For decades noise-induced hearing loss has been a concern of the Department of Defense (DoD). My research investigates noise generation and dispersion in supersonic jets and focuses on the fluid-dynamic regime typical of high-performance turbojet and turbofan engines. The goal of my research is to understand how dispersion and propagation of wavepackets can be modified by noise reduction strategies based on secondary injections of fluid with a different temperature from the main jet. The research is organized into three studies that focus on instability, large eddy simulations, and resolvent modes. The first study is a computational investigation of the role of thermal non-uniformity on the development of instability modes in the shear-layer of a supersonic $M= 1.5$, $Re=850,000$ jet. Cold fluid is injected at the axis of a heated jet to introduce radial non-uniformity and control the spatial development of the shear layer. The mean flow is analyzed with an efficient 2D and 3D Reynolds-averaged Navier-Stokes (RANS) approach using the SU2 code platform for 3 different cases -baseline, centered, and offset injection. Different turbulence models are tested and compared with the experiments. The coherent perturbation is analyzed using linear parallel and parabolized stability equations (PSEs). The second study investigates novel formulations of large eddy simulation models using an arbitrary high order discontinuous Galerkin scheme. The LES analysis focuses on both numerical issues (such as convergence against the polynomial order of the mesh), modeling issues (such as the choice of subgrid model), and underlying physics (such as vortex stretching and noise generation). Wall models are used to capture the viscous sublayer at the nozzle. The Ffowcs Williams-Hawkings (FW-H) method is used for far-field noise predictions for all cases. Three-dimensionality is studied to investigate how injection in the shear layer acts to create a rotational inviscid core and affects the mixing of the cold fluid and noise dispersion. The third study extends the (first) instability study by considering (global) resolvent modes. Such optimally forced modes of the turbulent mean flow field will identify the turbulent coherent structures (wavepackets) for different turbulence models at $M=1.5$. The LES simulations performed in the second study will be used to extract the mean flow and the dynamic modes for comparison. My research plan is to perform the resolvent analysis of the axisymmetric mean flow fields for the thermally activated case (i.e., the centered injection) and compare it to the baseline jet case. Different turbulence models will be investigated to determine the correct alignment of dynamic and resolvent modes. Finally, I will consider the three-dimensional, non-axisymmetric mean flow created by offset injection described in the second study, which requires evaluating the convolution products of resolvent modes and base flow. Such three-dimensional resolvent compressible modes have never been identified in the context of supersonic jets. / Doctor of Philosophy / For decades noise-induced hearing loss has been a concern of the Department of Defense (DoD). Research in this area is critical to US national security and valued by both the aircraft industry and government. The noise generated during take-off and landing is hazardous to the crew personnel who work around this vicinity. A reduction of noise can significantly decrease medical expenditure and allow the aircraft industry to meet the stringent community noise requirements. Among the various techniques of noise reduction analyzed over the years, thermal non-uniformity stands out for its simple implementation and cost-effectiveness, especially in after-burner turbojets. Thermal non-uniformity with a cold secondary stream introduces low-velocity fluid in a supersonic jet by locally increasing the density while matching the mass flow rate. Changes to the velocity profile are localized; different regions of the jet emit sound at different frequencies and radiation angles, thus the link between injection location and noise control is not well understood. Using different computational tools this research investigates the link connecting thermal non-uniformity, turbulent production, and sound generation. Injection at different radial locations affects the two mechanisms of sound radiation in different ways. The first mechanism, the Kelvin Helmholtz instability, can be studied as an eigenvalue problem that represents the spatial growth of normal modes. De-coherence of these modal fluctuations can be obtained by injecting secondary fluid directly into the shear layer. This injection mode is called offset injection. The present research shows that the thickening of the shear layer due to low-velocity fluid delays the formation of Kelvin-Helmholtz modes in the offset case. Thus, the outskirts of the jet produce pressure fluctuations with a lower spectral energy density. The second mechanism, the Orr instability, can be analyzed as non-modal growth of acoustic perturbation forced by the breakdown of the core of the jet. LES and stability analysis shows that centered injection is highly effective in reducing the Orr radiation. Resolvent modes explain that the rationale is the delay and reduction of a secondary resonant peak between spatial eddies and forcing caused by changes in the mean profile responsive to secondary injection. Our analysis also explains why the offset injection is more effective at a low polar angle, while centered injection reduces acoustic radiation towards high polar angles. Parametric studies of different injection strategies, i.e., location and number of injection ports are performed to demonstrate the best strategy for noise level reductions.

The evaluation of how Computational Fluid Dynamics (CFD) package may be incorporated into a conceptual design method is performed. The repeatability of the CFD solution as well as the accuracy of the calculated aerodynamic coefficients and pressure distributions was also evaluated on two different wing-body models. The overall run times of three different mesh densities was also evaluated to investigate if the mesh density could be reduced enough so that the computational stage of the CFD cycle may become affordable to use in the conceptual design stage. A farfield method was derived and used in this analysis to calculate the lift and drag coefficients. The CFD solutions were also compared with two methods currently used in conceptual design - the vortex lattice based program Vorview and ACSYNT. The unstructured Euler based CFD package FELISA was used in this study. / Master of Science

This thesis considers the design of a beamformer which can enhance desired signals in an environment consisting of broadband nearfield and/or farfield sources. The thesis contains: a formulation of a set of analysis tools which can provide insight into the intrinsic structure of array processing problems; a methodology for nearfield beamforming; theory and design of a general broadband beamformer; and a consideration of a coherent nearfield broadband adaptive beamforming problem. To a lesser extent, the source localization problem and background noise modeling are also treated. ¶: A set of analysis tools called modal analysis techniques which can be used to a solve wider class of array signal processing problems, is first formulated. The solution to the classical wave equation is studied in detail and exploited in order to develop these techniques. ¶: Three novel methods of designing a beamformer having a desired nearfield broadband beampattern are presented. The first method uses the modal analysis techniques to transform the desired nearfield beampattern to an equivalent farfield beampattern. A farfield beamformer is then designed for a transformed farfield beampattern which, if achieved, gives the desired nearfield pattern exactly. The second method establishes an asymptotic equivalence, up to complex conjugation, of two problems: (i) determining the nearfield performance of a farfield beampattern specification, and (ii) determining the equivalent farfield beampattern corresponding to a nearfield beampattern specification. Using this reciprocity relationship a computationally simple nearfield beamforming procedure is developed. The third method uses the modal analysis techniques to find a linear transformation between the array weights required to have the desired beampattern for farfield and nearfield, respectively. ¶: An efficient parameterization for the general broadband beamforming problem is introduced with a single parameter to focus the beamformer to a desired operating radius and another set of parameters to control the actual broadband beampattern shape. This parameterization is derived using the modal analysis techniques and the concept of the theoretical continuous aperture. ¶: A design of an adaptive beamformer to operate in a signal environment consisting of broadband nearfield sources, where some of interfering signals may be correlated with desired signal is also considered. Application of modal analysis techniques to noise modeling and broadband coherent source localization conclude the thesis.

In many engineering applications, including radar, sonar, communications and seismology, the direction of impinging signal wavefronts can be used to discriminate between competing sources. Often these source signals cover a wide bandwidth and conventional narrowband beamforming techniques are ineffective, since spatial resolution varies significantly across the band. In this thesis we consider the problem of beamforming for broadband signals, primarily when the spatial response remains constant as a function of frequency. This is called a frequency invariant beamformer (FIB).¶ Rather than applying the numerical technique of multi-parameter optimisation to solve for the beamformer parameters, we attempt to address the fundamental nature of the FIB problem. The general philosophy is to use a theoretical continuous sensor to derive relationships between a desired FI beampattern and the required signal processing structure. Beamforming using an array of discrete sensors can then be formulated as an approximation problem. This approach reveals a natural structure to the FIB which is otherwise buried in a numerical optimisation procedure.¶ Measured results from a microphone array are presented to verify that the simple FIB structure can be successfully implemented. We then consider imposing broadband pattern nulls in the FI beampattern, and show that (i) it is possible to impose an exact null which is present over all frequencies, and (ii) it is possible to calculate a priori how many constraints are required to achieve a null of a given depth in a FIB. We also show that the FIB can be applied to the problem of broadband direction of arrival (DOA) estimation and provides computational advantages over other broadband DOA estimators.¶ Through the theoretical continuous sensor approach, we show that the FIB theory can be generalised to the problem of designing a general broadband beamformer (GBB) which realizes a broadband angle-versus-frequency beampattern specification. Coupled with a technique for radial beampattern transformation, the GBB can be applied to a wide class of problems covering both nearfield beamforming (in which the shape of the impinging wavefront must be considered and farfield beamforming (which is simplified by the assumption of planar wavefronts) for a broadband beampattern specified over both angle and frequency.

Collision of the Yakutat Terrane with North America in southern Alaska has driven growth of the Chugach-St. Elias orogen. Glaciation of the St. Elias Range has periodically increased since the Miocene, but began dominating erosion and spurred enhanced exhumation since the mid-Pleistocene transition at ~1 Ma. Ice associated with this glacial intensification carved cross-shelf sea valleys that connect the St. Elias Range to the deep-sea Surveyor Fan. A newly increased terrigenous sediment flux into the fan triggered the formation and growth of the Surveyor Channel. The change in geomorphology observed throughout Fan sequences allows us to characterize the influence that a glaciated orogen can have in shaping margin processes and the sediment pathways from source to sink. Seismic data also reveal an isolated, large, short runout, mass-transport deposit (MTD) buried in the Surveyor Fan. The MTD geometry, size and location on a convergent margin lend support to recent studies suggesting seismic strengthening and infrequent sediment failure on active margins. This study provides insight into the magnitude and scope of events required to cause submarine mega-slides and overcome higher than normal sediment shear strength, including the influence of climate and sea level change. Beneath the Surveyor Fan, integrated geophysical data reveals massive intraplate shearing, and a lack of oceanic crust magnetic lineaments in regions of Pacific Plate crust. We argue that stress from the Yakutat-North America collision transferred outboard to the Pacific Plate is the major driver for the deformation causing these features. This stress would have resulted in significant strain in the NE corner of the Pacific Plate, creating pathways for sill formation in the crust and Surveyor Fan. The collision further intensified as the thickest Yakutat portion began to subduct during the Pleistocene, possibly providing the impetus for the creation of the Gulf of Alaska Shear Zone, a >200 km zone of shear extending out into the Pacific Plate. This study highlights the importance of farfield stress from complex tectonic regimes in consideration of large-scale oceanic intraplate deformation. / text

A dispersão dos efluentes do emissário submarino de Santos foi estudada por meio de modelagem numérica, acoplando-se modelos hidrodinâmico, de dispersão no campo próximo e no campo distante. As simulações foram realizadas para o projeto original do emissário de 1979, para a nova configuração de 2009 e para terceiro arranjo sugerido por este estudo, que dobra o comprimento do duto em relação ao projeto original. As diluições foram modeladas em cenários ambientais com propriedades marinhas e estuarinas climatológicas de verão, juntamente com forçantes atmosféricas climatológicas da mesma estação, simulando ausência de vento, presença de vento médio e presença de vento médio seguido por passagem de frente fria climatológica (obtida por este estudo). Com as devidas validações do modelo hidrodinâmico, a diluição, tanto no campo próximo quanto no campo distante, foi fortemente regida pela estratificação da coluna dágua e pela velocidade das correntes. O cenário sem vento apresentou as maiores estratificações, menores velocidades e originou as menores diluições em oposição ao cenário que simulou a passagem de frente fria. Dentre os projetos de emissário analisados, aquele proposto por este estudo apresentou plumas com menores comprimentos horizontais e menores profundidades, atingindo a costa uma só vez. O projeto original e o novo que será implantado em 2009 apresentaram, comparativamente, plumas mais extensas e profundas, interceptando a costa em diversas situações. / Sewage plume dispersion for the Santos outfall was studied using numerical models, coupling hydrodynamic, near field and far field models. Experiments were conducted for the 1979 original outfall design, for the new 2009 outfall configuration and also for a third arrangement suggested here, which duplicates the emissary length comparatively to the original 1979 project. Dilutions were modeled in environmental sceneries with summer climatological estuarine and marine properties, together with climatological atmospheric forcing for the same season, simulating no wind conditions, mean wind forcing and mean wind followed by a climatological cold front (developed at this study) passage. After the appropriate hydrodynamic numerical model validation, the dilution, at the near field as well as at the far field, was strongly determined by the vertical water stratification and by the current velocities. The no-wind scenery presented the highest stratifications, smallest velocities and originated the smallest dilutions, in opposition to the cold-front-scenery. Among the sewage outfall projects considered, the one presented at this study showed the shallowest plumes, with the smallest horizontal lengths, reaching the coast only once. The original 1979 project and the 2009 configuration showed, comparatively, the deepest and widest plumes reaching the coast in several situations.

A dispersão dos efluentes do emissário submarino de Santos foi estudada por meio de modelagem numérica, acoplando-se modelos hidrodinâmico, de dispersão no campo próximo e no campo distante. As simulações foram realizadas para o projeto original do emissário de 1979, para a nova configuração de 2009 e para terceiro arranjo sugerido por este estudo, que dobra o comprimento do duto em relação ao projeto original. As diluições foram modeladas em cenários ambientais com propriedades marinhas e estuarinas climatológicas de verão, juntamente com forçantes atmosféricas climatológicas da mesma estação, simulando ausência de vento, presença de vento médio e presença de vento médio seguido por passagem de frente fria climatológica (obtida por este estudo). Com as devidas validações do modelo hidrodinâmico, a diluição, tanto no campo próximo quanto no campo distante, foi fortemente regida pela estratificação da coluna dágua e pela velocidade das correntes. O cenário sem vento apresentou as maiores estratificações, menores velocidades e originou as menores diluições em oposição ao cenário que simulou a passagem de frente fria. Dentre os projetos de emissário analisados, aquele proposto por este estudo apresentou plumas com menores comprimentos horizontais e menores profundidades, atingindo a costa uma só vez. O projeto original e o novo que será implantado em 2009 apresentaram, comparativamente, plumas mais extensas e profundas, interceptando a costa em diversas situações. / Sewage plume dispersion for the Santos outfall was studied using numerical models, coupling hydrodynamic, near field and far field models. Experiments were conducted for the 1979 original outfall design, for the new 2009 outfall configuration and also for a third arrangement suggested here, which duplicates the emissary length comparatively to the original 1979 project. Dilutions were modeled in environmental sceneries with summer climatological estuarine and marine properties, together with climatological atmospheric forcing for the same season, simulating no wind conditions, mean wind forcing and mean wind followed by a climatological cold front (developed at this study) passage. After the appropriate hydrodynamic numerical model validation, the dilution, at the near field as well as at the far field, was strongly determined by the vertical water stratification and by the current velocities. The no-wind scenery presented the highest stratifications, smallest velocities and originated the smallest dilutions, in opposition to the cold-front-scenery. Among the sewage outfall projects considered, the one presented at this study showed the shallowest plumes, with the smallest horizontal lengths, reaching the coast only once. The original 1979 project and the 2009 configuration showed, comparatively, the deepest and widest plumes reaching the coast in several situations.

This thesis outlines an iterative approach for determining the scattered wave for two dimensional multiple acoustic scattering problems using high order local absorbing boundary conditions and second order finite difference. We seek to approximate the total wave as it is scattered off of multiple arbitrarily shaped obstacles. This is done by decomposing the scattered wave into the superposition of single scattered waves. We then repeatedly solve the single scattering system for each obstacle, while updating the boundary conditions based off the incident wave and the scattered wave off the other obstacles. We solve each single scattering by enclosing the obstacle in a circular artificial boundary and generating a curvilinear coordinate system for the computational region between the obstacle and the artificial boundary. We impose an absorbing boundary condition, specifically Karp's Farfield Expansion ABC, on the artificial boundary. We use a finite difference method to discretize the governing equations and to discretize the absorbing boundary conditions. This will create a linear system whose solution will approximate the single scattered wave. The forcing vector of the linear system is determined from the total influence on the obstacle boundary from the incident wave and the scattered waves from the other obstacles. In each iteration, we solve the singular acoustic scattering problem for each obstacle by using the scattered wave approximations from the other obstacles obtained from the previous iteration. The iterations continue until the solutions converge. This iterative method scales well to multiple scattering configurations with many obstacles, and achieves errors on the order of 1E-5 in less than five minutes. This is due to using LU factorization to solve the linear systems, paired with parallelization. I will include numerical results which demonstrate the accuracy and advantages of this iterative technique.