Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2002. / 198 leaves double sided printed, preliminary pages i-xx and numberd pages 1-1-12-6.Includes bibliography. List of tables, figures and appendices and acronyms. Scanned with a HP Scanjet 8250 Scanner to pdf format (OCR). / ENGLISH ABSTRACT: In this study the numerical short wave model SWAN is evaluated for application to a selected coastal region in South Africa. The aim of this study was to evaluate the degree of accuracy with which SWAN can simulate prototype nearshore wave spectra and wave parameters (e.g. wave height, mean wave direction and mean wave period) for an Algoa Bay field case. Algoa Bay represents a typical deep, sheltered embayment on the South African south coast, which is exposed to high-energy swell. Sensitivity analyses on various wave-related processes were also done, with the aim of establishing the dominant physical processes and appropriate model setup for the Algoa Bay field case. With the dominant wave-related processes and appropriate model setup for the Algoa Bay field case established, selected final runs were performed to determine the degree of accuracy with which SWAN can simulate prototype conditions, by comparing its results with available field recordings. This study comprises a review of the SWAN evaluation work conducted to date by others, an overview of South African coastal conditions, and numerical model simulations. The model simulations, which represent the main focus of this study, were conducted for a selection of available offshore wave conditions (at 85 m water depth) observed during the Algoa Bay field case and were compared to available nearshore observations (at 17 m water depth). Environmental conditions of waves, wind and currents were included in these simulations. The study focuses on model application and sensitivity analysis, rather than model development, and includes evaluation of all relevant processes, without focussing on any specific model aspect. The results of this study show that SWAN simulations correlated well with observations at the nearshore station in Algoa Bay, both in wave spectral shape and its associated parameters. Dominant processes identified for the field case were depth-induced refraction, bottom friction and directional spreading. This finding agrees with those of previous evaluations of SWAN and previous modelling experience by others. It is shown that high-energy swell is relatively more sensitive to the choices of model setup than wind sea. Based on the simulation results of high-energy swell, it is concluded that the calculation of depth-induced refraction in SWAN seem to contain a degree of inaccuracy. It is also concluded that the findings of this study could be used as a guideline to SWAN modelling studies along the South African south coast. / AFRIKAANSE OPSOMMING: In hierdie studie word die toepassingsmoontlikhede van die numeriese kortgolf model SWAN vir 'n geselekteerde gedeelde van die Suid-Afrikaanse kuslyn beoordeel. Die doel van hierdie studie is om die vlak van akkuraatheid waarmee SWAN prototipe golfspektra en golfparameters (bv. golfhoogte, gemiddelde golfrigting en gemiddelde golfperiode) in die vlakwater kan simuleer te beoordeel, vir 'n Algoabaai gevallestudie. Algoabaai verteenwoordig 'n tipiese diep, beskermde baai aan die Suid-Afrikaanse kuslyn, wat blootgestel is aan hoe-energie deining. Sensitiwiteitstoetse is ook uitgevoer vir verskillende golfprosesse, met die doel om die dominante fisiese prosesse en gepaste modelopstelling vir die Algoabaai gevallestudie te vind. Nadat die dominante golfprosesse geidentifiseer is, en die toepaslike modelopstelling gevind is, is finale simulasies uitgevoer vir geselekteerde gevalle om die mate van akkuraatheid te bepaal waarmee SWAN prototipe kondisies kan simuleer, deur simulasie resultate met beskikbare veldmetings te vergelyk. Hierdie studie bestaan uit 'n samevatting van die evaluasiewerk verrig op SWAN deur andere, 'n samevatting van golf-, wind- en stroomtoestande aan die Suid-Afrikaanse kus en numeriese modelsimulasies. Die modelsimulasies, wat die hooffokus van hierdie studie is, is uitgevoer vir 'n seleksie van beskikbare diepsee golftoestande (in 85 m waterdiepte) uit die Algoabaai gevallestudie en is vergelyk met beskikbare vlakwater metings (in 17 m waterdiepte). Omgewingstoestande van golwe, wind en seestrome is ingesluit in hierdie simulasies. Die studie fokus op modeltoepassing en sensitiwiteits-analise, eerder as modelontwikkeling, en behels die beoordeeling van alle toepaslike modelprosesse, sonder om te fokus op enige spesifieke model aspek. Die resultate van hierdie studie toon aan dat die SWAN simulasies goed korrileer met vlakwater meetings in Algoabaai, vir beide golfspektraalvorm en verwante golfparameters. Bodemrefraksie, bodemwrywing en rigtingsspreiding is geidentifiseer as dominante modelprosesse. Hierdie resultaat kom ooreen met bevindings van vroeere beoordeling van SWAN en modelleer-ervaring deur andere. Dit word aangetoon dat hoe-energie deining relatief meer sensitief is vir modelopstelling as wind-see. Gebasseer op resultate van simulasie met hoe-energie deining, word die gevolgtrekking gemaak dat die berekening van bodemrefraksie in SWAN 'n mate van onakkuraatheid toon. Die gevolgtrekking word ook gemaak dat die resultate van hierdie studie as riglyn gebruik kan word vir modelleerwerk met SWAN aan die Suid-Afrikaanse suidkus.

Ocean wind waves represent the atmosphere-ocean boundary, playing a central role in the air-sea exchanging processes. Heat, mass and momentum are transferred across this boundary, with waves mediating the exchange of principally the momentum between the winds and the ocean surface. During the generation process waves are called wind sea. When they leave their generation area or outrun their generating wind they are called swell. The wave field can be said to be dominated either by wind sea or swell. Depending on the wave regime the momentum and energy exchanging processes and the degree of coupling between the waves and the wind is different. During the growing process, waves act as a drag on the surface wind and the momentum flux is directed downward. When swell dominates the wave field a reverse momentum flux mechanism occurs triggered by swell waves traveling considerably faster than the surface winds. The momentum transfer is now directed from the waves to the atmosphere, and takes place because swell waves perform work on the atmosphere as part of their attenuation process. This upward momentum transfer has an impact on the lower atmosphere dynamics, and on the overall turbulence structure of the boundary layer. A detailed qualitative climatology of the global wind sea and swell fields from wave reanalysis data, is presented, revealing a very strong swell dominance of the World Ocean. The areas of larger potential impact of swell on the atmosphere, from a climatological point of view, are also studied. A model that reproduces the swell impact on the lower atmosphere dynamics, conceptually based on the energy transfer from the waves to the atmosphere, is presented – a  new parameterization for the wave-induced stress is also proposed. The model results are compared with field observations. A modeling simulation, using a coupled wave-atmosphere model system, is used to study the impact of swell in a regional climate model, by using different formulations on how to introduce the wave state effect in the modeling system. / Gränsen mellan hav och atmosfär beskrivs av vågor, dessa spelar en central roll i utbytesprocesser mellan hav och atmosfär. Värme, massa och rörelsemängd överförs vid ytan och utbytet av rörelsemängd mellan vind och havsyta styrs i stor utsträckning av vågorna. Då vågor skapas kallas de för vinddrivna vågor. När vågorna sedan lämnar området där de genererats eller rör sig fortare än den vind som genererat dem kallas de dyning. Ett vågfält kan sägas vara dominerat av antingen vinddrivna vågor eller dyningsvågor. Beroende på vilken vågregim som råder så är kopplingen mellan vågor och vind olika och därmed också utbytesprocesserna för rörelsemängd och energi. Då vågorna genereras fungerar de som en bromsande kraft för vinden och impulsutbytet är nedåtriktat. När dyning dominerar vågfältet inträffar en mekanism för omvänt impulsutbyte som sätts igång av dyningsvågor som färdas avsevärt snabbare än vinden. Rörelsemängd överförs då från vågorna till atmosfären, eftersom dyningsvågorna utför arbete på atmosfären då de dämpas. Den uppåtriktade transporten av rörelsemängd har en stor effekt på dynamiken och turbulensstrukturen i lägre delen av atmosfären. En detaljerad kvalitativ klimatologi av globala vågfält (vinddrivna och dyning) från återanalysdata presenteras och visar att dyning dominerar vågfältet på världshaven. Områden där man kan förvänta sig störst effekt av dyning på atmosfären har identifierats. En konceptuellt baserad modell som reproducerar effekten av dyning på dynamiken i lägre delen av atmosfären presenteras. Modellen styrs av överföring av energi från vågor till atmosfären. I modellen föreslås även en ny parameterisering för våginducerad kraft på havsytan. Modellresultaten är utvärderade mot fältmätningar. En regional klimatmodell, med ett kopplat våg-atmosfärssystem, har använts för att studera den långtida effekten av dyning vid klimatsimulering. Olika formuleringar för beskrivningen av vågornas effekt på atmosfären har använts, beroende på om vinddrivna vågor eller dyning dominerar vågfältet.

Atmospheric models are strongly dependent on the turbulent exchange of momentum, sensible heat and moisture (latent heat) at the surface. Oceans cover about 70% of the Earth’s surface and understanding the processes that control air-sea exchange is of great importance in order to predict weather and climate. In the atmosphere, for instance, hurricane development, cyclone intensity and track depend on these processes. Ocean waves constitute an obvious example of air-sea interaction and can cause the air-flow over sea to depend on surface conditions in uniquely different ways compared to boundary layers over land. When waves are generated by wind they are called wind sea or growing sea, and when they leave their generation area or propagate faster than the generating wind they are called swell. The air-sea exchange is mediated by turbulent eddies occurring on many different scales. Field measurements and high-resolution turbulence resolving numerical simulations have here been used to study these processes. The standard method to measure turbulent fluxes is the eddy covariance method. A spatial separation is often used between instruments when measuring scalar flux; this causes an error which was investigated for the first time over sea. The error is typically smaller over ocean than over land, possibly indicating changes in turbulence structure over sea. Established and extended analysis methods to determine the dominant scales of momentum transfer was used to interpret how reduced drag and sometimes net upward momentum flux can persist in the boundary layer indirectly affected by swell. A changed turbulence structure with increased turbulence length scales and more effective mixing was found for swell. A study, using a coupled wave-atmosphere regional climate model, gave a first indication on what impact wave mixing have on atmosphere and wave parameters. Near surface wind speed and wind gradients was affected especially for shallow boundary layers, which typically increased in height from the introduced wave-mixing. A large impact may be expected in regions of the world with predominant swell. The impact of swell waves on air-sea exchange and mixing should be taken into account to develop more reliable coupled Earth system models.

This thesis is an introduction to the modeling of electromagnetic fields in the tissue and is focused on the knowledge of electromagnetic field theory. Maxwell's equations and their solutions are described the spread of plane waves in the environment. It also discusses the exposure limit values of specific absorbed power and hygienic limits based on the standards in force in the Czech Republic on health protection against nonionizing radiation in accordance with Government Regulation No. 106/2010 Coll. It also deals with the software interface in COMSOL Multiphysics 4.2 for solving physical modeling and simulation. There is mention of the RF module, which is used for modeling. Work mentions in detail about the menu of the program and the most important part - the Model Builder.

In this thesis, we are interested in damped wave models with time-dependent propagation speed and time-dependent damping term both having a time-dependent oscillation term. The main goal of this thesis is to understand the influence of strong time-dependent oscillations on Sobolev solutions to the linear models and consequently, to the semilinear models. Especially, due to the deteriorating influence of oscillations on solutions, a stabilization condition and higher-order regularity of the time-dependent coefficients may compensate 'bad behaviors' arising from oscillations.:1. Introduction 2. The influence of oscillations on linear damped wave equation with time-dependent coefficients 3. Global in time existence results for damped wave models with power nonlinearity 4. Global in time existence results for damped wave models with different power nonlinearities 5. Lp-Lq estimates for wave equations with strong time-dependent oscillations 6. Further research topics A. Basic tools B. List of symbols and abbreviations Bibliography

Dans cette thèse, nous avons abordé plusieurs thématiques liées aux modes de variabilité climatique dans l'Atlantique tropical à l'échelle interannuelle. Les analyses statistiques nous ont permis dans un premier temps de mettre en évidence les deux principaux modes dominants de cette variabilité interannuelle: un mode équatorial et un mode méridien. Le mode équatorial est responsable d'anomalies de température de surface de la mer (SST) principalement dans le Golfe de Guinée et est identifié par des variations de la pente du niveau de la mer dans la bande équatoriale. Il est dû à des rétroactions dynamiques entre le vent, le niveau de la mer et la SST. Quant au mode méridien, il se manifeste par des fluctuations inter-hémisphériques de SST et est contrôlé par des rétroactions dynamiques et thermodynamiques entre le vent, l'évaporation et la SST. L'évaluation du couplage de ces variables clés du mode méridien nous a permis de proposer un modèle conceptuel pour expliquer les principaux mécanismes responsables des oscillations du mode méridien. Le modèle a montré que le mode méridien résulte de la superposition d'un mécanisme auto-entretenu basé sur les rétroactions positives et négatives générant des oscillations régulières de haute fréquence (2-3 ans) et d'un autre mécanisme d'oscillation basse fréquence (4-9 ans) lié à l'influence d'ENSO du Pacifique Est. Comme l'évolution de ces deux modes est fortement liée au déplacement méridien de la zone de convergence intertropicale (ITCZ) qui transporte les pluies, nous avons ensuite identifié la signature de ces modes sur la salinité de la surface de la mer à l'aide observations in situ et d'une simulation numérique régionale. Les processus océaniques et/ou atmosphériques responsables de la signature de chaque mode ont été également identifiés grâce à un bilan de sel dans la couche de mélange du modèle validé. Le bilan de sel a révélé que le forçage atmosphérique, lié à la migration de l'ITCZ, contrôle la région équatoriale tandis que l'advection, due à la modulation des courants, du gradient vertical et le mélange à la base de la couche de mélange, explique les variations de SSS dans les régions sous l'influence des panaches. [...] / In this thesis, we investigate several topics related to the interannual climatic modes in the tropical Atlantic. Statistical analyses allows us to extract the two main dominant modes of interannual variability: an equatorial mode and a meridional mode. The equatorial mode is responsible for Sea Surface Temperature (SST) anomalies mainly found in the Gulf of Guinea and is linked to variations of the sea-level slope in the equatorial band. It is due to dynamic feedbacks between zonal wind, sea level and SST. The meridional mode is characterised by inter-hemispheric SST fluctuations and is controlled by dynamic and thermodynamic feedbacks between the wind, evaporation and SST. After quantifying the coupling between key variables involved in the meridional mode, we develop a conceptual model to explain the main mechanisms responsible for meridional mode oscillations. The model shows that the meridional mode results from the superposition of a self-sustaining mechanism based on positive and negative feedbacks generating regular oscillations of high frequency (2-3 years) and another low frequency oscillation mechanism (4-9 years) related to the influence of ENSO. As the evolution of these two modes is strongly linked to the meridional shift of the Intertropical Convergence Zone (ITCZ) and associated rainfall maximum, we identify the signature of these modes on Sea Surface Salinity (SSS) using in situ observations and a regional numerical simulation. Oceanic and/or atmospheric processes responsible for the signature of each mode are also identified through a mixed-layer salt budget in the validated model. The salt balance reveals that the atmospheric forcing, related to the ITCZ migration, controls the equatorial region while the advection, due to the modulation of current dynamics, the vertical gradient and mixing at the base of the mixed layer, explains SSS variations in regions under the influence of plumes. Finally, we study the Equatorial Kelvin wave characteristics and influences on the density that are involved in the meridional and equatorial mode connection processes, using a very simplified model of gravity wave propagation along the equator. After a brief description of this model, which was initially constructed to study dynamics in the equatorial Pacific, we apply it to the specific case of the equatorial Atlantic by validating its analytical and numerical solutions under adiabatic conditions. [...]

La physique de la couche limite atmosphérique en domaine océanique est principalement régie par les processus couplés liés au vent, à l’état de mer local, et à des effets de flottabilité. Leur compréhension reste néanmoins parcellaire et leurs descriptions théoriques et stochastiques sont pour le moins lacunaires, lorsqu’elles ne sont tout simplement pas mises à mal par les rares observations. Dans un contexte d’exploitation croissante de la ressource éolienne offshore, la mise en place de méthodes numériques visant à une description plus fine des propriétés turbulentes de cette couche limite sera une étape déterminante dans la réduction des coûts et l’optimisation des structures pour des rendements de récupération d’énergie améliorés. Ainsi, un outil numérique a été mis en place afin d’étudier le couplage entre un écoulement atmosphérique et l’état de mer. Un code Large-Eddy Simulation massivement parallèle pour la simulation des écoulements atmosphériques incompressibles développé par P. Sullivan au National Center for Atmospheric Research est couplé à un code spectral d’états de mer non-linéaires développé au Laboratoire de recherche en Hydrodynamique, Energétique et Environnement Atmosphérique. De nombreuses configurations de vents et d’états de mer sont modélisées. On montre que les lois semi empiriques souvent utilisées pour représenter la distribution verticale de la vitesse moyenne du vent sont une bonne approximation dans les situations où un petit état de mer est soumis à un fort vent. Néanmoins, dans le cas de houles très rapides se propageant dans des zones de faible vent, la création d’un jet de vent par la houle invalide ces lois semi-empiriques. / Modelling the dynamic coupling of ocean-atmosphere systems requires a fundamental and quantitative understanding of the mechanisms governing the windwave interactions: despite numerous studies, our current understanding remains quite incomplete and, in certain conditions, sparse field observations contradict the usual theoretical and stochastic models. Within the context of a growing exploitation of the offshore wind energy and the development of met ocean models, a fine description of this resource is a key issue. Field experiments and numerical modelling have revealed that atmospheric stability and wave effects, including the dynamic sea surface roughness, are two major factors affecting the wind field over oceans. A numerical tool has been implemented in order to study the coupling between an atmospheric flow and the seastate. A massively parallel large-eddy simulation developed by P. Sullivan at the National Center for Atmospheric Research is then coupled to a High-Order Spectral wave model developed at the Hydrodynamics,Energetics & Atmospheric Environment Laboratory in Ecole Centrale de Nantes. Numerous configurations of wind and sea states are investigated. It appears that, under strongly forced wind conditions above a small sea state, the semi-empirical laws referred to as standards in the international guidelines are a good approximation for the vertical profile of the mean wind speed. However, for light winds overlying fast-moving swell, the presence of a wave induced wind jet is observed, invalidating the use of such logarithmic laws.

This thesis presents a novel analytical solution strategy for the zero-inertia (ZI) equations of free surface flow. These equations are utilized herein for routing flood flow in open channels and for simulating excess rainfall runoff on overland planes. The novel solution approach is shown to be both accurate and robust, especially under the complicated and intricate conditions of infiltrating flow on initially dry river beds or soils, e.g., as present in arid and semiarid areas. This is underlain by comparing modeling results of the novel analytical procedure with those of validated numerical solutions. Furthermore, it is shown that the analytical ZI model can deliver a process-oriented portrayal of runoff concentration in the flood-generating parts of the catchment. Subsequently, the novel analytical ZI model is applied for a real-world water management problem in the Sultanate of Oman, Arabian Peninsula. Within an integrated flash flood routing model—which is also presented in this thesis—the novel analytical routing approach helps in accurately matching the dynamics of advancing and infiltrating ephemeral river flow, established as a consequence of release from a groundwater recharge dam. The integrated modeling system houses the aforementioned analytical downstream model and tailor-made, state-of-the-art modeling components to portray the upstream flow processes, dam operation (including evaporation), and spillway release flow. The proposed modeling system can aid in rendering a realistic image of transient transmission losses and dependent flow dynamics. This is of extremely high importance for water resources assessment, as well as for optimizing recharge dam operation strategies in order to maximize downstream transmission losses and, thus, groundwater recharge. / Diese Dissertation präsentiert einen neuartigen analytischen Lösungsansatz für das beschleunigungsfreie Wellenmodell (bzw. „Zero-Inertia-Modell“, „ZI-Modell“, oder „diffusives Wellenmodell“). Im Rahmen der Arbeit wird das hergeleitete hydrodynamische Modell sowohl zur Simulation von Freispiegelabflüssen in nichtprismatischen und durchlässigen Gerinnen, als auch für die Beschreibung von auf der Landoberfläche abfließendem Infiltrationsüberschuss eingesetzt. Es wird gezeigt, dass der neuartige analytische Ansatz — im Hinblick auf Massenerhaltung und die exakte Abbildung der Abflussdynamik — akkurate Ergebnisse liefert und gleichzeitig unter komplexen und verwickelten Prozessbedingungen anwendbar ist. So belegt eine vergleichende Analyse mit validierten numerischen Lösungsansätzen die Robustheit des analytischen ZI-Modells. Insbesondere die im Sinne der numerischen Mathematik stabile und genaue Modellierung der gekoppelten Abfluss- und Infiltrationsvorgänge in anfänglich trockenen Gerinnen ist dabei ein Novum. Weiterhin wird die Eignung und Anwendbarkeit des neuartigen Modellansatzes zur Beschreibung der Abflusskonzentrationsprozesse gezeigt. Der neuartige Lösungsansatz wird im Folgenden für ein reales Wassermanagementproblem im Sultanat Oman, Arabische Halbinsel eingesetzt. Als Bestandteil eines integrierten Modellsystems, welches ebenfalls im Rahmen der Dissertation vorgestellt wird, dient das analytische ZI-Modell zur Simulation von infiltrierendem Wadiabfluss, welcher unterstrom von Grundwasseranreicherungsdämmen starke Verluste von Masse und Impuls erfährt. Zusammen mit maßgeschneiderten und dem Stand der Technik entsprechenden Komponenten für die Betriebssimulation des Anreicherungsdammes (inklusive Verdunstung von der freien Seefläche) sowie für die Abbildung der oberstromigen hydrodynamischen Prozesse (ebenfalls inklusive Infiltration) wird der neuartige analytische Ansatz in einem Modellsystem zusammengefasst. Das Modellsystem ist in der Lage ein realistisches Bild der raumzeitlichen Dynamik des Abflusses sowie der Grundwasserneubildung aus infiltrierendem Wadiabfluss zu liefern. Damit stellt das Modellsystem ein wertvolles Werkzeug sowohl zur Wasserdargebotsermittlung, als auch für die Optimierung des Betriebes von Grundwasseranreicherungsdämmen dar.

Cette thèse porte sur la modélisation, pour le contrôle, des profils de compositions dans les colonnes de distillation cryogénique. Nous obtenons un modèle non-linéaire de convection-diffusion par réduction d'un modèle d'équations-bilans singulièrement perturbé. Du point de vue de l'automatique, nous nous intéressons à la stabilité des profils de compositions résultants, ainsi qu'à leur observabilité. Du point de vue du procédé, la nouvauté de notre modèle réside dans la prise en compte d'une efficacité de garnissage dépendant des conditions d'opération de la colonne. Le modèle est validé par des comparaisons avec des données de fonctionnement dynamique issues d'une unité de séparation réelle, pour la séparation d'un mélange binaire. Sur le cas plus complexe d'une cascade de colonnes séparant un mélange ternaire, le modèle montre une grande sensibilité aux erreurs d'estimation des taux de reflux. Des résultats adaptés du champ de la chromatographie nous permettent de relier cette sensibilité à des erreurs d'estimation des vitesses d'ondes de compositions cohérentes. En parallèle, nous proposons et testons également un modèle de fonctions de transfert simple (fondé sur des gains statiques et des retards purs uniquement) pour les petites dynamiques de compositions, qui dépend explicitement de valeurs mesurables ou observables sur le procédé / This thesis addresses the problem of modeling the composition profiles dynamics inside cryogenic distillation columns, for control applications. We obtain a non-linear convection-diffusion model from the reduction of a singularly perturbed mass-balances model. In the control theory framework, we consider the stability of the resulting composition profiles and their observability. From the process viewpoint, we express the novelty of our model in terms of operating-conditions dependent packing efficiency. The model is validated against real dynamic plant data for a binary separation case. On a more complex, ternary separation columns cascade, the model shows highly sensitive to reflux rate estimation errors. Result adapted from the field of chromatography allows us to interpret this sensitivity in terms of erroneous coherent composition waves speeds. In parallel, we also propose and test a simple transfer functions model (based on static gains and pure delays only) for small composition dynamics, which explicitly depends on measurable or observable process data.

This thesis presents a novel analytical solution strategy for the zero-inertia (ZI) equations of free surface flow. These equations are utilized herein for routing flood flow in open channels and for simulating excess rainfall runoff on overland planes. The novel solution approach is shown to be both accurate and robust, especially under the complicated and intricate conditions of infiltrating flow on initially dry river beds or soils, e.g., as present in arid and semiarid areas. This is underlain by comparing modeling results of the novel analytical procedure with those of validated numerical solutions. Furthermore, it is shown that the analytical ZI model can deliver a process-oriented portrayal of runoff concentration in the flood-generating parts of the catchment. Subsequently, the novel analytical ZI model is applied for a real-world water management problem in the Sultanate of Oman, Arabian Peninsula. Within an integrated flash flood routing model—which is also presented in this thesis—the novel analytical routing approach helps in accurately matching the dynamics of advancing and infiltrating ephemeral river flow, established as a consequence of release from a groundwater recharge dam. The integrated modeling system houses the aforementioned analytical downstream model and tailor-made, state-of-the-art modeling components to portray the upstream flow processes, dam operation (including evaporation), and spillway release flow. The proposed modeling system can aid in rendering a realistic image of transient transmission losses and dependent flow dynamics. This is of extremely high importance for water resources assessment, as well as for optimizing recharge dam operation strategies in order to maximize downstream transmission losses and, thus, groundwater recharge.:List of Figures List of Tables List of Algorithms List of Symbols and Acronyms 1 Introduction 1.1 The Role of Ephemeral River Flow for Groundwater Recharge 1.2 Methods for Estimating Groundwater Recharge 1.3 Groundwater Augmentation Techniques and the Involved Processes 1.4 The Role of Overland Flow for Flash Flood Formation 1.5 Objectives of the Thesis 1.6 Structure of the Work 2 Literature Review 2.1 Surface-Water Based Studies on the Estimation of Indirect Recharge 2.2 Review of Literature on Process-Oriented Overland Flow Modeling 2.3 Summary 3 Principles of Physically-Based Modeling of Infiltrating Free Surface Flows 3.1 Hydraulic Phases of an Infiltrating Flow Event 3.2 Hydrodynamic Models 3.2.1 The Saint-Venant Equations 3.2.2 Zero-Inertia Approximation 3.2.3 Kinematic Wave Approximation 3.2.4 Other Simplifications of the Full Hydrodynamic Model 3.3 Initial and Boundary Conditions 3.4 Relating Friction and Flow Properties 3.5 Accounting for Losses or Gains 3.6 Including Arbitrary Cross-Sectional Geometries 3.7 Discussion of the Reviewed Flow Models 3.7.1 Discussion of Modeling Approaches for Ephemeral River Routing 3.7.2 A Suitable Hydrodynamic Model for Overland Flow 3.7.3 On the Portrayal of Shocks with the Kinematic Wave Model 3.8 Summary 4 Solution Procedures for the Reviewed Flow Models 4.1 Method of Characteristics 4.2 Numerical Solution Procedures 4.2.1 Introduction to Finite Difference Methods 4.2.2 Mathematical Principles of Finite Difference Methods 4.3 Analytical Solution Procedures 4.4 Discussion of the Reviewed Solution Procedures 4.5 Summary and Conclusions 5 Novel Analytical Solution Approaches for the Zero-Inertia Equations 5.1 Novel Analytical Solution Approach for Zero-Inertia Open Channel Flow 5.1.1 Governing Equations 5.1.2 Including Nonprismatic Channel Geometries 5.1.3 Boundary and Initial Conditions 5.1.4 Analytical Solution of the Momentum Equation 5.1.5 Analytical Solution of the Continuity Equation 5.1.6 Algorithm for the Iterative Solution of the Nonlinear Problem 5.1.7 Coupling Surface Flow and Infiltration 5.1.8 Additional Remarks 5.2 Novel Analytical Solution Approach for Zero-Inertia Overland Flow 5.2.1 Governing Equations 5.2.2 Boundary and Initial Conditions 5.2.3 Analytical Solution 5.2.4 Algorithm for the Iterative Solution of the Nonlinear Problem 5.3 Summary 6 Comparative Studies with Generally Accepted Approaches 6.1 Open Channel Flow in Prismatic and Nonprismatic Permeable Open Channels 6.1.1 Test Setup 6.1.2 Comparison of Flow Dynamics 6.1.3 Analysis of the Geometry Parameter Sensitivity 6.1.4 Evaluating the Stability of the Analytical ZI Model 6.1.5 Summary 6.2 Overland Flow on a Plane 6.2.1 Test Setup 6.2.2 Comparison of Modeling Results 6.2.3 Summary 7 Flash Flood Routing under Transmission Losses and Dam Operation 7.1 Outline of the Structure of a Novel Integrated Modeling System 7.1.1 Wadi Flow Routing Models 7.1.2 Dam Simulation Model with Evaporation Component 7.2 Real-World Application of the Modeling System for an Arid Region 7.2.1 Study Area and Available Data 7.2.2 Parameter Sensitivity Analysis 7.2.3 Optimization-Based Process Parameter Estimation 7.2.4 Model Application for Wadi Ma\\\\\\\'awil 7.3 Summary 8 Summary and Conclusions 9 Outlook 9.1 The Modeling System for Improving Water Resources Assessment 9.2 The Modeling System for Optimizing Groundwater Recharge Bibliography A Mathematical Supplements A.1 Explicit First-Order Finite Difference Scheme for the Kinematic Wave Model A.2 Explicit Second-Order Finite Difference Scheme for the Kinematic Wave Model A.3 Implicit Finite Difference Scheme with Interior Point (Preissmann Scheme) A.4 Analytical Solution of the Kinematic Wave Model A.5 Details on the Derivation of the Iterative Procedure (5.47);(5.48) A.6 Details on the Evaluation of Equation (5.60) B Selected Publications of the Author B.1 Analytical Model of Surge Flow in Nonprismatic Permeable Channels B.2 Analytical Model of Surface Flow on Hillslopes B.3 Integrated Modeling System for Flash Flood Routing in Ephemeral Rivers / Diese Dissertation präsentiert einen neuartigen analytischen Lösungsansatz für das beschleunigungsfreie Wellenmodell (bzw. „Zero-Inertia-Modell“, „ZI-Modell“, oder „diffusives Wellenmodell“). Im Rahmen der Arbeit wird das hergeleitete hydrodynamische Modell sowohl zur Simulation von Freispiegelabflüssen in nichtprismatischen und durchlässigen Gerinnen, als auch für die Beschreibung von auf der Landoberfläche abfließendem Infiltrationsüberschuss eingesetzt. Es wird gezeigt, dass der neuartige analytische Ansatz — im Hinblick auf Massenerhaltung und die exakte Abbildung der Abflussdynamik — akkurate Ergebnisse liefert und gleichzeitig unter komplexen und verwickelten Prozessbedingungen anwendbar ist. So belegt eine vergleichende Analyse mit validierten numerischen Lösungsansätzen die Robustheit des analytischen ZI-Modells. Insbesondere die im Sinne der numerischen Mathematik stabile und genaue Modellierung der gekoppelten Abfluss- und Infiltrationsvorgänge in anfänglich trockenen Gerinnen ist dabei ein Novum. Weiterhin wird die Eignung und Anwendbarkeit des neuartigen Modellansatzes zur Beschreibung der Abflusskonzentrationsprozesse gezeigt. Der neuartige Lösungsansatz wird im Folgenden für ein reales Wassermanagementproblem im Sultanat Oman, Arabische Halbinsel eingesetzt. Als Bestandteil eines integrierten Modellsystems, welches ebenfalls im Rahmen der Dissertation vorgestellt wird, dient das analytische ZI-Modell zur Simulation von infiltrierendem Wadiabfluss, welcher unterstrom von Grundwasseranreicherungsdämmen starke Verluste von Masse und Impuls erfährt. Zusammen mit maßgeschneiderten und dem Stand der Technik entsprechenden Komponenten für die Betriebssimulation des Anreicherungsdammes (inklusive Verdunstung von der freien Seefläche) sowie für die Abbildung der oberstromigen hydrodynamischen Prozesse (ebenfalls inklusive Infiltration) wird der neuartige analytische Ansatz in einem Modellsystem zusammengefasst. Das Modellsystem ist in der Lage ein realistisches Bild der raumzeitlichen Dynamik des Abflusses sowie der Grundwasserneubildung aus infiltrierendem Wadiabfluss zu liefern. Damit stellt das Modellsystem ein wertvolles Werkzeug sowohl zur Wasserdargebotsermittlung, als auch für die Optimierung des Betriebes von Grundwasseranreicherungsdämmen dar.:List of Figures List of Tables List of Algorithms List of Symbols and Acronyms 1 Introduction 1.1 The Role of Ephemeral River Flow for Groundwater Recharge 1.2 Methods for Estimating Groundwater Recharge 1.3 Groundwater Augmentation Techniques and the Involved Processes 1.4 The Role of Overland Flow for Flash Flood Formation 1.5 Objectives of the Thesis 1.6 Structure of the Work 2 Literature Review 2.1 Surface-Water Based Studies on the Estimation of Indirect Recharge 2.2 Review of Literature on Process-Oriented Overland Flow Modeling 2.3 Summary 3 Principles of Physically-Based Modeling of Infiltrating Free Surface Flows 3.1 Hydraulic Phases of an Infiltrating Flow Event 3.2 Hydrodynamic Models 3.2.1 The Saint-Venant Equations 3.2.2 Zero-Inertia Approximation 3.2.3 Kinematic Wave Approximation 3.2.4 Other Simplifications of the Full Hydrodynamic Model 3.3 Initial and Boundary Conditions 3.4 Relating Friction and Flow Properties 3.5 Accounting for Losses or Gains 3.6 Including Arbitrary Cross-Sectional Geometries 3.7 Discussion of the Reviewed Flow Models 3.7.1 Discussion of Modeling Approaches for Ephemeral River Routing 3.7.2 A Suitable Hydrodynamic Model for Overland Flow 3.7.3 On the Portrayal of Shocks with the Kinematic Wave Model 3.8 Summary 4 Solution Procedures for the Reviewed Flow Models 4.1 Method of Characteristics 4.2 Numerical Solution Procedures 4.2.1 Introduction to Finite Difference Methods 4.2.2 Mathematical Principles of Finite Difference Methods 4.3 Analytical Solution Procedures 4.4 Discussion of the Reviewed Solution Procedures 4.5 Summary and Conclusions 5 Novel Analytical Solution Approaches for the Zero-Inertia Equations 5.1 Novel Analytical Solution Approach for Zero-Inertia Open Channel Flow 5.1.1 Governing Equations 5.1.2 Including Nonprismatic Channel Geometries 5.1.3 Boundary and Initial Conditions 5.1.4 Analytical Solution of the Momentum Equation 5.1.5 Analytical Solution of the Continuity Equation 5.1.6 Algorithm for the Iterative Solution of the Nonlinear Problem 5.1.7 Coupling Surface Flow and Infiltration 5.1.8 Additional Remarks 5.2 Novel Analytical Solution Approach for Zero-Inertia Overland Flow 5.2.1 Governing Equations 5.2.2 Boundary and Initial Conditions 5.2.3 Analytical Solution 5.2.4 Algorithm for the Iterative Solution of the Nonlinear Problem 5.3 Summary 6 Comparative Studies with Generally Accepted Approaches 6.1 Open Channel Flow in Prismatic and Nonprismatic Permeable Open Channels 6.1.1 Test Setup 6.1.2 Comparison of Flow Dynamics 6.1.3 Analysis of the Geometry Parameter Sensitivity 6.1.4 Evaluating the Stability of the Analytical ZI Model 6.1.5 Summary 6.2 Overland Flow on a Plane 6.2.1 Test Setup 6.2.2 Comparison of Modeling Results 6.2.3 Summary 7 Flash Flood Routing under Transmission Losses and Dam Operation 7.1 Outline of the Structure of a Novel Integrated Modeling System 7.1.1 Wadi Flow Routing Models 7.1.2 Dam Simulation Model with Evaporation Component 7.2 Real-World Application of the Modeling System for an Arid Region 7.2.1 Study Area and Available Data 7.2.2 Parameter Sensitivity Analysis 7.2.3 Optimization-Based Process Parameter Estimation 7.2.4 Model Application for Wadi Ma\\\\\\\'awil 7.3 Summary 8 Summary and Conclusions 9 Outlook 9.1 The Modeling System for Improving Water Resources Assessment 9.2 The Modeling System for Optimizing Groundwater Recharge Bibliography A Mathematical Supplements A.1 Explicit First-Order Finite Difference Scheme for the Kinematic Wave Model A.2 Explicit Second-Order Finite Difference Scheme for the Kinematic Wave Model A.3 Implicit Finite Difference Scheme with Interior Point (Preissmann Scheme) A.4 Analytical Solution of the Kinematic Wave Model A.5 Details on the Derivation of the Iterative Procedure (5.47);(5.48) A.6 Details on the Evaluation of Equation (5.60) B Selected Publications of the Author B.1 Analytical Model of Surge Flow in Nonprismatic Permeable Channels B.2 Analytical Model of Surface Flow on Hillslopes B.3 Integrated Modeling System for Flash Flood Routing in Ephemeral Rivers