Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Kelvin-wave cascade in the vortex filament model

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

Numerical calculation of diffraction coefficients from building edges using FDTD method

Finite Difference Time Domain (FDTD) Method and software are applied to obtain diffraction waves from modulated Gaussian plane wave illumination for right angle wedges and Fast Fourier Transform (FFT) is used to get diffraction coefficients in a wideband in the illuminated lit region. Theta and Phi polarization in 3-dimensional, TM and TE polarization in 2-dimensional cases are considered respectively for soft and hard diffraction coefficients. Results using FDTD method of perfect electric conductor (PEC) wedge are compared with asymptotic expressions from Uniform Theory of Diffraction (UTD). Extend the PEC wedges to some homogenous conducting and dielectric building materials for diffraction coefficients that are not available analytically in practical conditions. ^

Time-domain simulation of wave-induced ship motions by a Rankine panel method

In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.

Evaluating the urban heat island for cities of Emilia-Romagna region through numerical simulations

Lo scopo di questo studio è la comprensione della dinamica dello strato limite urbano per città dell’Emilia Romagna tramite simulazioni numeriche. In particolare, l’attenzione è posta sull’ effetto isola di calore, ovvero sulla differenza di temperatura dell’aria in prossimità del suolo fra zone rurali e urbane dovuta all’urbanizzazione. Le simulazioni sono state effettuate con il modello alla mesoscala "Weather Research and Forecasting" (WRF), accoppiato con le parametrizzazioni urbane "Building Effect Parametrization" (BEP) e "Building Energy Model" (BEM), che agiscono a vari livelli verticali urbani. Il periodo di studio riguarda sei giorni caldi e senza copertura nuvolosa durante un periodo di heat wave dell’anno 2015. La copertura urbana è stata definita con il "World Urban Databes and Access Portal Tools" (WUDAPT), un metodo che permette di classificare le aree urbane in dieci "urban climate zones" (UCZ), attraverso l’uso combinato di immagini satellitari e "training areas" manualmente definite con il software Google Earth. Sono state svolte diverse simulazioni a domini innestati, con risoluzione per il dominio più piccolo di 500 m, centrato sulla città di Bologna. Le differenze fra le simulazioni riguardano la presenza o l’assenza delle strutture urbane, il metodo di innesto e tipo di vegetazione rurale. Inoltre, è stato valutato l’effetto dovuto alla presenza di pannelli fotovoltaici sopra i tetti di ogni edificio e le variazioni che i pannelli esercitano sullo strato limite urbano. Per verificare la bontà del modello, i dati provenienti dalle simulazioni sono stati confrontati con misure provenienti da 41 stazioni all’interno dell’area di studio. Le variabili confrontate sono: temperatura, umidità relativa, velocità e direzione del vento. Le simulazioni sono in accordo con i dati osservativi e riescono a riprodurre l’effetto isola di calore: la differenza di temperatura fra città e zone rurali circostanti è nulla durante il giorno; al contrario, durante la notte l’isola di calore è presente, e in media raggiunge il massimo valore di 4°C alle 1:00. La presenza dei pannelli fotovoltaici abbassa la temperatura a 2 metri dell’aria al massimo di 0.8°C durante la notte, e l’altezza dello strato limite urbano dell’ordine 200mrispetto al caso senza pannelli. I risultati mostrano come l’uso di pannelli fotovoltaici all’interno del contesto urbano ha molteplici benefici: infatti, i pannelli fotovoltaici riescono a ridurre la temperatura durante un periodo di heat wave, e allo stesso tempo possono parzialmente sopperire all’alto consumo energetico, con una conseguente riduzione del consumo di combustibili fossili.

Optical wave turbulence and wave condensation in a nonlinear optical experiment

We present theory, numerical simulations and experimental observations of a 1D optical wave system. We show that this system is of a dual cascade type, namely, the energy cascading directly to small scales, and the photons or wave action cascading to large scales. In the optical context the inverse cascade is particularly interesting because it means the condensation of photons. We show that the cascades are induced by a six-wave resonant interaction process described by weak turbulence theory. We show that by starting with weakly nonlinear randomized waves as an initial condition, there exists an inverse cascade of photons towards the lowest wavenumbers. During the cascade nonlinearity becomes strong at low wavenumbers and, due to the focusing nature of the nonlinearity, it leads to modulational instability resulting in the formation of solitons. Further interaction of the solitons among themselves and with incoherent waves leads to the final condensate state dominated by a single strong soliton. In addition, we show the existence of the direct energy cascade numerically and that it agrees with the wave turbulence prediction.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Performance study of the Galway Bay wave energy test site floating power system

The Galway Bay wave energy test site promises to be a vital resource for wave energy researchers and developers. As part of the development of this site, a floating power system is being developed to provide power and data acquisition capabilities, including its function as a local grid connection, allowing for the connection of up to three wave energy converter devices. This work shows results from scaled physical model testing and numerical modelling of the floating power system and an oscillating water column connected with an umbilical. Results from this study will be used to influence further scaled testing as well as the full scale design and build of the floating power system in Galway Bay.

Hydrodynamics of oscillating water column wave energy converters

This work deals with the numerical studies on hydrodynamics of oscillating water column (OWC) wave energy converters and its damping optimization on maximizing wave energy conversion by the OWC device. As a fundamental step, the hydrodynamic problems have been systematically studied by considering the interactions of the wave-structure and of the wave-internal water surface. Our first attention is on how the hydrodynamic performance can be reliably assessed, especially when it comes to the time-domain analysis, and what the physics behind the considerations is. Further on, a damping optimization for the OWC wave energy converter is also present based on the dynamics of the linear system, and a study on how we can optimize the damping for the given sea states so that the power conversion from irregular waves from irregular waves can be maximized.

Primary wave energy conversions of oscillating water columns

This paper presents a study on the numerical simulation of the primary wave energy conversion in the oscillating water column (OWC) wave energy converters (WECs). The new proposed numerical approach consists of three major components: potential flow analysis for the conventional hydrodynamic parameters, such as added mass, damping coefficients, restoring force coefficients and wave excitations; the thermodynamic analysis of the air in the air chamber, which is under the assumptions of the given power take-off characteristics and an isentropic process of air flow. In the formulation, the air compressibility and its effects have been included; and a time-domain analysis by combining the linear potential flow and the thermodynamics of the air flow in the chamber, in which the hydrodynamics and thermodynamics/aerodynamics have been coupled together by the force generated by the pressurised and de-pressurised air in the air chamber, which in turn has effects on the motions of the structure and the internal water surface. As an example, the new developed approach has been applied to a fixed OWC device. The comparisons of the measured data and the simulation results show the new method is very capable of predicting the performance of the OWC devices.

Solitons in Exciton-Polariton System: Reduced Modelling, Analysis, and Numerical Studies

In this dissertation, we study the behavior of exciton-polariton quasiparticles in semiconductor microcavities, under the sourceless and lossless conditions.

First, we simplify the original model by removing the photon dispersion term, thus effectively turn the PDEs system to an ODEs system,

and investigate the behavior of the resulting system, including the equilibrium points and the wave functions of the excitons and the photons.

Second, we add the dispersion term for the excitons to the original model and prove that the band of the discontinuous solitons now become dark solitons.

Third, we employ the Strang-splitting method to our sytem of PDEs and prove the first-order and second-order error bounds in the $H^1$ norm and the $L_2$ norm, respectively.

Using this numerical result, we analyze the stability of the steady state bright soliton solution. This solution revolves around the $x$-axis as time progresses

and the perturbed soliton also rotates around the $x$-axis and tracks closely in terms of amplitude but lags behind the exact one. Our numerical result shows orbital

stability but no $L_2$ stability.

Effects of tidal range on mooring systems of wave energy converters

Wave energy converters are currently proposed to be deployed near coastal area for the closeness to the infrastructure and for ease of maintenance in order to reduce operational costs. The motivation behind this work is the fact that the deployment depths during the highest and lowest tides will have a significant effect on the mooring system of WECs. In this paper, the issue will be investigated by numerical modelling (using ANSYS AQWA) for both catenary and taut moorings to examine the performance of the mooring system in varying tides. The case study being considered is the ¼- scale wave energy test site in Galway Bay off the west coast of Ireland where some marine renewable energy devices can be tested. In this test site, the tidal range is macro-tidal with a range of approximately 6 m which is a large value relative to the water depth. In the numerical analysis, ANSYS AQWA suite has been used to simulate moored devices under wave excitation at varying tidal ranges. Results show that the highest tide will give rise to larger forces. While at lower depths, slackening of the mooring occurs. Therefore, the mooring lines must be designed to accommodate both situations.

Wave energy conversion of oscillating water column devices including air compressibility

This paper presents an investigation on air compressibility in the air chamber and its effects on the power conversion of oscillating water column (OWC) devices. As it is well known that for practical OWC plants, their air chambers may be large enough for accommodating significant air compressibility, the “spring effect,” an effect that is frequently and simply regarded to store and release energy during the reciprocating process of a wave cycle. Its insight effects on the device’s performance and power conversion, however, have not been studied in detail. This research will investigate the phenomena with a special focus on the effects of air compressibility on wave energy conversion. Air compressibility itself is a complicated nonlinear process in nature, but it can be linearised for numerical simulations under certain assumptions for frequency domain analysis. In this research work, air compressibility in the OWC devices is first linearised and further coupled with the hydrodynamics of the OWC. It is able to show mathematically that in frequency-domain, air compressibility can increase the spring coefficients of both the water body motion and the device motion (if it is a floating device), and enhance the coupling effects between the water body and the structure. Corresponding to these changes, the OWC performance, the capture power, and the optimised Power Take-off (PTO) damping coefficient in the wave energy conversion can be all modified due to air compressibility. To validate the frequency-domain results and understand the problems better, the more accurate time-domain simulations with fewer assumptions have been used for comparison. It is shown that air compressibility may significantly change the dynamic responses and the capacity of converting wave energy of the OWC devices if the air chamber is very large.

Results of wave modelling for Moreton Bay, Southeast Queensland, and a reef lagoon off Lizard Island, Great Barrier Reef, Australia

The distribution, abundance, behaviour, and morphology of marine species is affected by spatial variability in the wave environment. Maps of wave metrics (e.g. significant wave height Hs, peak energy wave period Tp, and benthic wave orbital velocity URMS) are therefore useful for predictive ecological models of marine species and ecosystems. A number of techniques are available to generate maps of wave metrics, with varying levels of complexity in terms of input data requirements, operator knowledge, and computation time. Relatively simple "fetch-based" models are generated using geographic information system (GIS) layers of bathymetry and dominant wind speed and direction. More complex, but computationally expensive, "process-based" models are generated using numerical models such as the Simulating Waves Nearshore (SWAN) model. We generated maps of wave metrics based on both fetch-based and process-based models and asked whether predictive performance in models of benthic marine habitats differed. Predictive models of seagrass distribution for Moreton Bay, Southeast Queensland, and Lizard Island, Great Barrier Reef, Australia, were generated using maps based on each type of wave model. For Lizard Island, performance of the process-based wave maps was significantly better for describing the presence of seagrass, based on Hs, Tp, and URMS. Conversely, for the predictive model of seagrass in Moreton Bay, based on benthic light availability and Hs, there was no difference in performance using the maps of the different wave metrics. For predictive models where wave metrics are the dominant factor determining ecological processes it is recommended that process-based models be used. Our results suggest that for models where wave metrics provide secondarily useful information, either fetch- or process-based models may be equally useful.