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The far field acoustics generated by turbulent flow over rough surfaces has been experimentally investigated in an acoustically treated wall jet facility. The facility allows direct measurement of the far field sound from small patches of surface roughness, without contamination from edge or other aerodynamic noise sources. The facility is capable of generating turbulent boundary layer flows with momentum thickness Reynolds numbers between 450 and 1160. The variation of surface conditions tested cover the range from hydrodynamically smooth surfaces through most of the transitional range, with h+ variations from 3 to 85. Single microphone narrow band acoustic spectra, measured in the far field, show sound levels as much as 15 dB above the background from 0.186 m2 roughness patches. The measurements revealed the spectral shape and level variations with flow velocity, boundary layer thickness, and roughness size; providing the first data set large enough to assess the affects of many aerodynamic properties on the acoustic spectra. Increases in the size of grit type roughness produced significant increases in acoustic levels. Patches of hydrodynamically smooth roughness generated measurable acoustic levels, confirming that acoustic scattering is at least one of the physical mechanisms responsible for roughness noise. The shapes of the measured spectra show a strong dependence on the form of the surface roughness. The acoustic spectra generated by periodic two-dimensional surfaces have a much narrower louder peak than that generated by three-dimensional grit type roughness. Measurements also show the orientation of the two-dimensional surface significantly affects the acoustic levels and directivity. The variation of sound levels with flow velocity and roughness size suggests the acoustic field is significantly affected by changes in the near wall flow due to the presence of the roughness. Current models of noise generated by rough surfaces predict the general trends seen in measurements for flows over grit and two-dimensional roughness in the range of 20<h+<50. However, in cases with a low Reynolds number or large grit size, where the roughness is likely to significantly affect the hydrodynamic pressure field, the scattering models did not perform as well. / Ph. D.

The movement of granular material along a streambed has been a challenging subject for researchers for more than a century. Predicting the limiting case of nearly zero bedload transport, usually referred to as threshold of motion or critical condition, is even more challenging due to the highly fluctuating nature of turbulent flow. Numerous works have advocated that the peak turbulent forces, randomly occurring in time and space with magnitudes higher than the average, initiate the bed material motion. More recent findings have shown that not only the magnitude of the peak turbulent forces acting on individual grains but their duration as well have to be considered for determining the incipient conditions. Their product, or impulse, is better suited for specifying such conditions. The goal of this study was to investigate the mechanism responsible for initiation of sediment motion under turbulent flow conditions. The impulse concept was investigated by utilizing appropriate measurement methods in the laboratory for determining the condition of incipient motion. The experimental program included measurements of particle entrainment rates of a mobile grain and turbulence induced forces acting upon a fixed grain for a range of flow conditions. In addition, near bed flow velocities were measured synchronously with both the entrainment and pressure measurements at turbulent resolving frequencies. Results of this work covered the limitations and uncertainties associated with the experimental methods employed, and the description of the inadequacies of existing incipient motion models via the impulse framework. The extreme sensitivity of bed material activity to minute adjustments in flow conditions was explained by the associated change in the frequency of impulse events. The probability density function proposed for impulse was used together with the critical impulse to estimate the particle entrainment rate for a range of flow conditions. It was shown that the impulse events with potential to dislodge the grain were occurring mostly during sweep type of flow structures. The impulse events were also typically accompanied by positive lift forces. The force patterns showed that the positive peaks in the lift consistently occurred before and after the impulse events in the drag force. The magnitude of these lift forces were significantly higher in the wake of a cylinder compared to that of uniform flow conditions. The time average lift force in the wake of a cylinder was also observed to be positive with magnitudes reaching more than 30% of the submerged weight of the particle. The cylinder caused the downstream turbulence intensity to increase slightly but the particle entrainment rate to increase significantly. This finding provided a physically based explanation for the modification of turbulent force fluctuations and resulting changes in the particle movement rates by such unsteady flow conditions. / Ph. D.

A numerical study of electromagnetic scattering by one-dimensional perfectly conducting randomly rough surfaces with an ocean-like Pierson-Moskowitz spectrum is presented. Simulations are based on solving the Magnetic Field Integral Equation (MFIE) using the numerical technique called the Method of Ordered Multiple Interactions (MOMI). The study focuses on the application and validation of this integral equation-based technique to scattering at low grazing angles and considers other aspects of numerical simulations crucial to obtaining correct results in the demanding low grazing angle regime. It was found that when the MFIE propagator matrix is used with zeros on its diagonal (as has often been the practice) the results appear to show an unexpected sensitivity to the sampling interval. This sensitivity is especially pronounced in the case of horizontal polarization and at low grazing angles. We show - both numerically and analytically - that the problem lies not with the particular numerical technique used (MOMI) but rather with how the MFIE is discretized. It is demonstrated that the inclusion of so-called "curvature terms" (terms that arise from a correct discretization procedure and are proportional to the second surface derivative) in the diagonal of the propagator matrix eliminates the problem completely. A criterion for the choice of the sampling interval used in discretizing the MFIE based on both electromagnetic wavelength and the surface spectral cutoff is established. The influence of the surface spectral cutoff value on the results of scattering simulations is investigated and a recommendation for the choice of this spectral cutoff for numerical simulation purposes is developed. Also studied is the applicability of the tapered incident field at low grazing incidence angles. It is found that when a Gaussian-like taper with fixed beam waist is used there is a characteristic pattern (anomalous jump) in the calculated average backscattered cross section at incidence angles close to grazing that indicates a failure of this approximate (non-Maxwellian) taper. This effect is very pronounced for the horizontal polarization and is not observed for vertical polarization and the differences are explained. Some distinctive features associated with the taper failure are visible in the surface current (solution to the MFIE) as well. Based on these findings we are able to refine one of the previously proposed criteria that relate the taper waist to the angle of incidence and demonstrate its robustness. / Ph. D.

This research solves current RF propagation modeling gaps by modifying a single-frequency electromagnetic propagation analysis technique for use on communication signals and propagation channels. This research extended the Methods of Ordered Multiple Interactions (MOMI) algorithm to communication signal propagation studies through the use of Fourier decomposition thereby allowing the analysis and prediction of communication signals propagating over rough surfaces. Current methods of predicting and analyzing communication signal propagation rely on either using only a single frequency instead of a band of frequencies, stochastic techniques that model the environmental effect on the propagated signal, or on empirical models based of large amounts of measured situational data. None of these methods fully capture the actual effect that an environment imparts on a communication signal as it propagates. This research also modifies the Physical Optics (PO) algorithm utilizing Fourier decomposition to compare the Extended MOMI algorithm to. Both algorithms are applied to propagation scenarios utilizing frequencies in the 1-GHz and 5-GHz bands against a series of signal bandwidths and surface roughnesses. The results are analyzed singularly for Extended-MOMI and against Extended-Physical Optics to better understand the benefits associated with using the Extended-MOMI, the limits of the narrowband approximation, the errors incurred when utilizing a simpler or faster propagation algorithm, and to generally characterize these rough surface propagation channels. This research also defines and explores which metrics provide the best characterization and utility for communication signal propagation with the additional insights of amplitude-frequency-phase relationships the new algorithm provides. / Doctor of Philosophy / Communication signal propagation, defined as the propagation of signals that have non-zero bandwidths from one point to another, has significant importance in communication signal design, system design, and deployment as well as in spectrum planning applications. Current methods of predicting and analyzing communication signal propagation rely on either using only a single frequency instead of a band of frequencies, stochastic techniques that model the environmental effect on the propagated signal, or on empirical models based of large amounts of measured situational data. None of these methods fully capture the actual effect that an environment imparts on a communication signal as it propagates. A technique that accurately models the environmental effect on propagating communication signals would result in knowledge about a communication signal strength and shape as it passes through the propagation space. Analyzing communication signals with single frequency propagation algorithms requires assuming all the frequencies that make up the communication signal propagate exactly the same way, an assumption known as the narrowband approximation. It is not known when the narrowband approximation breaks down in various circumstances. Consequently a more rigorous approach needed to be identified to enable a more accurate and complete analysis of communication signals, which is the objective of the research. This research solves these modeling gaps by modifying a single-frequency electromagnetic propagation analysis technique, the Method of Ordered Multiple Interactions, for use on communication signals and propagation channels. The new algorithm, Extended-MOMI, allows for an examination of communication signal propagation over rough surfaces. This new algorithm incorporates all of the information needed for communication signal propagation analysis; something that is missing from current methods. This technique enables tailored communication signal propagation studies as well as an investigations into when the narrowband assumption is valid and when simpler and faster algorithms could be utilized for a now known increase in error. This research also explores which metrics are best utilized with the additional signal information the new algorithm enables.

Laboratory experiments were conducted to investigate the effect of low relative depth and high Froude number on the dimensionless critical shear stress (Shields parameter). Spherical particles of four different densities and an 8mm diameter were used as movable test material. The relative depth ranged from 2 to 12 and the Froude number ranged from 0.36 to 1.29. The results show that the traditional Shields diagram cannot be used to predict the incipient motion of coarse sediment particles when the relative depth is below 10 and the Froude number is above 0.5, approximately. Experiments using glass balls, whose density is almost identical to that of natural gravel, show that the Shields parameter can be twice as large in shallow flows than in deep flows. The results also show that the Shields parameter is dependent on the density of the particles. Data obtained from other studies support the findings of the present work. These findings can result in significant cost savings for riprap. Additionally, velocity profiles using a laser-Doppler velocimeter (LDV) were taken for the glass ball incipient motion experiments. The purpose of this was to study possible changes in the velocity distribution with decreasing relative depth and increasing Froude number. The results show that the von Karman and integral constants in the law of the wall do not change in the range of relative depths and Froude numbers tested. / Master of Science

There have been very few studies investigating the rough wall pressure spectra under fully rough flows, which are relevant to many common engineering applications operating within this regime. This investigation uses the Virginia Tech Stability Wind Tunnel to perform experiments on a series of high Reynolds number zero pressure gradient turbulent boundary layers formed over rough walls in an effort to better understand and characterize the behavior of the rough wall pressure spectrum. The boundary layers were fully rough, and the boundary layer height remained sufficiently larger than the height of the roughness elements. Two rough surfaces were tested. One consisted of an array of 1-mm ordered hemispherical elements spaced 5.5-mm apart, and the other contained 3-mm hemispherical elements randomly spaced, but with the same element density as 1/3 of the 1-mm ordered roughness. The wall pressure spectrum and its scaling were then studied in detail, and it was found that the rough wall turbulent pressure spectrum at vehicle relevant conditions is defined by three scaling regions. One of which is a newly discovered high frequency scaling defined by viscosity, but controlled by the friction velocity adjusted to exclude the pressure drag on the roughness elements. Based on these three scaling regions an empirical model describing the wall pressure spectra for hydraulically smooth, traditionally rough, and fully rough flows was explored. Two point wall pressure fluctuations were also analyzed for each surface condition, and it was found that the roughness inhibits the convective velocities within the inner portions of the boundary layer. / Master of Science

The pressure fluctuations under a high Reynolds Number, rough-wall, turbulent, boundary layer have been studied in the Virginia Tech Stability Wind Tunnel. Rough surfaces of varying element height (1-mm, 3-mm), shape (hemispheres, cylinders) and spacing (5.5-mm, 10.4-mm, 16.5-mm) were investigated in order to ascertain how the turbulent pressure fluctuations change with changes in roughness geometry. Rough surfaces which contain two types of elements are investigated and relationships between the combination surface and the individual surfaces have been uncovered. Measurements of the wall pressure fluctuations were made using pinhole microphones and hotwire measurements were made to obtain the velocity and turbulence field. Among the principal findings is the development of two scaling laws for the low frequency pressure fluctuations. Both of these are based on the idea that the defect between the edge velocity and some local boundary layer velocity sustains the pressure fluctuations in the outer regions of the flow. The first scaling uses the broadband convection velocity as the local velocity of the large scale pressure fluctuations. The second scaling uses the mean boundary layer velocity. Both these scalings appear more robust than the previously proposed scalings for the low frequency region and are able to scale the pressure spectra of all the data to within 3.5-dB. In addition, it was proven that the high frequency shear friction velocity scaling of Meyers et al. (2015) is universal to rough surfaces of different element shape and density. Physical insights into the shear friction velocity, on which this scaling is based, have been revealed. This includes an empirical formula which estimates the element pressure drag coefficient from the roughness density and the Reynolds number. The slopes in the mid-frequency region were found to vary with element density and microphone location such that a useful scaling could not be determined for this region. The possibility of an overlap region is explored and the expectation of a -1 slope is disproved. It is hypothesised that an evanescent decay of the mid-frequency pressure fluctuations occurs between their actual location and the wall where they are measured. A method for accounting for this decay is presented in order to scale the pressure fluctuations in this region. Lastly, a piecewise interpolation function for the pressure spectrum of rough wall turbulent boundary layers was proposed. This analytical function is based on the low frequency scaling on mean velocity and the high frequency scaling of Meyers et al. (2015) The mid-frequency is estimated by a spline interpolation between these two regions. / Ph. D. / Most flows of practical interest are turbulent in nature, typically occurring next to a rigid surface such as a submarine hull or aircraft wing. This boundary layer flow is of engineering importance because its pressure fluctuations are the source of unwanted structural vibrations and undesired acoustic noise. From a purely scientific perspective, it is useful to study the turbulent pressure fluctuations in order to learn more about the workings of the region of the flow closest to the surface. Turbulent flow over smooth walls has been researched extensively. However, one cannot ignore the fact that surfaces of practical interest are not smooth. Thus, it is important to account for the effect of roughness on the turbulent boundary layer. It has been found that there are significantly greater pressure fluctuations over rough walls when compared to smooth walls. Consequently the extent of vibrations and noise which occur in rough walls is larger than that experienced in smooth walls. The present study seeks to shed light on the nature of the rough-wall turbulent boundary layer through wind tunnel experiments. The nature of the velocity, pressure fluctuations, and turbulence within the boundary layer are examined as well as the existence of universal relationships which are applicable to all rough-wall turbulent boundary layers. A method for predicting the pressure fluctuations (to within 4-dB) over a specific rough wall is also proposed.

This study focuses on measuring and normalizing the roughness noise of multiple roughness types across numerous layouts and flow speeds. Using the Virginia Tech Anechoic Wall Jet Facility, far field noise was recording for the flow of a turbulent wall jet boundary layer over cubes, hemispheres, and gravel, with element heights in the range of 14.3 - 55.2% of the boundary layer thickness. The sound radiated from the various layouts showed that the elements acted as independent sources when separated by three element diameters center-to-center or more. When the elements were placed shoulder to shoulder, interaction between the elements and shielding of the higher velocity flow lowered the noise per element produced. The far field roughness noise was then normalized using the theory of Glegg et al. (2007), which assumes a dipole efficiency factor. Comparisons were made between the theoretical drag spectrum model proposed by Glegg et al. (1987) and a modified version of this model made using the empirical data gathered. Overall, the theory of Glegg et al. (2007) succeeds greatly in collapsing the data into its non-dimensional drag spectra, but the original model spectrum did not fit well. The modified spectrum showed much greater fit with the data at all layouts and speeds. The collapse of the data using the theory of Glegg et al. (2007) confirms that roughness noise is dipole in nature. / Master of Science