This thesis represents an attempt to reveal and explain the mysterious excitation sources which cause global wave induced vibrations of ships. The wave induced vibrations of the hull girder are referred to as springing when they are associated with a resonance phenomenon, and whipping when they are caused by a transient impact loading. Both phenomena excite the governing vertical 2-node mode and possibly higher order modes, and consequently increase the fatigue and extreme loading of the hull girder. These effects are currently disregarded in conventional ship design. The thesis focuses on the additional fatigue damage on large blunt ships. The study was initiated by conducting an extensive literature study and by organizing an international workshop. The literature indicated that wave induced vibrations should be expected on any ship type, but full scale documentation (and model tests) was mainly related to blunt ships. While the theoretical investigation of whipping mostly focused on slender vessels with pronounced bow flare, full scale measurements indicated that whipping could be just as important for blunt as for slender ships. Moreover, all estimates dealing with the fatigue damage due to wave induced vibration based on full scale measurements before the year of 2000 were nonconservative due to crude simplifications. The literature on the actual importance of the additional fatigue contribution is therefore scarce. The workshop was devoted to the wave induced vibrations measured onboard a 300m iron ore carrier. Full scale measurements in ballast condition were compared with numerical predictions from four state-of-the-art hydroelastic programs. The predicted response was unreliable, and the programs in general underestimated the vibration level. The excitation source was either inaccurately described or lacking. The prediction of sea state parameters and high frequency tail behavior of the wave spectra based on wave radars without proper setting and calibration was also questioned. The measurements showed that vibrations in ballast condition were larger than in the cargo condition, the vibration was more correlated with wind speed than wave height, head seas caused higher vibration levels than following seas, the vibration level towards beam seas decayed only slightly, and the damping ratio was apparently linear and about 0.5%. The additional vibration damage constituted 44% of the total measured fatigue loading in deck amidships in the North Atlantic iron ore trade, with prevailing head seas encountered in ballast condition. Four hypotheses, which may contribute to explain the high vibration levels, were formulated. They include the effect of the steady wave field and the interaction with the unsteady wave field, amplification of short incident waves due to bow reflection, bow impacts including the exit phase and sum frequency excitation due to the bow reflection. The first three features were included in a simplified program to get an idea of the relative importance. The estimates indicated that the stem flare whipping was insignificant in ballast condition, but contributed in cargo condition. The whipping was found to be sensitive to speed. Simplified theory was employed to predict the speed reduction, which was about 5kn in 5m significant wave height. The estimated speed reduction was in fair agreement with full scale measurements of the iron ore carrier. Extensive model tests of a large 4-segmented model of an iron ore carrier were carried out. Two loading conditions with three bow shapes were considered in regular and irregular waves at different speeds. By increasing the forward trim, the increased stem flare whipping was again confirmed to be of less importance than the reduced bottom forces in ballast condition. The bow reflection, causing sum frequency excitation, was confirmed to be important both in ballast and cargo condition. It was less sensitive to speed than linear springing. The second order transfer function amplitude displayed a bichromatic sum frequency springing (at resonance), which was almost constant independent of the frequency difference. The nondimensional monochromatic sum frequency springing response was even higher. The sum frequency pressure was mainly confined to the bow area. Surprisingly, for the sharp triangular bow with vertical stem designed to remove the sum frequency effect, the effect was still pronounced, although smaller. The reflection of incident waves did still occur. In irregular head sea states in ballast condition whipping occurred often due to bottom bilge (flare) impacts, starting with the first vibration cycle in hogging. This was also observed in cargo condition, and evident in full scale. This confirmed that the exit phase, which was often inaccurately represented or lacking in numerical codes, was rather important. Flat bottom slamming was observed at realistic speeds, but the vibratory response was not significantly increased. Stern slamming did not give any significant vibration at realistic forward speeds. The fatigue assessment showed that the relative importance of the vibration damage was reduced for increasing peak period, and secondly that it increased for increasing wave heights due to nonlinearities. All three bows displayed a similar behavior. For the sharp bow, the additional fatigue damage was reduced significantly in steep and moderate to small sea states, but the long term vibration damage was less affected. The effect of the bulb appeared to be small. The contribution of the vibration damage was reduced significantly with speed. For a representative North Atlantic iron ore trade with head sea in ballast and following sea in cargo condition the vibration damage reduced from 51% at full speed to 19% at realistic speeds. This was less than measured in full scale, but the damping ratio of 1-3.5% in model tests was too high, and the wave damage in following seas in cargo condition was represented by head sea states (to high wave damage due to too high encounter frequency). Furthermore, the contribution from vibration damage was observed to increase in less harsh environment from 19% in the North Atlantic to 26% in similarWorld Wide trade. This may also be representative for the effect of routing. The dominating wave and vibration damage came from sea states with a significant wave height of 5m. This was in agreement with full scale results. In ballast condition, the nonlinear sum frequency springing appeared to be more important than the linear springing, and the total springing seemed to be of equivalent importance as the whipping process, which was mainly caused by bottom bilge (flare) impacts. All three effects should be incorporated in numerical tools. In full scale, the vibration response reached an apparently constant level as a function of wave height in both ballast and cargo condition in head seas. This behaviour could be explained by the speed reduction in higher sea states. The vibration level in cargo condition was 60-70% of the level in ballast condition. Although common knowledge implies that larger ships may experience higher springing levels due to a lower eigenfrequency, a slightly smaller ore carrier displayed a higher contribution from the vibration damage (57%) in the same trade, explained by about 1m smaller draft. Moreover, the strengthening of the larger ship resulted in a 10% increase of the 2-node eigenfrequency. The subsequent measurements confirmed that an increased hull girder stiffness was not an effective means to reduce the relative importance of the vibration damage. The relative importance of the excitation sources causing wave induced vibration may differ considerably for a slender compared to a blunt vessel. Therefore, full scale measurements on a 300m container vessel were briefly evaluated. The damping ratio was almost twice as high as for several blunt ships, possibly due to significant contribution from the container stacks. The reduced relative importance of the vibration damage with increasing wave height for the iron ore carrier in full scale was opposite to the trend obtained for the container vessel. Less speed reduction in higher sea states was confirmed, and the whipping process was apparently relatively more important for the container vessel. Both for the blunt and slender ship of roughly 300m length, the total fatigue damage due to vibration was of similar importance as the conventional wave frequency damage. The contribution to fatigue damage from wave induced vibrations should be accounted for, for ships operating in harsh environment with limited effect of routing, especially when they are optimized with respect to minium steel weight. The four hypotheses were all relevant in relation to wave induced vibrations on blunt ships. Further numerical investigation should focus on the sum frequency springing caused by bow reflection and the whipping impacts at the bow quarter. The wave amplification, steady wave elevation and the exit phase must be properly incorporated. When it comes to design by testing, an optimized model size must be selected (wall interaction versus short wave quality). The speed must be selected in combination with sea state. The wave quality must be monitored, and a realistic damping ratio should be confirmed prior to testing. For the purpose of investigating sum frequency excitation, a large restrained bow model tested in higher waves may be utilized to reduce uncertainties in the small measured pressures.

This thesis concerns the stability of plane Couette flow and pipe Poiseuille flow in three space dimensions. The mathematical model for both flows is the incompressible Navier--Stokes equations. Both analytical and numerical techniques are used. We present new results for the resolvent corresponding to both flows. For plane Couette flow, analytical bounds on the resolvent have previously been derived in parts of the unstable half-plane. In the remaining part, only bounds based on numerical computations in an infinite parameter domain are available. Due to the need for truncation of this infinite parameter domain, these results are mathematically insufficient. We obtain a new analytical bound on the resolvent at s=0 in all but a compact subset of the parameter domain. This is done by deriving approximate solutions of the Orr--Sommerfeld equation and bounding the errors made by the approximations. In the remaining compact set, we use standard numerical techniques to obtain a bound. Hence, this part of the proof is not rigorous in the mathematical sense. In the thesis, we present a way of making also the numerical part of the proof rigorous. By using analytical techniques, we reduce the remaining compact subset of the parameter domain to a finite set of parameter values. In this set, we need to compute bounds on the solution of a boundary value problem. By using a validated numerical method, such bounds can be obtained. In the thesis, we investigate a validated numerical method for enclosing the solutions of boundary value problems. For pipe Poiseuille flow, only numerical bounds on the resolvent have previously been derived. We present analytical bounds in parts of the unstable half-plane. Also, we derive a bound on the resolvent for certain perturbations. Especially, the bound is valid for the perturbation which numerical computations indicate to be the perturbation which exhibits largest transient growth. The bound is valid in the entire unstable half-plane. We also investigate the stability of pipe Poiseuille flow by direct numerical simulations. Especially, we consider a disturbance which experiments have shown is efficient in triggering turbulence. The disturbance is in the form of blowing and suction in two small holes. Our results show the formation of hairpin vortices shortly after the disturbance. Initially, the hairpins form a localized packet of hairpins as they are advected downstream. After approximately $10$ pipe diameters from the disturbance origin, the flow becomes severely disordered. Our results show good agreement with the experimental results. In order to perform direct numerical simulations of disturbances which are highly localized in space, parallel computers must be used. Also, direct numerical simulations require the use of numerical methods of high order of accuracy. Many such methods have a global data dependency, making parallelization difficult. In this thesis, we also present the process of parallelizing a code for direct numerical simulations of pipe Poiseuille flow for a distributed memory computer. / QC 20100825

Among sources of renewable energy, development of tidal energy has traditionally been plagued by relatively high costs and limited availability of sites with sufficiently high tidal amplitudes or flow velocities. However, many recent technology developments and improvements, both in design (e.g. dynamic tidal power, tidal lagoons) and turbine technology (e.g. new axial turbines, crossflow turbines), showed that the economic and environmental costs may be brought down to competitive levels comparing to other conventional energy sources. It has long been identified that the Bay of Fundy is one of the world’s premier locations for the development of tidal power generating systems, since it has some of the world’s largest tidal ranges. Consequently, several proposals have been made in the recent years to find economical ways to harness the power of tides. Presently, there is considerable interest in installing tidal lagoons in the Bay of Fundy. The lagoon concept involves temporarily storing seawater behind an impoundment dike and generating power by gradually releasing the impounded seawater through conventional low-head hydroelectric turbines. A tidal lagoon will inherently modify the tides and tidal currents regime in the vicinity of the lagoon, and possibly induce effects that may be felt throughout the entire Bay of Fundy. The nature of these hydrodynamic impacts will likely depend on the size of the tidal lagoon, its location, and its method of operation. Any changes in the tidal hydrodynamics caused by a tidal lagoon may also impact on the transport of sediments throughout the region and upset ecosystems that are well adapted to existing conditions. The scale and character of the potential hydrodynamic impacts due to tidal lagoons operating in the Bay of Fundy have not been previously investigated. The present study endeavours to investigate these potential impacts to help the development of sustainable, science-based policies for the management and development of clean energy for future generations. After outlining fundamental aspects of tidal power projects taken in consideration in the Bay of Fundy, an analysis of present knowledge on tidal lagoons was conducted in order to provide a focus for subsequent investigations. Hydrodynamic modeling was used to quantify any of the potential hydrodynamic changes induced in the Bay of Fundy due to the presence of tidal lagoons. In the last part of the thesis, new relationships were derived in order to describe the amount of energy removed from tidal lagoons associated with its hydrodynamic impacts.

Tsunamis are among the most terrifying and complex physical phenomena potentially affecting almost all coastal regions of the Earth. Tsunami waves propagate in the ocean over thousands of kilometres away from their generating source at considerable speeds. Among several other tsunamis that occurred during the past decade, the 2004 Indian Ocean Tsunami and the 2011 Tohoku Tsunami in Japan, considered to be the deadliest and costliest natural disasters in the history of mankind, respectively, have hit wide stretches of densely populated coastal areas. During these major events, severe destruction of inland structures resulted from the action of extreme hydrodynamic forces induced by tsunami flooding. Subsequent field surveys in which researchers from the University of Ottawa participated ultimately revealed that, in contrast to seismic forces, such hydrodynamic forces are not taken into proper consideration when designing buildings for tsunami prone areas. In view of these limitations, a novel interdisciplinary hydraulic-structural engineering research program was initiated at the University of Ottawa, in cooperation with the Canadian Hydraulic Centre of the National Research Council, to help develop guidelines for the sound design of nearshore structures located in such areas. The present study aims to simulate the physical laboratory experiments performed within the aforementioned research program using a single-phase three-dimensional weakly compressible Smoothed Particle Hydrodynamics (SPH) numerical model. These experiments consist in the violent impact of rapidly advancing tsunami-like hydraulic bores with individual slender structural elements. Such bores are emulated based on the classic dam-break problem. The quantitatively compared measurements include the time-history of the net base horizontal force and of the pressure distribution acting on columns of square and circular cross-sections, as well as flow characteristics such as bore-front velocity and water surface elevation. Good agreement was obtained. Results show that the magnitude and duration of the impulsive force at initial bore impact depend on the degree of entrapped air in the bore-front. The latter was found to increase considerably if the bed of the experimental flume is covered with a thin water layer of even just a few millimetres. In order to avoid large fluctuations in the pressure field and to obtain accurate simulations of the hydrodynamic forces, a Riemann solver-based formulation of the SPH method is utilized. However, this formulation induces excessive numerical diffusion, as sudden and large water surface deformations, such as splashing at initial bore impact, are less accurately reproduced. To investigate this particular issue, the small-scale physical experiment of Kleefsman et al. (2005) is also considered and modeled. Lastly, taking full advantage of the validated numerical model to better understand the underlying flow dynamics, the influence of the experimental test geometry and of the bed condition (i.e. dry vs. wet) is investigated. Numerical results show that when a bore propagates over a wet bed, its front is both deeper and steeper and it also has a lower velocity compared to when it propagates over a dry bed. These differences significantly affect the pressure distributions and resulting hydrodynamic forces acting on impacted structures.

A MEMS-based micro-electro-discharge machining technique that is enabled by the actuation of micromachined planar electrodes defined on the surfaces of the workpiece is developed that eliminates the need of numerical control machines. First, the planar electrodes actuated by hydrodynamic force is developed. The electrode structures are defined by patterning l8-µm-thick copper foil laminated on the stainless steel workpiece through an intermediate photoresist layer and released by sacrificial etching of the resist layer. The planer electrodes are constructed to be single layer structures without particular features underneath. All the patterning and sacrificial etching steps are performed using dry-film photoresists towards achieving high scalability of the machining technique to large-area applications. A DC voltage of 80-140 V is applied between the electrode and the workpiece through a resistance-capacitance circuit that controls the pulse energy and timing of spark discharges. The parasitic capacitance of the electrode structure is used to form a resistance capacitance circuit for the generation of pulsed spark discharge between the electrode and the workpiece. The suspended electrodes are actuated towards the workpiece using the downflow of dielectric machining fluid, initiating and sustaining the machining process. Micromachining of stainless steel is experimentally demonstrated with the machining voltage of 90V and continuous flow of the fluid at the velocity of 3.4-3.9 m/s, providing removal depth of 20 µm. The experimental results of the electrode actuation match well with the theoretical estimations. Second, the planar electrodes are electrostatically actuated towards workpiece for machining. In addition to the single-layer, this effort uses double-layer structures defined on the bottom surface of the electrode to create custom designed patterns on the workpiece material. The suspended electrode is electrostatically actuated towards the wafer based on the pull-in, resulting in a breakdown, or spark discharge. This instantly lowers the gap voltage, releasing the electrode, and the gap value recovers as the capacitor is charged up through the resistor. Sequential pulses are produced through the self-regulated discharging-charging cycle. Micromachining of the stainless-steel wafer is demonstrated using the electrodes with single-layer and double-layer structures. The experimental results of the dynamic built-capacitance and mechanical behavior of the electrode devices are also analyzed.

This thesis investigates physical processes in Lake Erie, a large, shallow mid-latitude lake, from two perspectives: climate change impacts on the thermal structure and dissolved oxygen concentration and small-scale eddy dynamics generated by internal Kelvin wave propagation. A three-dimensional hydrodynamic and aquatic ecological coupled model ELCOM-CAEDYM, validated by the field data collected in 2008, is first used to investigate the responses of the thermal structure and dissolved oxygen concentration in Lake Erie to potential changes in air temperature and wind speed. A new method is presented to define spatially and temporally varying regions for the epilimnion, thermocline, and hypolimnion. Four metrics are selected to quantify the characteristics of the thermal structure: mean epilimnion temperature, mean hypolimnion temperature, onset and breakdown of stratification, and thermocline depth. Exploiting the power of the three dimensional model to provide a more authentic characterization of thermal structure in such large lakes, it is shown that patterns inferred from simple isotherm dynamics, as typically done with one dimensional models, are not always accurate. In the dissolved oxygen studies similar analyses are presented. Three factors related to lake hydrodynamics have strong influences on hypolimnetic hypoxia: water temperature, stratification duration, and hypolimnion thickness. The present results show the potential for complicated and interactive effects of climate forcing on important biogeochemical processes in Lake Erie as well as other large mid-latitude lakes. Taking advantage of high performance computing, the generation of eddies when a baroclinic Kelvin wave propagates past a peninsula is studied using the MITgcm. The grid resolution can be refined from 2 km to 200 m in the parallel computing environment. With the finer resolution small-scale processes which cannot be resolved in the coarse resolution applied previously are able to be explored. The eddy dynamics are studied in detail in both an idealized lake and in Lake Erie. This work presents a first attempt at simulating small-scale hydrodynamic processes in large lakes and contributes to our understanding of how energy is moved from large scales (the scale of the basins in Lake Erie) to smaller scales (the scale of the peninsula or Point Pelee).

This thesis focuses on the analysis of the role of adhesion between substrate and cell and factors of Quorum sensing on the migration of Dictyostelium amoeba. Tools to automate the recordings of videomicroscopy and image analysis have been developed to work with very large samples of cells and toquantify cell migration. A microfluidic device for cell detachment in hydrodynamic flow combined witha motorized stage has allowed a statistical study of adhesion but also the dynamics of detachment. The analysis of the migration of Dictyostelium in non nutritive medium highlights the role of density on celldifferentiation and migration capacity. We observe the presence of a maximum speed of migration after6 hours of starvation. We show that the adhesion to glass is twice as low in deprivation buffer as inthe nutrient medium. The experiences of migration in growth medium revealed the presence of a factorof detection of density secreted by the cells and regulating their random migration. The diffusion coefficient, the persistence of the movement and morphology of cells vary depending on the concentrationof this factor. This factor does not affect cell adhesion but only the dynamics of detachment. Finally, the testing protocol developed allowed us to make a comparative study of migration by varying otherparameters such as surface or the chemical composition of experimental medium. This work concludesby outlining the possible role of adhesion to the migration of Dictyostelium in nutrient medium.

The discovery of carbon nanotubes by Iijima in 1991 has created a torrent of new research activities. Research on carbon nanotubes ranges from studying their fundamental properties, such as their electron band structure and plasma frequencies, to developing new applications, such as self-assembled nano-circuits and field emission displays. Robust models are now needed to enable a better understanding of the electronic response of carbon nanotubes. We use time-dependent density functional theory to derive a two-fluid two-dimensional (2D) hydrodynamic model describing the collective response of a multiwalled carbon nanotube with dielectric media embedded inside or surrounding the nanotube. We study plasmon hybridization of the nanotube system in the UV range, the stopping force for ion channelling, the dynamical image potential for fast ions, channelled diclusters and point dipoles, and the energy loss for ions with oblique trajectories. Comparisons are made of results obtained from the 2D hydrodynamic model with those obtained from an extension of the 3D Kitagawa model to cylindrical geometries.

<p>A GL(2,R)-structure on a smooth manifold of dimension n+1 corresponds to a distribution of non-degenerate rational normal cones over the manifold. Such a structure is called k-integrable if there exist many foliations by submanifolds of dimension k whose tangent spaces are spanned by vectors in the cones.</p><p>This structure was first studied by Bryant for n=3 and k=2. The work included here (n=4 and k=2,3) was suggested by Ferapontov, et al., who showed that the cases (n=4,k=2) and (n=4, k=3) can arise from integrability of second-order PDEs via hydrodynamic reductions.</p><p>Cartan--Kahler analysis for n=4 and k=3 leads to a complete classification of local structures into 54 equivalence classes determined by the value of an essential 9-dimensional representation of torsion for the GL(2,R)-structure. These classes are described by the factorization root-types of real binary octic polynomials. Each of these classes must arise from a PDE, but the PDEs remain to be identified. </p><p>Also, we study the local problem for n >= 5 and k=2,3 and conjecture that similar classifications exist for these cases; however, the interesting integrability results are essentially unique to degree 4. The approach is that of moving frames, using Cartan's method of equivalence, the Cartan--Kahler theorem, and Cartan's structure theorem.</p> / Dissertation

Abstract This study aims to measure the flow field distribution in a microchannel with different heights adjusted. Two different materials, PDMS and Coverglass, were used to observe the flow velocity distribution change resulting from the difference in Zeta potential. The velocity distribution data were also obtained. In the experiment, 1¡Ñ TBE buffer solution with viscosity of 1 cp was used with the electric field intensity controlled under 5, 7.5 and 10 kV/m, respectively. Micrometer resolution Particle Image Velocimetry (£gPIV) was used to measure partial velocity distribution in order to explore the hydrodynamic stretch effect on DNA molecules when the microchannel, where the solution was placed, was adjusted to different heights. This study also statistically analyzed the stretch length distribution of DNA molecules in the microchannel and calculated the time of DNA molecule deformation and stress relaxation time in order to understand the stretch condition under different heights as well as the stretch and deformation of DNA molecules in microchannels.