom boundary nonlinearity improves the predictions of the amplitude of the leading waves, and the potential energy within the wave field. However, both of the inviscid models do not predict the extent of wave trapping behaviour behind the landslide observed in the experiments. A viscous model, formulated in the DNS solver Gerris, improves the predictions of wave trapping (and amplitude in general) in one experiment. Although the model still under-predicts the amplitudes of the generated waves, it correctly predicts the amplification of the waves behind the landslide during its constant-velocity motion. The failure of the inviscid models to predict the amplitudes of these waves can be mostly attributed to the linearised free surface condition used by both models. The presence of the turbulent wake may also have a secondary effect on these predictions. An extension of the linear inviscid-irrotational model to three dimensions allows the effect of the landslide width on the amplitudes of the generated waves to be determined. As the width increases, the behaviour of the waves approaches the two-dimensional limiting case.

Circulation control involves tangentially blowing air around a rounded trailing edge in order to augment the lift of a wing. The advantages of this technique over conventional mechanical controls are reduced maintenance and lower observability. Despite the technology first being proposed in the 1960s and well-studied since, circulation control is not in widespread use today. This is largely due to the high mass flow requirements. Increasing the jet velocity increases both the efficiency (in terms of mass flow) and effectiveness. However, as the jet velocity exceeds the speed of sound, shock structures form which cause the jet to separate. Recent developments in the field of fluidic thrust vectoring (FTV) have shown that an asymmetrical convergent-divergent nozzle capable of producing an irrotational vortex (IV) has the potential to prevent separation through eliminating stream-wise pressure gradients. In this study, the feasibility of preventing separation at arbitrarily high jet velocities through the use of asymmetrical nozzle geometries designed to maintain irrotational (and stream-wise pressure gradient free) flow is explored. Furthermore, the usefulness of an adaptive nozzle geometry for the purpose of extending circulation control device efficiency and effectiveness is defined. Through a series of experiments, the flow physics of supersonic curved wall jets is characterised across a range of nozzle geometries. IV and equivalent area ratio symmetrical convergent-divergent nozzles are compared across three slot height to radius ratios (H/R): H/R = 0.1, H/R = 0.15, H/R = 0.2. The conclusion of this study is that at low H/R (0.1 and 0.15), there is no significant difference in behaviour between IV and symmetrical nozzles, whilst at high H/R (0.2), the IV nozzles begin separating whilst correctly expanded due to the propagation of pressure upstream from the edge of the reaction surface via the boundary layer. Consequently, it is shown that symmetrical nozzles of equivalent mass flow at high H/R have a higher separation NPR compared to IV nozzles. Specifically, the elimination of favourable, in addition to adverse stream-wise pressure gradients contradicts the expected behaviour of IV nozzles. The separation NPR for nozzles tested in this study, in addition to past studies is subsequently plotted against the throat height to radius ratios (A*/R). This shows that in fact, no previous experiments have shown a higher separation NPR for IV nozzles compared to symmetrical nozzles of equivalent mass flow. The overall outcome is that neither fixed geometry IV, nor adaptive nozzles are justified to maintain attachment, or to improve efficiency. This is because fixed nozzle geometries designed for higher separation NPR do not show any performance deficit when operating at lower NPRs. However, the throat height could be varied to maximise effectiveness (at the expense of mass flow). The contributions to new knowledge made by this study are as follows: the development of a new method of combining shadowgraph and schlieren images to simplify and enhance visualisation of supersonic flows; the use of pressure sensitive paint (PSP) to study the structure of the supersonic curved wall jet before and after separation; the identification of a clear mechanism for the separation of supersonic curved wall jets, valid over a broad range of nozzle geometries (including a clarification of previously unexplained behaviour witnessed in prior studies); the explanation that reattachment hysteresis occurs due to the upstream movement of the point of local separation at full separation (specifically, this explains why certain geometries such as backward-facing steps prevent reattachment hysteresis).

<p>We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.</p>

We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.