This investigation is designed to find the net rate of decrease in the component of velocity parallel to the original direction of motion of a proton moving through an electron gas exhibiting a non-spherical velocity distribution.

A blade-to-blade computer program, using the method of finite differences has been written to calculate the velocity distributions on the rotor blade of an axial-flow compressor. The shape of the blade has been approximated in two different ways employing a rather elaborate method and one whose primary goal was simplicity. The ensuing velocity distributions were compared and can be judged to be satisfactory in that they follow the expectations and show a reasonable behavior, even close to the leading and trailing stagnation point. The latter fact represents an improvement to results obtained from a previous work [ref. 3], however the calculations still need to be confirmed by the experiment. In the second part of this thesis, following a recommendation of reference 3, the blade boundary layer effects have been calculated from the velocity distributions of the first part. Considering certain assumptions, these results also may be judged as satisfactory and the rather important conclusion may be drawn that turbulent separation, if it occurs at all, takes place close to the rear stagnation point of the blade for the applied range of upstream velocities. Another conclusion may be drawn from the displacement thickness distribution in that the flow values would not affect greatly the potential flow calculation and hence an iterative procedure between the potential flow field and the blade boundary layer should converge rapidly. The results from the second part also require a confirmation by the experiment. / Master of Science

Implementation of the National Water Act in South Africa requires that an ecological Reserve be determined for all significant resources. The ecological Reserve determination is the estimation of the amount of water required to maintain the system in a particular ecological condition. Because aquatic habitats are defined in terms of local hydraulic variables rather than amounts of water, hydraulic analysis provides a crucial link in relating hydrological conditions and river ecosystem integrity. Over the last decade, considerable effort has been devoted to developing hydraulics for the Reserve determination. The hydraulics needs for Reserve determination are primarily for low flow analysis, and appropriate methods still need to be developed. This thesis deals with hydraulics under low flow conditions. Its emphasis is on developing appropriate methods for describing the hydraulic characteristics of South African rivers under conditions of low discharge, and the influence of vegetation and large bed roughness. The following methods have been developed: · A new equation for prediction of overall flow resistance under large-scale roughness, and a new approach for estimation of intermediate-scale roughness resistance that distinguishes the influences of large and intermediate scale roughness components. · Prediction methods for velocity distributions with large roughness elements. Under low flows, rocks and boulders may control the local velocity and depth distributions. Distributions of velocities and depth are related to rapidly spatially varied flow caused by the boundary geometry rather than flow resistance phenomena. With increasing discharge, the multiple local controls become submerged and the flow tends towards a resistance controlled condition. Available information addressing the distinction between resistance controlled and multiple local controls conditions is limited. This thesis contributes to understanding the transformation between multiple local controls and the resistance controlled conditions. · Practical conveyance prediction methods for three situations pertaining to the occurrence of vegetation in rivers and wetlands. In-channel and riparian vegetation makes an important contribution to the creation of physical habitats for aquatic animals, but also has significant effects on flow resistances that need to be predicted.

The variation of velocity and temperature distribution in arbitrary profile along the centerline in turbulent which encounters non-linearity regular progressive gravity wave and steady uniform flow right in front are investigated analytically and verified by existing experiments. Firstly, the action of periodic waves and current are incorporated into the equation of motion as an external force and applied radiation stress for evaluating the velocity distribution over arbitrary lateral cross section. Based on the momentum exchange after the interaction between turbulent plane jet and oppositive non-linearity wave and uniform flow, the physical characteristics of jet-wave and current are able to be determined theoretically. Secondly, there are critical sections in both velocity and temperature transport processes when the turbulent plane jet influenced by wave and current motion. Fluctuating function will be close to infinity, is the order of wave sharpness; Average velocity for every wave period along the centerline approach to zero, That¡¦s thanks to the momentum of plane jet is extruded by the momentum of wave and current, Beyond the critical section, characteristics of the jet is no longer existing, such phenomena mean that only the wave and current dominating. Velocity and temperature distribution in the zone of flow developed are Gaussian curve, as has been measured in experiment. The momentum extrusion of counter flow in jet is significant in the deep water and small wave; The velocity distribution coefficient is changing with the increasing of counter flow velocity, owing to the entrainment effect, and the potential core will reducing with the increasing of counter flow velocity.

Turbulent structures are known to be important physical processes in gravel-bed rivers. A number of limitations exist that prohibit the advancement and prediction of turbulence structures for optimization of civil infrastructure, biological habitats and sediment transport in gravel-bed rivers. This includes measurement limitations that prohibit characterization of size and strength of turbulent structures in the riverine environment for different case studies as well as traditional numerical modeling limitations that prohibit modeling and prediction of turbulent structure for heterogeneous beds under high Reynolds number flows using the Navier-Stokes equations. While these limitations exist, researchers have developed various theories for the structure of turbulence in boundary layer flows including large eddies in gravel-bed rivers. While these theories have varied in details and applicable conditions, a common hypothesis has been a structural organization in the fluid which links eddies formed at the wall to coherent turbulent structures such as large eddies which may be observed vertically across the entire flow depth in an open channel. Recently physics has also seen the advancement of topological fluid mechanical ideas concerned with the study of vortex structures, braids, links and knots in velocity vector fields. In the present study the structural organization hypothesis is investigated with topological fluid mechanics and experimental results which are used to derive a vortex model for gravel-bed flows. Velocity field measurements in gravel-bed flow conditions in the laboratory were used to characterize temporal and spatial structures which may be attributed to vortex motions and reconnection phenomena. Turbulent velocity time series data were measured with ADV and decomposed using statistical decompositions to measure turbulent length scales. PIV was used to measure spatial velocity vector fields which were decomposed with filtering techniques for flow visualization. Under the specific conditions of a turbulent burst the fluid domain is organized as a braided flow of vortices connected by prime knot patterns of thin-cored flux tubes embedded on an abstract vortex surface itself having topology of a Klein bottle. This model explains observed streamline patterns in the vicinity of a strong turbulent burst in a gravel-bed river as a coherent structure in the turbulent velocity field.

Spray models are increasingly becoming the principal tools in the design and development of gas turbine combustors. Spray modeling requires a knowledge of the liquid atomization process, and the sizes and velocities of subsequently formed droplets as initial conditions. In order to have a better understanding of the liquid atomization process,the breakup characteristics of plane liquid sheets in co-flowing gas streams are investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process is studied for initial sinuous and varicose modes of disturbance. It is observed that the sheet breakup occurs at half-wavelength intervals for an initial sinuous disturbance and at full-wavelength intervals for an initial varicose disturbance. It is also found that under certain operating conditions, the breakup process is dictated by the initial varicose disturbance compare to its sinuous counterpart. Further, the breakup process is studied for the combined mode and it is found that the sheet breakup occurs at half- or full-wavelength intervals depending on the proportion of the individual sinuous and varicose disturbances. In general, the breakup length decreases with the increase in the Weber number, gas-to-liquid velocity and density ratios. A predictive model of the initial droplet size and velocity distributions for the subsequently formed spray is also formulated here. The present model incorporates the deterministic aspect of spray formation by calculating the breakup length and the mass-mean diameter and the stochastic aspect by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub-models are coupled together by the various source terms signifying the liquid-gas interaction and a prior distribution based on instability analysis, which provides information regarding the unstable wave elements on the two liquid-gas interfaces. Experimental investigation of the breakup characteristics of the liquid sheet is performed by a high speed CCD camera and the measurement of the initial droplet size and distributions is conducted by phase-Doppler interferometry. Good agreement of the theoretical breakup length with the experiment is obtained for a planar, an annular and a gas turbine nozzle. The predicted initial droplet size and velocity distributions show reasonably satisfactory agreement with experimental data for all the three types of nozzles. Hence this spray model can be utilized to predict the initial droplet size and velocity distributions in sprays, which can then be implemented as a front-end subroutine to the existing computer codes.

Spray models are increasingly becoming the principal tools in the design and development of gas turbine combustors. Spray modeling requires a knowledge of the liquid atomization process, and the sizes and velocities of subsequently formed droplets as initial conditions. In order to have a better understanding of the liquid atomization process,the breakup characteristics of plane liquid sheets in co-flowing gas streams are investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process is studied for initial sinuous and varicose modes of disturbance. It is observed that the sheet breakup occurs at half-wavelength intervals for an initial sinuous disturbance and at full-wavelength intervals for an initial varicose disturbance. It is also found that under certain operating conditions, the breakup process is dictated by the initial varicose disturbance compare to its sinuous counterpart. Further, the breakup process is studied for the combined mode and it is found that the sheet breakup occurs at half- or full-wavelength intervals depending on the proportion of the individual sinuous and varicose disturbances. In general, the breakup length decreases with the increase in the Weber number, gas-to-liquid velocity and density ratios. A predictive model of the initial droplet size and velocity distributions for the subsequently formed spray is also formulated here. The present model incorporates the deterministic aspect of spray formation by calculating the breakup length and the mass-mean diameter and the stochastic aspect by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub-models are coupled together by the various source terms signifying the liquid-gas interaction and a prior distribution based on instability analysis, which provides information regarding the unstable wave elements on the two liquid-gas interfaces. Experimental investigation of the breakup characteristics of the liquid sheet is performed by a high speed CCD camera and the measurement of the initial droplet size and distributions is conducted by phase-Doppler interferometry. Good agreement of the theoretical breakup length with the experiment is obtained for a planar, an annular and a gas turbine nozzle. The predicted initial droplet size and velocity distributions show reasonably satisfactory agreement with experimental data for all the three types of nozzles. Hence this spray model can be utilized to predict the initial droplet size and velocity distributions in sprays, which can then be implemented as a front-end subroutine to the existing computer codes.

Vehicle velocity distributions are of utmost relevance for the efficiency, safety, and sustainability of road traffic. Yet, due to technical limitations, they are often empirically analyzed using spatiotemporal averages. Here, we instead study a novel set of microscopic traffic data from Dresden comprising 346 million data points with a resolution of one vehicle from 145 detector sites with a particular focus on extreme events and distribution tails. By fitting q-exponential and Generalized Extreme Value distributions to the right flank of the empirical velocity distributions, we establish that their tails universally exhibit a power-law behavior with similar decay exponents. We also find that q-exponentials are best suitable to model the vast extent to which speed limit violations in the data occur. Furthermore, combining velocity and time headway distributions, we obtain estimates for free flow velocities that always exceed average velocities and sometimes even significantly exceed speed limits. Likewise, congestion effects are found to play a very minor, almost negligible role in traffic flow at the detector sites. These results provide insights into the current state of traffic in Dresden, hinting toward potentially necessary policy amendments regarding road design, speed limits, and speeding prosecution. They also reveal the potentials and limitations of the data set at hand and thereby lay the groundwork for further, more detailed traffic analyses.

The Sun is surrounded by a 10^6 K hot atmosphere, the corona. The corona and the solar wind are fully ionized, and therefore in the plasma state. Magnetic fields play an important role in a plasma, since they bind electrically charged particles to their field lines. EUV spectroscopes, like the SUMER instrument on-board the SOHO spacecraft, reveal a preferred heating of coronal ions and strong temperature anisotropies. Velocity distributions of electrons can be measured directly in the solar wind, e.g. with the 3DPlasma instrument on-board the WIND satellite. They show a thermal core, an anisotropic suprathermal halo, and an anti-solar, magnetic-field-aligned, beam or "strahl". For an understanding of the physical processes in the corona, an adequate description of the plasma is needed. Magnetohydrodynamics (MHD) treats the plasma simply as an electrically conductive fluid. Multi-fluid models consider e.g. protons and electrons as separate fluids. They enable a description of many macroscopic plasma processes. However, fluid models are based on the assumption of a plasma near thermodynamic equilibrium. But the solar corona is far away from this. Furthermore, fluid models cannot describe processes like the interaction with electromagnetic waves on a microscopic scale. Kinetic models, which are based on particle velocity distributions, do not show these limitations, and are therefore well-suited for an explanation of the observations listed above. For the simplest kinetic models, the mirror force in the interplanetary magnetic field focuses solar wind electrons into an extremely narrow beam, which is contradicted by observations. Therefore, a scattering mechanism must exist that counteracts the mirror force. In this thesis, a kinetic model for electrons in the solar corona and wind is presented that provides electron scattering by resonant interaction with whistler waves. The kinetic model reproduces the observed components of solar wind electron distributions, i.e. core, halo, and a "strahl" with finite width. But the model is not only applicable on the quiet Sun. The propagation of energetic electrons from a solar flare is studied, and it is found that scattering in the direction of propagation and energy diffusion influence the arrival times of flare electrons at Earth approximately to the same degree. In the corona, the interaction of electrons with whistler waves does not only lead to scattering, but also to the formation of a suprathermal halo, as it is observed in interplanetary space. This effect is studied both for the solar wind as well as the closed volume of a coronal magnetic loop. The result is of fundamental importance for solar-stellar relations. The quiet solar corona always produces suprathermal electrons. This process is closely related to coronal heating, and can therefore be expected in any hot stellar corona. In the second part of this thesis it is detailed how to calculate growth or damping rates of plasma waves from electron velocity distributions. The emission and propagation of electron cyclotron waves in the quiet solar corona, and that of whistler waves during solar flares, is studied. The latter can be observed as so-called fiber bursts in dynamic radio spectra, and the results are in good agreement with observed bursts. / Die Sonne ist von einer 10^6 K heißen Atmosphäre, der Korona, umgeben. Sie ist ebenso wie der Sonnenwind vollständig ionisiert, also ein Plasma. Magnetfelder spielen in einem Plasma eine wichtige Rolle, da sie elektrisch geladene Teilchen an ihre Feldlinien binden. EUV-Spektroskope, wie SUMER auf der Raumsonde SOHO, zeigen eine bevorzugte Heizung koronaler Ionen sowie starke Temperaturanisotropien. Geschwindigkeitsverteilung von Elektronen können im Sonnenwind direkt gemessen werden, z.B. mit dem 3DPlasma Instrument auf dem Satelliten WIND. Sie weisen einen thermischen Kern, einen isotropen suprathermischen Halo, sowie einen anti-solaren, magnetfeldparallelen Strahl auf. Zum Verständnis der physikalischen Prozesse in der Korona wird eine geeignete Beschreibung des Plasms benötigt. Die Magnetohydrodynamik (MHD) betrachtet das Plasma einfach als elektrisch leitfähige Flüssigkeit. Mehrflüssigkeitsmodelle behandeln z.B. Protonen und Elektronen als getrennte Fluide. Damit lassen sich viele makroskopische Vorgänge beschreiben. Fluidmodelle basieren aber auf der Annahme eines Plasmas nahe am thermodynamischen Gleichgewicht. Doch die Korona ist weit davon entfernt. Ferner ist es mit Fluidmodellen nicht möglich, Prozesse wie die Wechselwirkung mit elektromagnetischen Wellen mikroskopisch zu beschreiben. Kinetische Modelle, die Geschwindigkeitsverteilungen beschreiben, haben diese Einschränkungen nicht und sind deshalb geeignet, die oben genannten Messungen zu erklären. Bei den einfachsten Modellen bündelt die Spiegelkraft im interplanetaren Magnetfeld die Elektronen des Sonnenwinds in einen extrem engen Strahl, im Widerspruch zur Beobachtung. Daher muss es einen Streuprozess geben, der dem entgegenwirkt. In der vorliegenden Arbeit wird ein kinetisches Modell für Elektronen in der Korona und im Sonnenwind präsentiert, bei dem die Elektronen durch resonante Wechselwirkung mit Whistler-Wellen gestreut werden. Das kinetische Modell reproduziert die beobachteten Bestandteile von Elektronenverteilungen im Sonnenwind, d.h. Kern, Halo und einen Strahl endlicher Breite. Doch es ist nicht nur auf die ruhige Sonne anwendbar. Die Ausbreitung energetischer Elektronen eines solaren Flares wird untersucht und dabei festgestellt, dass Streuung in Ausbreitungsrichtung und Diffusion in Energie die Ankunftszeiten von Flare-Elektronen bei der Erde in etwa gleichem Maße beeinflussen. Die Wechselwirkung von Elektronen mit Whistlern führt in der Korona nicht nur zu Streuung, sondern auch zur Erzeugung eines suprathermischen Halos, wie er im interplanetaren Raum gemessen wird. Dieser Effekt wird sowohl im Sonnenwind als auch in einem geschlossenen koronalen Magnetfeldbogen untersucht. Das Ergebnis ist von fundamentaler Bedeutung für solar-stellare Beziehungen. Die ruhige Korona erzeugt stets suprathermische Elektronen. Dieser Prozeß ist eng mit der Koronaheizung verbunden, und daher in jeder heißen stellaren Korona zu erwarten. Im zweiten Teil der Arbeit wird beschrieben, wie sich aus der Geschwindigkeitsverteilung der Elektronen die Dämpfung oder Anregung von Plasmawellen berechnen lässt. Die Erzeugung und Ausbreitung von Elektronenzyklotronwellen in der ruhigen Korona und von Whistlern während solarer Flares wird untersucht. Letztere sind als sogenannte fiber bursts in dynamischen Radiospektren beobachtbar, und die Ergebnisse stimmen gut mit beobachteten Bursts überein.

Dans des milieux tels que les gaz, les plasmas et les milieux granulaires, un objet se déplaçant à des vitessessupersoniques, compresse et chauffe le fluide devant lui, formant ainsi une onde de choc. La zone hors-équilibreappelée front d’onde, où ont lieu de brusques variations de température, pression et densité, présente unestructure particulière, avec notamment des distributions des vitesses des particules fortement non-gaussienneset difficiles à visualiser. Dans une avancée importante en 1951, Mott-Smith décrit le front d’onde comme lasuperposition des deux états que sont le gaz supersonique initial et le gaz subsonique compressé et chauffé,impliquant ainsi l’existence de distributions des vitesses bimodales. Des expériences à grands nombres de Machont confirmé cette structure globalement bimodale. Ce modèle n’explique cependant pas la présence d’un surplusde particules à des vitesses intermédiaires, entre le gaz supersonique et le gaz subsonique.Ce travail de thèse porte sur l’étude des ondes de choc dans les gaz granulaires, où les particules interagissentuniquement par des collisions binaires inélastiques. Dans ces gaz dissipatifs, la température granulaire, traduisantl’agitation des particules, permet de définir l’équivalent d’une vitesse du son par analogie aux gaz moléculaires.Les basses valeurs de ces vitesses du son dans les gaz granulaires, permettent de générer facilement des ondes dechoc dans lesquelles chaque particule peut être suivie, contrairement aux gaz moléculaires. La première partie decette étude porte sur l’effet de la dissipation d’énergie, due aux collisions inélastiques, sur la structure des ondesde choc dans les gaz granulaires. Les modifications induites sur la température, la densité et la vitesse moyennemesurées, sont interprétées à l’aide d’un modèle basé sur l’hypothèse bimodale de Mott-Smith et intégrant ladissipation d’énergie. La deuxième partie est consacrée à l’interprétation des distributions des vitesses dans lefront d’onde. À partir des expériences réalisées dans les gaz granulaires, une description trimodale, incluant unétat intermédiaire supplémentaire, est proposée et étendue avec succès aux distributions des vitesses dans lesgaz moléculaires. / In different materials such as gases, plasmas and granular material, an object, moving at supersonic speed,compresses and heats the fluid ahead. The shock front is the out-of-equilibrium area, where violent changesin temperature, pressure and density occur. It has a particular structure with notably strongly non-Gaussianparticle velocity distributions, which are difficult to observe. In an important breakthrough in 1951, Mott-Smithdescribes the shock front as a superposition of two states: the initial supersonic gas and the compressed andheated subsonic gas, implying existence of bimodal velocity distributions. Several experiences at high Machnumbers show this overall bimodal structure. However this model does not explain the existence of a surplusof particles with intermediate velocities, between the supersonic and the subsonic gas.This thesis focuses on shock waves in granular gases, where particles undergo only inelastic binary collisions.In these dissipative gases, the granular temperature, reflecting the particle random motion, allows to definethe equivalent to the speed of sound by analogy with molecular gases. The low values of this speed of soundpermit to generate easily shock waves in which each particle can be tracked, unlike molecular gases. The firstpart of this work focuses on the effect of the energy dissipation, due to inelastic collisions, on the shock frontstructure in granular gases. Modifications induced on temperature, density and mean velocity, are captured bya model based on the bimodal hypothesis of Mott-Smith and including energy dissipation. The second part isdevoted to the study of velocity distributions in the shock front. From experiences in granular gases, a trimodaldescription, including an additional intermediate state, is proposed and successfully extended to the velocitydistributions in molecular gases.