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Approved for public release; distribution is unlimited / Reissued 30 May 2017 with Second Reader’s non-NPS affiliation added to title page. / The scalar reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. That method, however, does not work when calculating the orthogonal components of the velocity field measured by a fixed receiver. This thesis derives a vector-scalar reciprocity equation that accounts for both monopole and dipole sources. This equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each received field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-independent and a range-dependent environment using a parabolic equation model. / Electronics Engineer, Naval Undersea Warfare Center

Underwater noise pollution is a significant environmental issue that can have detrimental effects on marine ecosystems. One of the main sources of underwater noise pollution is ship traffic, which has been shown to negatively impact marine animals by masking communication signals, altering their behaviors, and even causing hearing loss. In the Red Sea, ships are the main contributor to underwater noise pollution, particularly in areas with high shipping traffic. This thesis aims to understand the spatial and temporal distribution of underwater ship noise in the Red Sea using an acoustic propagation model, namely the Range-dependent Acoustic Model (RAM). RAM takes into account anthropogenic and environmental inputs including water temperature, salinity, and bathymetry to predict sound propagation in the Red Sea. By running RAM with inputs of ship traffic data, maps of underwater ship noise in the Red Sea were generated. These maps are important tools for policymakers and marine resource managers to identify areas of high noise pollution, target mitigation efforts accordingly, and guide future research on the effects of underwater noise pollution on marine life in the Red Sea.

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In this work, two approaches for computing the near-field distribution around wind turbines are proposed, including: (1) Huygens Principle and (2) the parabolic equation technique. In order to simplify the problem, the cylinder model is utilized to represent the wind turbines and transform the problem into a two-dimensional case. To make Huygens Principle computationally tractable, several approximations are made based on the problem geometry especially modelling the cylinder as a plate. The expression of the electromagnetic field radiated by the equivalent magnetic current can be analytically solved by the error function. To verify the results, FEKO is utilized to simulate the scattering of infinitely long cylinders using periodic boundary condition (PBC). In order to solve the problem of multiple cylinders, a modified method is derived. For more accurate results, the parabolic equation (PE) technique is utilized to solve this problem, which is usually utilized to solve wave propagation problems. In this case, wide-angle approximation is used to solve the parabolic equation, which can obtain accurate results in a region of up to 45 degrees. Although these two approaches are not full-wave simulation, the calculation time is significantly reduced and the error is acceptable. To further verify the computed results by the parabolic equation technique, two commercial transceivers from Time Domain Corporation are used to measure the field distribution behind a finite-length metal pole. The frequency-domain results are obtained from the measured time-domain results using the fast Fourier transform. It is shown that the computed results by the parabolic equation technique agree well with the measurement results. / text

The introduction of software radio has meant that standards for radio communication can evolve in a much more natural way, changing only a little at a time without making all of the hardware obsolete. It has become apparent that these changes may affect some systems more favourably than others so allowing the software radio to decide how to adapt can actually improve the link quality. This development is known as cognitive radio and can improve the performance of a single radio link. As an extension of this progress is being made on designing cognitive networks where the software radios which make up the network not only optimise their own link but share information about their goals and situation with other nodes in the network, using all of this data together can optimise overall end-to-end performance of the network. These advances in network design and optimisation come at a time where many parts of the world are re-structuring the television broadcast bands. These have been allocated for a long time and are a generous allocation of a valuable resource. With the power of a cognitive network it is possible to design equipment that can automatically avoid the licensed TV transmitters which only take a fraction of the total bandwidth in any one area. This allows many smaller cells to be fitted between the main transmitters. Assessing the availability of bandwidth and generating maps of available spectrum for these new cognitive networks requires a new approach to radio propagation modelling in the TV bands. Previous models use a worst case scenario to make sure that there is at least enough signal to receive the public service broadcasts in the majority of homes. Predicting where the limits of reception are and where it would be safe to broadcast on these channels requires a better, terrain dependent transmission model. In this thesis the Parabolic Equation Model is applied to the problem of predicting TV band occupancy and the results of this modelling is compared to field measurement to get an idea of how accurate the model is in practice.

Motivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann or third-type boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third type boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.

Motivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann or third-type boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third type boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.

<p>Low-frequency, long-range sound propagation over a seasurface has been calculated using a wide-angel Cranck-NicholsonParabolic Equation method. The model is developed toinvestigate noise from off-shore wind turbines. Thecalculations are made using normal meteorological conditions ofthe Baltic Sea. Special consideration has been made to a windphenomenon called low level jet with strong winds on rather lowaltitude.</p><p>The effects of water waves on sound propagation have beenincorporated in the ground boundary condition using a bossmodel. This way of including roughness in sound propagationmodels is valid for water wave heights that are small comparedto the wave length of the sound. Nevertheless, since only lowfrequency sound is considered, waves up to the mean wave heightof the Baltic Sea can be included in this manner.</p><p>The calculation model has been tested against benchmarkcases and agrees well with measurements. The calculations showthat channelling of sound occurs at downwind conditions andthat the sound propagation tends towards cylindrical spreading.The effects of the water waves are found to be fairlysmall.</p><p><b>Keywords:</b>wind turbine noise, off-shore wind power,long-range sound propagation, parabolic equation, scattering,water waves</p>

Darbe nagrinėjamas parabolinių lygčių su nelokaliąja daugiataške sąlyga ir tikrinių reikšmių uždaviniai antrosios eilės paprastajam diferencialiniam operatoriui. Uždavinio specifika yra ta, kad vietoje vienos arba abiejų klasikinių kraštinių sąlygų duota nelokalioji sąlyga. Tokio tipo kraštiniai uždaviniai diferiancialinėms lygtims paskutiniaisiais metais gana intensyviai nagrinėjami matematinėje literatūroje. Darbe naudojamas M. Sapagovo ir A. Štikono 2005 straipsnio metodika tikrinių reikšmių savybėms tirti. / The parabolic equation with nonlocal multi-point condition and the eigenvalue problem for differential operation with nonlocal multi-point condition is investigated in the work. Nonlocal condition is given instead one or both classical boundary conditions. These problems are investigated in the mathematical literature in recent years. The method of analysis to eigenvalue of the article [5] by M. Sapagovas and A. Štikonas on 2005 are used in the work.