The simulation of solitary wave run up on a slope is evaluated using a volume of fluid method in OpenFOAM. The simulated results are compared to experimental and nonlinear potential flow results for a 1 to 15 run up slope. The breaking region profile is shown to agree well with previous results except a larger jet tip calculated by OpenFOAM. Elevation through the run up of the wave is compared to the same data set. OpenFOAM shows a decreased peak amplitude when compared. A grid study is completed. The dissipation is investigated and a correction is applied to the OpenFOAM results. Corrected data shows a more accurate profile in the breaking region. Results shown indicate that more work is needed to improve two phase modeling within OpenFOAM for application to the case of solitary wave run up on a slope. Simulations are also completed for a vehicle fording case.

Internal solitary waves (ISW) have been detected on the interface of a stratified water column in the ocean. It is believed that ISW could affect oil drilling operations, nutrient pumping, and acoustic signal obstruction. In the ocean, the thickness of a pycnocline is finite which differs with the theoretical assumption as being a thin layer. This thesis reports the effect of an ISW propagation in various pycnocline thicknesses. Laboratory experiments were conducted in an internal wave flume (0.5¡Ñ0.7¡Ñ12m) at the National Sun Yat-sen University, Kaohsiung, Taiwan. ISW in depression or elevation type were generaled using a stratified two-layer fresh/brine water system with a total depth of 50 cm in the flume. Upon creating an ISW propagating on a flat bed or over a triangular obstacle later, several physical parameters of the ISW (i.e. wave amplitude, phase speed, characteristic wave length, and wave energy) were measured or calculated for different thicknesses of the pycnocline. The major controlling factors in the experiments included the depth ratio of the upper to lower layer H1/H2, interface displacement £b0 between the wave generating chamber and the main flume, and the thickness of the pycnocline. The thickness of the pycnocline was estimated from the result of density profile in the vertical direction in the flume, experiments under the same H1/H2 and £b was terminated when the pycnocline thickness became large enough. As the thickness of the pycnoline increased, the values of all the physical parameters (including wave amplitude, phase speed, and wave energy) under consideration decreased. Their reduction rates were more significant in the case of small interface displacement (£b0=10cm) than that with large £b0=15cm. On the other hand, the changes in the physical variables associated with a depression ISW were more significant than those in an elevation ISW.

Numerical simulation of wave behaviour in shallow and deep water is often a key aspect of ocean, coastal, and river hydrodynamic studies. This thesis derives nonlinear one- and two-dimensional level I Green-Naghdi (GN) equations that model the motions of free surface waves in shallow water over non-uniform bed topography. By assuming fitted velocity profiles through the depth, GN equations are simpler than Boussinesq equations, while retaining the wave dispersion property. Implicit matrix solvers are used to solve the spatially discretised 1D and 2D GN equations, with a 4th order Runge Kutta scheme used for time integration. To verify the developed numerical solvers of 1D GN equations, a series of simulations are undertaken for standard benchmark tests including sloshing in a tank and solitary wave propagation over a flat bed. In all cases, grid convergence tests were conducted. In the sloshing test, both numerical schemes and the analytical solution were in complete agreement for small-amplitude free surface motions. At larger values of initial sloshing amplitude, the nonlinear effects caused the free surface waves to steepen, and eventually the numerical simulations became unstable. This could be resolved in future using a shock-capturing scheme. Excellent agreement was achieved between the numerical predictions and analytical solution for solitary waves propagating. The 2D GN equation solver was then verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in closed basin. The predicted free surface motions for Gaussian hump sloshing were in good agreement with linear Fourier analytical solutions for a certain initial period, after which nonlinear effects started to dominate the numerical solution. A reversibility check was undertaken. Nonlinear effects were investigated by increasing the amplitude of the hump, and applying harmonic separation (by comparison against slosh predictions for a corresponding Gaussian trough). It was found that the even harmonic components provided a useful indication of the nonlinear behaviour of the 2D GN equations. 2D GN simulations of a 0.6 m amplitude solitary wave propagation in 1 m deep water over a flat, horizontal bed confirmed that nonlinear interaction was correctly modelled, when the solitary wave hit a solid wall and its runup reached 2.36 m which was 0.36m more than the linear analytical solution and almost identical to a second order solution.

A laboratory experiment was performed to investigate the three-dimensional turbulence and kinematic properties that develop due to a breaking solitary and an irregular shallow water bathymetry. A large basin equipped with a piston-type wavemaker was used to generate the wave, while the free surface elevations and fluid velocities were measured using wave gauges and three-dimensional acoustic-Doppler velocimeters (ADVs), respectively. From the free surface elevations, the evolution and runup of the wave was revealed; while from the ADVs, the velocity and turbulent energy was determined to identify specific turbulent events and coherent structures. It was found that shoaling was confined to areas with gentler sloping bathymetry near the basin side walls and the runup shoreward of the still water shoreline was not uniform. The runup was characterized by a jetting mechanism caused by the convergence of water mass near the basin centerline as the wave refracted during breaking. The jetting mechanism caused the greatest cross-shore velocities to be located near the basin centerline. The greatest turbulent events were well correlated to borefronts, resembling hydraulic jumps, where the greatest shear and fluid accelerations occurred. Because of an abrupt change in the bathymetry, a coherent structure developed which was found to have a three-dimensional flow field. It was proposed that variations in the internal flow with depth were due to the orientation of multiple vortex rings.

Laboratory experiments were conducted to investigate the propagation of internal solitary waves on a uniform slope in a two-layered free surface fluid system. The laboratory facilities employed in this study is the first in Taiwan, which include a stainless steel wave flume (dimensions: 12 meters long with cross-section 0.5 m wide and 0.7m deep) and experimental apparatus for generating and measuring internal waves. The flume incorporates a movable vertical gate at one end for generating internal solitary waves, and a uniform slope (either £c = 30o, 50o, 60o, 90o, 120o or 130o) at the other end. The upper layer had fresh water with density £l1 (999kg/m3), to a depth H1; the lower layer was saline brine density £l2 (1030 kg/m3), which was slowly filled into the flume to a depth of H2 by gravity through several openings at the bottom of the flume, Boussinesq parameter . A mini pump was used to remove a small quantity of fresh water from one side of the vertical gate to another side. By creating a prescribed difference £bo in the interface levels on either side of the gate beforehand, internal solitary wave was generated by the mechanism of overturning the brine and fresh water behind the movable gate. Five ultrasonic probes at equidistant distance recorded the interface fluctuations, one density probe measured the change of density at the interface, while two electrical capacitance gauges for the free surface displacements likely to occur. Digital cameras were also used to record the motions of internal wave in the flume and on the slope for further analysis. Laboratory test on internal solitary wave were arranged from one of the combinations using different layer thickness ratios H1/H2, interface differences £bo, density ratios £l1/£l2, and bottom slopes £c. In addition to internal solitary wave reflection from a uniform slope, laboratory investigations included internal wave propagation on a rigid impermeable bottom and evolution on a uniform slope. Keeping the total water depth in the flume at H = 40cm, an increase in the depth parameter |H2-H1|/H produced large internal wave amplitude, reduced phase velocity, and enhanced soliton feature. From the experimental result analyzed, it suggests that the Korteweg-de Vries (KdV) theory fits solitary waves of small amplitude, and the modified KdV is suitable for large amplituded waves. Considering wave motion in an inviscid fluid, the dissipation of internal solitary waves propagating in a flume may occur through bottom friction and wave breaking. Subjected to bottom friction alone, the amplitude of most internal solitary waves in the experiments decayed approximate by 10% over a journey of 6 meters. Two types of wave breaking mechanism were found to produce strong mixing and local vortex in the fluid, causing significant energy losses. For internal solitary waves of large amplitudes, reflection coefficient for wave amplitude or energy decreased, as amplitude or energy increased. Under this condition, however, the reflection coefficient due to bottom friction may be assumed as constant. Using the experimental results obtained, empirical equation is now proposed to account for wave dissipation due to for non-breaking internal waves. The equation indicates that decrease in reflection coefficient as wave amplitude or energy increases may be expressed using a second order polynomial. Overall, experimental results suggest that good agreement can be found between experimental data and the empirical equation so derived. Upon assuming the wave reflection coefficient is solely dependent on the incoming wave amplitude or energy, prediction for reflection coefficient can be calculated in a straight forward manner. Either large-scale, high-frequency internal wave motion or internal solitary waves have been observed in natural lakes. The observed rapid decay of internal wave energy after severe breaking events seemed to be mostly due to dissipation on various sloping boundaries in a lake. From the basic laboratory experiments on internal wave reflection from various single slopes, the results many benefit provide researchers to promote further research on practical applications related to limnology.

Laboratory work were conducted to investigate the behaviors of an internal solitary wave (ISW) in a two-layer free surface fluid system in a wave flume (12m¡Ñ0.5m¡Ñ0.7m) at the National Sun Yat-sen University, Kaohsiung, Taiwan. A series of fundamental experiments on wave generation, propagation and interaction with uniform slopes and topographic features were carried out in the flume with stratified two-layer fresh/brine water. Factors governing the experiments included the thickness ratio of the upper and lower layers H1/H2, interface difference

In this dissertation we present theoretical and experimental investigation of the performance quality of fiber optical communication systems, and find new and inexpansive ways of increasing the rate of theinformation transmission.The first part of this work discuss the two major factors limiting the quality of information channels in the fiber optical communication systems. Using methods of large deviation theory from statisticalphysics, we carry out analytical and numerical study of error statistics in optical communication systems in the presence of the temporal noise from optical amplifiers and the structural disorder of optical fibers. In the slowly varying envelope approximation light propagation through optical fiber is described by Schr\{o}dinger's equation. Signal transmission is impeded by the additive (amplifiers) and multiplicative (birefringence) noise This results in signal distortion that may lead to erroneous interpretation of the signal. System performance is characterized by the probability of error occurrence. Fluctuation of spacial disorder due to changing external factors (temperature, vibrations, etc) leads to fluctuations of error rates. Commonly the distribution of error rates is assumed to be Gaussian. Using the optimal fluctuation method we show that this distribution is in fact lognormal. Sucha distribution has ""fat"" tails implying that the likelihood of system outages is much higher than itwould be in the Gaussian approximation. We present experimental results that provide excellent confirmation of our theoretical predictions.In the second part of this dissertation we present some published work on bisolitons in the dispersion managed systems. Modern communication systems use light pulses to transmit tremendous amounts of information. These systems can be modeled using variations of the Nonlinear Shrodinger Equation where chromatic dispersion and nonlinear effects in the glass fiber are taken into account. The best system performance to date is achieved using dispersion management. We will see how the dispersion management works and how it can be modeled. As you pack information more tightly the interaction between the pulsesbecomes increasingly important. In Fall 2005, experiments in Germany showed that bound pairs of pulses (bisolitons) could propagate significant distances. Through numerical investigation we found parametric bifurcation of bisolitonic solutions, and developed a new iterative method with polynomial correction for the calculation of these solutions. Using these solutions in the signal transmission could increase the transmission rates.

Internal solitary waves (ISWs) are commonly observed in the ocean, and they play important roles in many ways, such as transport of mass and various nutrients through propagation. The fluids considered in this thesis are assumed to be incompressible, inviscid, non-diffusive and to be weakly affected by the Earth's rotation. Comparisons of the evolution of an initial solitary wave predicted by a fully nonlinear model, IGW, and two weakly-nonlinear wave equations, the Ostrovsky equation and a new alternative Ostrovsky equation, are done. Resolution tests have been run for each of the models to confirm that the current choices of the spatial and time steps are appropriate. Then we have run three numerical simulations with varying initial wave amplitudes. The rigid-lid approximation has been used for all of the models. Stratification, flat bottom and water depth stay the same for all three simulations. In the simulation analysis, we use the results from the IGW as the standard. Both of the two weakly nonlinear models give fairly good predictions regarding the leading wave amplitudes, shapes of the wave train and the propagation speeds. However, the weakly nonlinear models over-predict the propagation speed of the leading solitary wave and that the alternative Ostrovsky equation gives the worst prediction. The difference between the two weakly nonlinear models decreases as the initial wave amplitude decreases.

Yes / A two-dimensional numerical model is developed to study the propagation of a solitary wave in the presence of a steady current flow. The numerical model is based on the Reynolds-averaged Navier-Stokes (RANS) equations with a k-ε turbulence closure scheme and an internal wave-maker method. To capture the air-water interface, the volume of fluid (VOF) method is used in the numerical simulation. The current flow is initialized by imposing a steady inlet velocity on one computational domain end and a constant pressure outlet on the other end. The desired wave is generated by an internal wave-maker. The propagation of a solitary wave travelling with a following/opposing current is simulated. The effects of the current velocity on the solitary wave motion are investigated. The results show that the solitary wave has a smaller wave height, larger wave width and higher travelling speed after interacting with a following current. Contrariwise, the solitary wave becomes higher with a smaller wave width and lower travelling speed with an opposing current. The regression equations for predicting the wave height, wave width and travelling speed of the resulting solitary wave are for practical engineering applications. The impacts of current flow on the induced velocity and the turbulent kinetic energy (TKE) of a solitary wave are also investigated. / National Natural Science Foundation of China Grant #51209083, #51137002 and #41176073, the Natural Science Foundation of Jiangsu Province (China) Grant #BK2011026, the 111 Project under Grant No. B12032, the Fundamental Research Funds for the Central University, China (2013B31614), and the Carnegie Trust for Scottish Universities

Yes / An incompressible Smoothed Particle Hydrodynamics (SPH) method is put forward to simulate non-linear and dispersive solitary wave reflection and transmission characteristics after interacting with a partially immersed curtain-type breakwater. The Naviers¿Stokes equations in Lagrangian form are solved using a two-step split method. The method first integrates the velocity field in time without enforcing incompressibility. Then the resulting deviation of particle density is projected into a divergence-free space to satisfy incompressibility by solving a pressure Poisson equation. Basic SPH formulations are employed for the discretization of relevant gradient and divergence operators in the governing equations. The curtainwall and horizontal bottom are also numerically treated by fixed wall particles and the free surface of wave is tracked by particles with a lower density as compared with inner particles. The proposed SPH model is first verified by the test of a solitary wave with different amplitudes running against a vertical wall without opening underneath. Then it is applied to simulate solitary wave interacting with a partially immersed curtain wall with different immersion depths. The characteristics ofwave reflection, transmission, dissipation and impacting forces on the curtain breakwater are discussed based on computational results