No description available.

Nonlinear free-surface flows generated by the motion of a surface-piercing body in an ideal fluid are studied. A numerical scheme employing a mixed Eulerian-Lagrangian approach and involving time stepping is used to simulate the flow. At each time step, the boundary value problem is solved using the Complex Boundary Element Method. The numerical performance of the method is studied by considering cases where the exact solution is known. Computational results for the impulsive wavemaker problem and the wedge entry problem for wedges of half-angles up to 15 degrees are presented. The obtained results are found to be in good agreement with existing analytical and numerical solutions. / Master of Science

The nonlinear dynamic characteristics and stability of floating vehicles are investigated theoretically and experimentally. Mathematical models of such floating bodies are used to investigate their complicated motions in regular waves. In particular, we address the phenomenon of indirectly exciting the roll motion of a vessel due to nonlinear couplings of the heave, pitch, and roll modes. In the analytical approach the method of multiple scales is used to determine first-order approximations to the solutions, yielding a system of nonlinear first-order equations governing the modulation of the amplitudes and phases of the system. The fixed-point solutions of these equations are determined and their bifurcations are investigated. Hopf bifurcations are found. Numerical simulations are used to investigate the bifurcations of the ensuing limit cycles and how they produce chaos. Experiments are conducted with tanker and destroyer models. They demonstrate some of the nonlinear effects, such as the jump phenomenon, the subcritical instability, and the coexistence of multiple solutions. The experimental results are qualitatively in good agreement with the results predicted by the theory. Coupling of the pitch and roll motions of a vessel when their frequencies are in the ratio of two-to-one is modeled by a two-degree-of-freedom system. The damping in the pitch mode is modeled by a linear viscous damping, whereas that of the roll mode is modeled by the sum of a linear viscous part and a quadratic viscous part. The effect of the quadratic damping is investigated when either mode is externally excited through a primary resonance. Force-response and frequency-response curves are generated. Coexistence of multiple solutions is found. The jump phenomenon continues to exist, whereas the saturation phenomenon ceases in the presence of quadratic damping. Hopf bifurcations are found. They indicate conditions for the nonexistence of steady-state periodic responses. Instead, the response is an amplitude- and phase-modulated motion consisting of both modes. Floquet theory is used to determine the stability of limit-cycle solutions. They undergo a pitchfork bifurcation followed by a cascade of period-doubling bifurcations, leading to chaos and hence chaotically modulated motions. When the roll mode is excited, the quadratic damping causes the region between the two Hopf bifurcation frequencies to shrink. However, the quadratic damping which may be introduced by attaching antirolling devices does not eliminate complicated motions completely in this region. The dynamic stability and excessive motion of the roll mode of a vessel in following or head regular waves is investigated theoretically and experimentally. The motion is modeled by a three-degree-of-freedom system with quadratic and cubic nonlinearities. The heave and pitch modes are linearized and their harmonic solutions are coupled into the roll mode. The resulting nonlinear ordinary-differential equation with time-varying coefficients is used to determine the stability of the roll mode for the case of principal parametric resonance. Experiments with a tanker model were conducted to validate the theory. They demonstrate the jump phenomenon and subcritical instability. They also reveal that the large-amplitude roll response depends not only on the encounter frequency but also on the position of the model relative to the waves. / Ph. D.

The Tigris River is one of two primary rivers in Iraq and is, along with the Euphrates, the main source for drinking and irrigation water in the country. The Tigris River originates in the Taurus Mountains in Turkey, and is 1850 km long. The majority of the river lies within Iraq. The river passes through, and is the primary drinking water source for major cities such as Mosul, Baeji, Samarra, Baghdad (the capital), and Kut. The Tigris River joins the Euphrates River in Qurna city within Basra province to form the Shatt Al-Arab River which eventually discharges into the Persian Gulf. As a result of fluctuations in flow rate along the Tigris River that cause both potential flooding and drought, Mosul Dam was built on the mainstem of the Tigris River upstream of the city of Mosul and was operated starting in July 1986 to control the river flow and to generate hydroelectricity. Some canals were also constructed to divert excess fresh water from the mainstem of the river at Samarra Barrage located 125 km north (upstream) of Baghdad to Tharthar Lake, an artificial lake located 100 km northwest Baghdad city. The Tigris-Tharthar canal, 75 km long, was constructed in 1956 to divert excess water from Samarra Barrage to Tharthar Lake and to prevent potential flooding in Baghdad. During dry seasons, high total dissolved solids (TDS) water is diverted from Tharthar Lake into the mainstem of the Tigris River through the 65 km long Tharthar-Tigris canal, which is located 25 km upstream Baghdad. Due to rapid population growth and increasing industrial activates, the Tigris River is also facing many water quality challenges from inflows of contaminated wastewater from treatment plant stations. A water quality model that simulates the Tigris River system is therefore needed to study the effects of these discharges and how water quality of the Tigris River could be managed. To address this issue, CE-QUAL-W2 was used to develop a 2-D (longitudinal and vertical) hydrodynamic and water quality model of the mainstem Tigris River from Mosul Dam (Rkm 0) to Kut Barrage (Rkm 880). In addition, Tharthar Lake and its canals were modeled. A full suite of hydrodynamic and water quality variables were simulated for the year 2009, including flowrates, water level, and water temperature. Additionally, water quality constituents such as total dissolved solids (TDS), phosphate (PO4), ammonium (NH4), nitrate (NO3), biochemical oxygen demand (BOD), chlorophyll-a (Chl-a), and dissolved oxygen (DO) were also simulated. Bathymetry of the Tigris River and field data such as flowrate, water level, TDS, NO3 were obtained from the Ministry of Water Resources in Iraq, while surface water temperatures of the Tigris River were estimated remotely using Landsat satellites. These satellites provided a continuous observation record of remote sites. Other water quality field data, such as PO4, NH4, BOD, and DO, were estimated from literature values. Meteorological data, including, wind speed, wind direction, air and dew point temperatures, cloud cover, and solar radiation were obtained from the Iraqi Ministry of Transportation, the General Organization for Meteorology and Seismic Monitoring. Model predictions of flow and water level were compared to field data at three stations along the mainstem of the Tigris River, including Baeji, downstream of Samarra Barrage, and Baghdad. The absolute mean error in the flow varied from 12.6 to 3.4 m3/s and the water level absolute mean error varied from 0.036 to 0.018 m. The percentage error of the overall flowrate at Baeji, downstream Samarra Barrage and Baghdad was 1.9%, 0.8%, and 0.8% respectively. Injecting a conservative tracer at Mosul Dam showed that a parcel of water reaches to Baeji, Samarra Barrage, Baghdad, and Kut Barrage after approximately 3 days, 5 days, 10 days, and 19 days, respectively. Water temperature field data in Iraq are limited and there was no archive of existing field data. Therefore, I obtained estimates of surface water temperature on the Tigris River using the thermal band of the Landsat satellite, one of a series of satellites launched by the National Aeronautics and Space Administration (NASA). The calibration between satellite data and water temperature was validated using sparse field data from 2004, and the calibration then applied to 82 Landsat images from the year 2009. Landsat estimates showed a bias of -2°C compared to model results in winter months, possibly due to uncertainty in Landsat estimations. The absolute mean errors of the CE-QUAL-W2 model predictions of water temperature compared to Landsat estimated temperatures were 0.9 and 1.0°C at Baeji and Baghdad respectively. Temperature calibration in the Tigris River system was highly sensitive to meteorological input data. Landsat Images were also used to estimate longitudinal variation in surface water temperature of Tharthar Lake. It was found that surface water temperature in Tharthar Lake varied longitudinally along the North-South axis with warmer temperatures in the lower part compared with the upper part of the lake. Total dissolved solids concentrations in the Tigris River significantly increased from Mosul Dam to Kut Barrage with peak concentrations of 900 mg/l and 1050 mg/l at Baghdad and Kut, respectively, due to high TDS water diverted from Tharthar Lake, irrigation return flow, urban runoff, and uncontrolled discharge of wastewater effluents. NO3 concentrations did not significantly increase between Samarra Barrage and Baghdad city. BOD concentrations within Baghdad were extremely high due to direct discharge of industrial wastewater into the mainstem of the Tigris River from outlets located within the city. Management scenarios were simulated with the model of the Tigris River system and were compared with the base model. The main scenarios implemented on the Tigris River system were altering upstream hydrology, increasing air temperature due to the effect of climate change, disconnecting Tharthar Lake from the Tigris River system, and simulating long-term effects on Tharthar Lake. Increasing upstream inflows caused a decrease in TDS concentrations from 495 mg/l to 470 mg/l over all the mainstem of the river. In addition, CBOD concentrations decreased somewhat from 5.9 mg/l to 5.74 mg/l. On the other hand, decreasing upstream flows caused a significant increase in average TDS concentrations over the entire Tigris mainstem from 495 mg/l to 527 mg/l. Also, an increase in CBOD concentrations from 5.9 mg/l to 6.2 mg/l was predicted over all the mainstem of the river. Implementing the climate change scenario on the base model of the Tigris River system showed a 5% increase in annually averaged water temperature from 20.7°C to 21.68°C over the mainstem river. Climate change scenarios produced no significant impacts on TDS and CBOD concentrations in the mainstem, while DO concentrations decreased from 8.15 mg/l to 7.98 mg/l with a slight increase in Chl-a concentration from 1.97 µg/l to 2 µg/l in the mainstem. Disconnecting Tharthar Lake from the system showed a remarkable 25% decrease in TDS concentrations, with an average concentration changed from 495 mg/l to 397 mg/l in the mainstem due to an extra 36% increase in flow discharged downstream of Samarra Barrage. Also, Chl-a concentration significantly decreased by 40% with an average concentration changed from 2 µg/l to 1.2 µg/l. Additionally, a 6-year model simulation of the Tigris River system was performed to evaluate the long-term effects on Tharthar Lake. No significant impact was observed in the average temperature of the lake. TDS concentrations in the lake decreased from 1239 mg/l to 1041 mg/l. PO4, NH4 and NO3 concentrations decreased by 2%, 66% and 26%, respectively. Chl-a concentration in Tharthar Lake decreased from 2.0 µg/l to 1.61 µg/l. After decreasing BOD concentrations of the Tigris River by 50%, BOD concentrations in the mainstem decreased by 24%, while DO concentrations increased by 2.8%. There were no significant impacts on Chl-a concentrations in the mainstem of the river. Finally, for a scenario where extremely low dissolved oxygen release from Mosul Dam in the summer, it was found that approximately 50 km below Mosul Dam was affected before DO concentrations reached an equilibrium concentration. For further work on the Tigris River system, it is recommended to model the Tigris River from Kut Barrage to the confluence with the Euphrates River, about 400 km long, and connect it with the current model to have a complete model of the Tigris River system from Mosul Dam to the confluence with the Euphrates River. This is necessary to manage water the entire system of the Tigris River and also to provide enough water with good quality in Basra.

The instabilities of shallow shear flows are analyzed to study exchanges processes across shear flows in inland and coastal waters, coastal and ocean currents, and winds across the thermal-and-moisture fronts. These shear flows observed in nature are driven by gravity and governed by the shallow water equations (SWE). A highly accurate, and robust, computational scheme has been developed to solve these SWE. Time integration of the SWE was carried out using the fourth-order Runge-Kutta scheme. A third-order upwind bias finite difference approximation known as QUICK (Quadratic Upstream Interpolation of Convective Kinematics) was employed for the spatial discretization. The numerical oscillations were controlled using flux limiters for Total Variation Diminishing (TVD). Direct numerical simulations (DNS) were conducted for the base flow with the TANH velocity profile, and the base flow in the form of a jet with the SECH velocity profile. The depth across the base flows was selected for the' balance of the driving forces. In the rotating flow simulation, the Coriolis force in the lateral direction was perfectly in balance with the pressure gradient across the shear flow during the simulation. The development of instabilities in the shear flows was considered for a range of convective Froude number, friction number, and Rossby number. The DNS of the SWE has produced linear results that are consistent with classical stability analyses based on the normal mode approach, and new results that had not been determined by the classical method. The formation of eddies, and the generation of shocklets subsequent to the linear instabilities were computed as part of the DNS. Without modelling the small scales, the simulation was able to produce the correct turbulent spreading rate in agreement with the experimental observations. The simulations have identified radiation damping, in addition to friction damping, as a primary factor of influence on the instability of the shear flows admissible to waves. A convective Froude number correlated the energy lost due to radiation damping. The friction number determined the energy lost due to friction. A significant fraction of available energy produced by the shear flow is lost due the radiation of waves at high convective Froude number. This radiation of gravity waves in shallow gravity-stratified shear flow, and its dependence on the convective Froude number, is shown to be analogous to the Mach-number effect in compressible flow. Furthermore, and most significantly, is the discovery from the simulation the crucial role of the radiation damping in the development of shear flows in the rotating earth. Rings and eddies were produced by the rotating-flow simulations in a range of Rossby numbers, as they were observed in the Gulf Stream of the Atlantic, Jet Stream in the atmosphere, and various fronts across currents in coastal waters.

The reduced fresh water input into the St Lucia Estuary combined with the increase of sediment in the St Lucia Lake System has necessitated the implementation of a dredging programme. To ensure the effectiveness of the dredging programme, the behaviour of the sediment under various flow and tidal conditions needs to be determined. To establish how sediment will move, it is necessary to understand the hydrodynamics of the estuary. To achieve this, a hydrodynamic model which can be linked to a sediment transport model needs to be developed. Various existing types of hydrodynamic and sediment transport models are reviewed, to determine their suitability for the above purpose. Results of the analysis indicate that a two-dimensional hydrodynamic model is required. The two-dimensional hydrodynamic model developed is based on the momentum and continuity equations for an unsteady, non-uniform, free-surface flow for an incompressible fluid. The two dimensions are in the horizontal plane and flow is averaged over the depth. The equations are non-linear and are not decoupled, thus a numerical technique was needed to solve them. An Alternating Direction Implicit technique has been used. Boundary conditions in the modelled region were specified as flow velocity at the upstream boundary, and water levels, relative to the Mean Lake Level, at the downstream boundary. Two short simulations using hypothetical data were run on a 80826 IBM compatible. Results of the simulation indicate two areas where irregularities in the model output are a consequence of the use of hypothetical data in defining the boundary conditions. Recommendations for the collection of data in order to improve and calibrate the model are discussed. / Thesis (M.Sc.)-University of Natal, 1993.

[Truncated abstract] Observations are presented from Lake Biwa (Japan) and Lake Kinneret (Israel) showing the ubiquitous and often periodic nature of high-frequency internal waves in large stratified lakes. In both lakes, high-frequency wave events were observed within two distinct categories: (1) Vertical mode one solitary waves with wavelength ˜100-500 m and frequency near 103 Hz and (2) sinusoidal vertical mode one waves with wavelength ˜5-30 m and frequency just below the local maximum buoyancy frequency near 102 Hz. The sinusoidal waves were associated with shear instability and were shown to dissipate their energy sporadically within the lake interior. Conversely, the solitary waves were found to be capable of propagating to the lake perimeter where they may break upon sloping topography, each releasing ˜1% of the total basin-scale internal wave energy to the benthic boundary layer.

One of the most important purposes of surface water resource management is to develop predictive models to assist in identifying and evaluating operational and structural measures for improving water quality. To better understand the effects of external and internal nutrient and organic loading and the effects of reservoir operation, a model is often developed, calibrated, and used for sensitivity and management simulations. The importance of modeling and simulation in the scientific community has drawn interest towards methods for automated calibration. This study addresses using an automatic technique to calibrate the water quality model CE-QUAL-W2 (Cole and Wells, 2013). CE-QUAL-W2 is a two-dimensional (2D) longitudinal/vertical hydrodynamic and water quality model for surface water bodies, modeling eutrophication processes such as temperature-nutrient-algae-dissolved oxygen-organic matter and sediment relationships. The numerical method used for calibration in this study is the particle swarm optimization method developed by Kennedy and Eberhart (1995) and inspired by the paradigm of birds flocking. The objective of this calibration procedure is to choose model parameters and coefficients affecting temperature, chlorophyll a, dissolved oxygen, and nutrients (such as NH4, NO3, and PO4). A case study is presented for the Karkheh Reservoir in Iran with a capacity of more than 5 billion cubic meters that is the largest dam in Iran with both agricultural and drinking water usages. This algorithm is shown to perform very well for determining model parameters for the reservoir water quality and hydrodynamic model. Implications of the use of this procedure for other water quality models are also shown.

Thesis: Ph. D., Joint Program in Oceanography/Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references. / Holes and channels were excavated in the surf zone on an ocean beach near Duck, NC, and observations of the subsequent evolution of waves, currents, and the modified seafloor were used to investigate nearshore dynamics. In one set of seafloor perturbation experiments, deep holes with steeply sloping sides were excavated in the inner surfzone seafloor. Observations of the infilling holes were used to make the first field estimates of the surfzone morphological diffusivity, which describes the rate of seafloor smoothing by downslope sediment transport. To improve the temporal resolution of bathymetric estimates, a mapping method was developed to combine infrequent, spatially dense watercraft surveys with continuous, spatially sparse in situ altimeter estimates of the seafloor location. In another set of seafloor perturbation experiments, channels were dredged across the surf zone with the propellers of a landing craft. Alongshore variations in wave breaking caused by the perturbed bathymetry resulted in strong rip currents in the channels under some conditions, whereas alongshore currents bypassed the channels under other conditions. The dynamics of the circulation response for changing wave forcing, bathymetry, and tidal elevation are investigated using the observations, a numerical model, and a parameter based on wave properties and bathymetry. / by Melissa Moulton. / Ph. D.

No description available.