The majority of internal gravity wave energy in the ocean is produced by tidal flow over bottom topography. Regions of critical topography, where the topographic slope is equal to the slope of the internal gravity waves, is often believed to contribute most significantly to the radiated internal gravity wave power. Here, we present 2D computational studies of internal gravity wave generation by tidal flow over several types of topographic ridges. We vary the criticality parameter [epsilon], which is the ratio of the topographic slope to the wave beam slope, by independently changing the tidal frequency, stratification and topographic slope, which allows to study subcritical ([epsilon] < 1), critical ([epsilon] = 1), and supercritical ([epsilon] > 1) topography. This parameter variation allows us to explore a large range of criticality parameter, namely 0.1< [epsilon] < 10, as well as beam slope S, 0.05< S < 10. As in prior work [Zhang et al., Phys. Rev. Lett. (2008)], we observe resonant boundary currents for [epsilon] = 1. However, we find that the normalized radiated power monotonically increases with internal wave beam slope. We show that an appropriate normalization condition leads to a universal scaling of the radiated power that is proportional to the inverse of the beam slope 1/S and the tidal intensity I[subscript tide], except near [epsilon] = 1 where the behavior undergoes a transition. We characterize this transition and the overall scaling with the criticality parameter f([epsilon]), which is weak compared to the scalings mentioned before and only varies by a factor of two over the entire range of criticality parameter that we explored. Our results therefore suggest that estimates of the ocean energy budget must account for the strong scaling with the local beam slope, which dominates the conversion of tidal motions to internal wave energy. Thus we argue that detailed characterization of the stratification in the ocean is more important for global ocean models than high-resolution bathymetry to determine the criticality parameter. / text

As an alternative to spherical harmonics in modeling the gravity field of the Earth, we built a multiresolution gravity model by employing spherical regularization wavelets in solving the inverse problem, i.e. downward propagation of the gravity signal to the Earth.s surface. Scale discrete Tikhonov spherical regularization scaling function and wavelet packets were used to decompose and reconstruct the signal. We recovered the local gravity anomaly using only localized gravity measurements at the observing satellite.s altitude of 300 km. When the upward continued gravity anomaly to the satellite altitude with a resolution 0.5° was used as simulated measurement inputs, our model could recover the local surface gravity anomaly at a spatial resolution of 1° with an RMS error between 1 and 10 mGal, depending on the topography of the gravity field. Our study of the effect of varying the data volume and altering the maximum degree of Legendre polynomials on the accuracy of the recovered gravity solution suggests that the short wavelength signals and the regions with high magnitude gravity gradients respond more strongly to such changes. When tested with simulated SGG measurements, i.e. the second order radial derivative of the gravity anomaly, at an altitude of 300 km with a 0.7° spatial resolution as input data, our model could obtain the gravity anomaly with an RMS error of 1 ~ 7 mGal at a surface resolution of 0.7° (< 80 km). The study of the impact of measurement noise on the recovered gravity anomaly implies that the solutions from SGG measurements are less susceptible to measurement errors than those recovered from the upward continued gravity anomaly, indicating that the SGG type mission such as GOCE would be an ideal choice for implementing our model. Our simulation results demonstrate the model.s potential in determining the local gravity field at a finer scale than could be achieved through spherical harmonics, i.e. less than 100 km, with excellent performance in edge detection. / text

The primary objectives of this research were to understand the potential for gravity-stable surfactant floods for enhanced oil recovery without the need for mobility control agents and to optimize the performance of such floods. Surfactants are added to injected water to mobilize the residual oil and increase the oil production. Surfactants reduce the interfacial tension (IFT) between oil and water. This reduction in IFT reduces the capillary pressure and thus the residual oil saturation, which then results in an increase in the water relative permeability. The mobility of the surfactant solution is then greater than the mobility of the oil bank it is displacing. This unfavorable mobility ratio can lead to hydrodynamic instabilities (fingering). The presence of these instabilities results in low reservoir sweep efficiency. Fingering can be prevented by increasing the viscosity of the surfactant solution or by using gravity to stabilize the displacement below a critical velocity. The former can be accomplished by using mobility control agents such as polymer or foam. The latter is called gravity-stable surfactant flooding, which is the subject of this study. Gravity-stable surfactant flooding is an attractive alternative to surfactant polymer flooding under certain favorable reservoir conditions. However, a gravity-stable flood requires a low velocity less than the critical velocity. Classical stability theory predicts the critical velocity needed to stabilize a miscible flood by gravity forces. This theory was tested for surfactant floods with ultralow interfacial tension and found to over-estimate the critical velocity compared to both laboratory displacement experiments and fine-grid simulations. Predictions using classical stability theory for miscible floods were not accurate because this theory did not take into account the specific physics of surfactant flooding. Stability criteria for gravity-stable surfactant flooding were developed and validated by comparison with both experiments and fine-grid numerical simulations. The effects of vertical permeability, oil viscosity and heterogeneity were investigated. Reasonable values of critical velocity require a high vertical permeability without any continuous barriers to vertical flow in the reservoir. This capability to predict when and under what reservoir conditions a gravity-stable surfactant flood can be performed at a reasonable velocity is highly significant. Numerical simulations were also used to show how gravity-stable surfactant flooding can be optimized to increase critical velocity, which shortens the project life and improves the economics of the process. The critical velocity for a stable surfactant flood is a function of the microemulsion viscosity and it turns out there is an optimum value that can be used to significantly increase the velocity and maintain stability. For example, the salinity gradient can be optimized to gradually decrease the microemulsion viscosity. Another alternative is to inject a polymer drive following the surfactant solution, but using polymer complicates the process and adds to its cost without significant benefit in most gravity-stable surfactant floods. A systematic approach was introduced to make decisions on using polymer in applications based on stability criteria and cost. Also, the effect of an aquifer on gravity-stable surfactant floods was investigated as part of a field-scale study and strategies were developed to minimize its effect on the process. This study has provided new insights into the design of an optimized gravity-stable surfactant flood. The results of the numerical simulations show the potential for high oil recovery from gravity-stable surfactant floods using horizontal wells. Application of gravity-stable surfactant floods reduces the cost and complexity of the process. The widespread use of horizontal wells has greatly increased the attractiveness and potential for conducting surfactant floods in a gravity-stable mode. This research has provided the necessary criteria and tools needed to determine when gravity-stable surfactant flooding is an attractive alternative to conventional surfactant-polymer flooding. / text

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Conformal holonomy theory is the holonomy theory of the tractor connection on a conformal manifold. In this thesis, we present the first application of conformal holonomy theory to theoretical physics and determine the conformal holonomy groups/algebras of physically relevant spaces. After recalling some necessary background on conformal structures, tractor bundles and conformal holonomy theory in chapter 1, we begin in chapter 2 by discussing the role of conformal holonomy in the gauge-theoretic MacDowell-Mansouri formulation of general relativity. We show that the gauge algebra of this formulation is uniquely determined by the conformal structure of spacetime itself, in both Lorentzian and Riemannian metric signatures, through the conformal holonomy algebra. We then show that one may construct a MacDowell-Mansouri action functional for scale-invariant gravity, and we discuss a geometric interpretation for the scalar field therein. In chapter 3 we study a class of spacetimes relevant to Maldacena's AdS5=CFT4 correspondence in quantum gravity. It is well known that a Lie group coincidence lies at the heart of this correspondence: the proper isometry group of the bulk precisely matches the conformal group of the boundary. It has previously been proposed that the AdS5=CFT4 correspondence be extended to so-called Poincar e-Einstein spacetimes, which need not be as symmetric as anti-de Sitter space. We show that the conformal holonomy groups of the boundary and bulk furnish such a Lie group coincidence for 5-dimensional Poincar e-Einstein spacetimes in general. We completely characterise this boundary-bulk conformal holonomy matching for the Riemannian theory and present partial results for the Lorentzian theory. In chapter 4 we use the tools developed in the preceding chapters to further the classiification of the conformal holonomy groups of conformally Einstein spaces. Specifically, we determine the conformal holonomy groups of generic neutral signature conformally Einstein 4-manifolds subject to a condition on the conformal holonomy representation. Lastly, in chapter 5, we investigate the conformal holonomy reduction of the Fefferman conformal structures of residual twistor CR manifolds. A sufficient condition for reducible conformal holonomy is that the (Fefferman conformal structure of a) residual twistor CR manifold admit a parallel tractor. We show that this occurs if and only if the residual twistor CR manifold admits a Sasakian structure.

The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. We propose propose two possible approaches to establish this correspondence: perturbative expansion for shear modes and large mean curvature expansion for algebraically special metrics. / Physics

Understanding how global ice volume on the Earth has changed is of significant importance to improving our understanding of the climate system. Fortunately, the geographically unique perturbations in sea level that result from rapid changes in the mass of, otherwise difficult to measure, land-ice reservoirs can be used to infer the sources and magnitude of melt water. We explore the history of land-ice mass changes through the effect that these mass fluxes have had on both global and regional gravity and sea-level fields. / Earth and Planetary Sciences

The Iranian economy has over 30-years been under several of US sanctions due to differences in their political objectives, affecting primarily their economic lifeblood, the oil business. Therefore during this period the Iranian economy has experienced setbacks in their development of national prosperity. This paper investigates the effect of the economic sanctions, during the time period 1975-2006, on Iran’s trade flows by incorporating the gravity model. Also, including geographical proximity and cultural ties further extends the model, which has been shown to strongly influence trade. The findings suggest that sanctions have negative impact on trade flows and are consistent with previous findings. Further estimation methods such as the Heckman- and PPML method are applied accounting for zero trade flows. The empirical  results indicate that sanctions have had a large negative effect on trade flows as expected. When further dividing the sanctions into five different time periods the results conclude the previous ones, however the five time periods have been influenced by sanctions in different varieties. Hence sanctions hamper trade and prevent the Iranian economy to thrive to its fullest potential.

In the generation of the standard GRACE gravity fields, the K-Band Ranging (KBR) system data is used in its range-rate mode. Because time derivatives attenuate the gravity signal relative to the data noise at the lower frequencies, it is thought that solutions using range data might have better low-degree (low-frequency) characteristics. The purpose of this work is to detail the methods required to generate range-based solutions, to determine some of the properties of these solutions and then to compare them to range-rate based solutions. It is demonstrated that the range-based solutions are feasible. Different subarc lengths and parameterizations were considered. Although, the most effective combination of subarc lengths and parameterizations are not picked, it is concluded that estimating the mixed periodic term along with bias, bias-rate, bias-acceleration and periodic terms degrades the quality of the range based solution and therefore should not be used. Further study is necessary to pick the optimal combination of subarc length and parameterization which would be used in the time-series analysis. / text