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Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential forms, i.e., differential form spaces built using smooth splines. We first present an algorithm for computing Bézier extraction operators for univariate spline differential forms that allow local degree elevation. Then, using tensor-products of the univariate splines, a complex of discrete differential forms is built on meshes that contain polar singularities, i.e., edges that are singularly mapped onto points. We prove that the spline complexes share the same cohomological structure as the de Rham complex. Several examples are presented to demonstrate the applicability of the proposed methodology. In particular, the splines spaces derived are used to simulate generalized Stokes flow on arbitrarily curved smooth surfaces and to numerically demonstrate (a) optimal approximation and inf–sup stability of the spline spaces; (b) pointwise incompressible flows; and (c) flows on deforming surfaces.

Spaces of discrete differential forms can be applied to numerically solve the partial differential equations that govern phenomena such as electromagnetics and fluid mechanics. Robustness of the resulting numerical methods is complemented by pointwise satisfaction of conservation laws (e.g., mass conservation) in the discrete setting. Here we present the construction of isogeometric discrete differential forms, i.e., differential form spaces built using smooth splines. We first present an algorithm for computing Bézier extraction operators for univariate spline differential forms that allow local degree elevation. Then, using tensor-products of the univariate splines, a complex of discrete differential forms is built on meshes that contain polar singularities, i.e., edges that are singularly mapped onto points. We prove that the spline complexes share the same cohomological structure as the de Rham complex. Several examples are presented to demonstrate the applicability of the proposed methodology. In particular, the splines spaces derived are used to simulate generalized Stokes flow on arbitrarily curved smooth surfaces and to numerically demonstrate (a) optimal approximation and inf–sup stability of the spline spaces; (b) pointwise incompressible flows; and (c) flows on deforming surfaces.

Même si des avancées importantes ont été réalisées au cours des dernières années quant à la compréhension des dynamiques hydrologiques des environnements de pergélisol, un manque de connaissances limite toujours notre capacité à prédire précisément les impacts dynamiques hydrologiques des bassins versants Arctique. Ce mémoire se divise selon deux principales études effectuées respectivement à l’échelle d’une pente et à l’échelle du bassin versant de la rivière Niaqunguk, près d’Iqaluit, Nunavut, ont été réalisées. La première étude démontre que les dynamiques de drainage d’une pente sont intrinsèquement liées aux patrons de dégel de la couche active du pergélisol. Les connaissances développées à l’échelle de la pente ont été essentielles à la compréhension des dynamiques émergentes à l’échelle du bassin versant. Quatre périodes hydrologiques distinctes correspondant au début de la fonte des neiges, à la récession de la fonte, au débit de base et aux crues estivales ont été délimitées selon les caractéristiques physicochimiques de l’eau échantillonnée dans le bassin versant de la rivière Niaqunguk. Les principaux processus associés à ces périodes sont respectivement la contribution de la fonte des neiges, la distinction entre la contribution des neiges résiduelles et des lacs, les écoulements à travers la portion minérale de la couche active et les écoulements en surface à travers la microtopographie de la couche organique. Globalement, cette recherche propose des connaissances fondamentales qui sont essentielles à la compréhension des dynamiques hydrologiques en milieu de pergélisol. De plus, elle fournit des connaissances significatives pour une exploitation durable de la rivière comme source d’eau potable., Despite recent advances in the hydrological knowledge of permafrost regions, precise predictions or modelling of hydrological dynamics in Arctic watersheds remains difficult. In this master thesis a combination of field measurements, chemistry and statistical analysis were conducted at the hillslope scale and at watershed scale within the Niaqunguk River catchment, to improve our understanding of the processes controlling the water delivery to rivers in permafrost landscape. The first study show that hillslope drainage dynamics were intrinsically linked to permafrost active layer thawing patterns. The microtopography of the surficial organic layer has a great influence on the distribution across the hillslope, by first enhancing the accumulation of water in surficial depressions, which in return enhance localized thaw and the accumulation of water in subsurface depressions. The second study conducted at the watershed scale allowed to delineated, based on the particularities of the water chemistry along the river network, four distinct periods, corresponding respectively to early snowmelt, snowmelt recession, baseflow and summer rainfall events. Since dominant hydrological processes within the watershed changed from one period to another, this period division is relevant the understand the behaviour of the river system. The primary processes associated with each of the four periods were: snowmelt contributions, the distinction between late lying snowpack melt and lake contributions, subsurface flows through mineral deposits and surface flows through the organic layer. Fundamental hydrological knowledge generated in this research will greatly help to improve our ability to predict the response of Arctic hydrological systems to climate changes, but is also indispensable for a sustainable management of a future exploitation of the Niaqunguk River as a potable water for the City of Iqaluit.

Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2020-03-25T17:57:04Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Luciane Gryczak.pdf: 5544729 bytes, checksum: c2461cedeb0e5f235f3684e638a2aa81 (MD5) Made available in DSpace on 2020-03-25T17:57:04Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Luciane Gryczak.pdf: 5544729 bytes, checksum: c2461cedeb0e5f235f3684e638a2aa81 (MD5) Previous issue date: 2018-08-31 As características do relevo influenciam a distribuição dos solos ao longo das vertentes, podendo também interferir nos processos de difusão e mobilização de contaminante no solo, mantendo-o imobilizado ou disponível à absorção pelas plantas ou ao carreamento até as fontes de água para o abastecimento humano e animal. Os processos de transporte e sedimentação associados às características físico-químicas da cobertura pedológica, e do agente químico, configuram a vulnerabilidade morfopedológica a um determinado contaminante. Nesse contexto, essa pesquisa se propôs a avaliar os indicadores do relevo e os atributos dos solos relacionados à vulnerabilidade à contaminação quando expostos a ação de algum produto químico. A metodologia empregada incluiu procedimentos como o levantamento topográfico altimétrico, a elaboração de modelo digital de elevação, a discretização de atributos topográficos, a abertura de trincheiras, coletas e análises de amostras de solos. A área de estudo, localizada no município de Ponta Grossa, corresponde a uma porção agrícola sob plantio direto há mais de quarenta anos, na cercania do corredor industrial Norte, proximidades da Rodovia PR-151, e de bairros residenciais. Constitui uma forma geomorfológica de topo plano e alongado, com orientação SE-NW, composta por duas vertentes com diferentes formas, sob condições similares de uso e manejo do solo, climáticas e de matriz litológica, favorecendo o melhor entendimento da influência do relevo nos processos de formação do solo, no potencial de lixiviação e carreamento de partículas e substâncias químicas. Suas características morfolitológicas são consideras representativas do município de Ponta Grossa. As topossequências estudadas configuram um transecto perpendicular ao eixo da colina, abrangendo dois segmentos de vertente; o ocidental (Vc) e o oriental (Vr). O segmento Vc se apresenta convexo em planta, marcadamente na terço superior, e com segmentos côncavos, convexos e retilíneos em perfil. O segmento Vr é predominantemente convexo-planar de topo à base. A influência do relevo ficou evidente na distribuição dos solos e no controle dos processos hidrológicos, condicionados pela declividade e forma do relevo. Tal influência também foi observada nos resultados das análises químicas das amostras de solo, como no teor de matéria orgânica e valores de óxidos de ferro e alumínio. A influência litológica foi evidenciada pelos elevados teores de argila no solo, mesmo nos mais jovens. As porções côncavas do relevo, onde há maior concentração do fluxo hídricos com a formação de zonas úmidas, tendem a ser os locais mais vulneráveis à contaminação difusa, no entanto são necessários maiores estudos, especialmente no sentido de quantificar o potencial de carreamento de contaminantes, por escoamento superficial, para os rios. A modelagem dos atributos topográficos/morfopedológicos foi considerada representativa e uma importante ferramenta para análise da vulnerabilidade por contaminação difusa. The characteristics of the relief influence the distribution of soils along the slopes and may also interfere in the diffusion and mobilization processes of the contaminant through the soil, keeping it immobilized or under disponibility for plant absorption and transport untill water sources for animal and human consumption. The transport and sedimentation processes associated with the physico-chemical characteristics of the pedological cover, and the chemical agent, constitute the morphopedological vulnerability to a certain contaminant. In this context, this research aimed to evaluate the relief indicators and the most relevant soil attributes linked to their vulnerability face to a possible contamination by chemical products. For this research, the methodology included technical procedures from the altimetrical topographic survey, the elaboration of a digital elevation model, the discretization of topographic attributes, to the opening of trenches, collections and analysis of soil samples. The study area, located in the municipality of Ponta Grossa, corresponds to an agricultural portion under no-tillage system for more than forty years, surrounded by the industrial corridor (N), Highway PR151 and by residential quarters. It is a flat and elongated geomorphological form with SE-NW orientation, consisting of two strands with different forms, under similar conditions of soil use and management, climatic and lithological matrix, favoring a better understanding of the influence of relief on the processes soil formation, potential for leaching and hauling of particles and chemicals. Its characteristics of relief and lithology are considered representative for the municipality of Ponta Grossa. The studied topsequences constitute a transect perpendicular to the axis of the hill, covering two segments of slope; one west (Vc) and one east (Vr). The segment Vc is convex in plan, more striking in the upper portion, and with concave, convex and rectilinear segments in its lateral view. The Vr segment is predominantly convex-planar from top to bottom. The influence of the relief was evident in the distribution of soils and in the control of the hydrological processes, conditioned by the declivity and shape of the relief. Such influence was also observed in the results of the chemical analyzes of soil samples, as well as in the organic matter content and iron and aluminum oxide values. The lithological influence was evidenced by the high levels of clay in the soil, even in the youngest ones. The concave portions of the relief, where there is greater concentration of hydric flow with the formation of wetlands, tend to be the most vulnerable to diffuse contamination, however, further studies are necessary, especially aiming to quantify the potential of contaminants transport, by surface runoff, to the rivers. The modeling of topographic/morphopedological attributes was considered representative and an important tool for the analysis of vulnerability to the diffuse contamination.

The development of the computer technologies enables us to solve the ecological problems in water management practice very efficiently. Hydrodynamical models which simulating transport of pollution in surface water are very demanding on input data and calculation time, but on the other side, they are able to simulate detailed effect of dispersion in surface waters. The paper deals with 1-dimensional numerical model HEC-RAS and its response on various values of dispersion coefficient. This parameter is one of the most important input data for simulation of pollution spreading in streams. Getting fair value, however, is in practice very difficult. One option is the most accurate simulation of tracer experiments carried out on the ground on the natural surface flow. For the pilot application was selected flow Small Nitra. Of longitudinal dispersion coefficient in the flow, or the flow of a similar nature (with and limit the rate of flow), were in the range 0.05 to 2.5 m2 · s–1. The next task was carrying out the model sensitivity analysis, which means to evaluate input data influences, especially longitudinal dispersion coefficient, on outputs computed by 1-dimensional simulation model HEC-RAS. Sensitivity analysis model HEC-RAS also showed its adequate response to changes of the input parameter. Given the present results it can be stated that the HEC-RAS model responds to changes in the values of the longitudinal dispersion coefficient appropriately. HEC-RAS model has demonstrated its applicability to simulation of pollution in streams, and therefore is an appropriate tool for decision making related to the quality of water resources.

Granular flows, which are common in nature and industry, have particular characteristics that are different from the ordinary flow of liquid (eg. water, oil, etc.) and are not yet well understood in the literature. This case underlines the lack of knowledge on the exchange rate between solid and liquid states of granular flows which is the origin of the erosion - deposition phenomenon and constitutes the core of this thesis. To address the issue of the exchange rate solid - liquid, this work is based mainly in two subjects. The first subject is to study the processes of erosion and deposition of a flow generated by the grains stocked in a reservoir. By releasing naturally with zero-velocity the grains to generate the granular flow, we quantified the relation between the erosion and deposition for determining the neutral angle which defines the slope where these two processes balance. The second subject is to analyze the fall of grains in Sinai step problem by studying the spread of the march. For both works, we conduct not only the experimental but also theoretical studies based on the phenomenological models of the exchange rate proposed by BCRE (Bouchaud, Cates, Ravi Prakash and Edwards) and BDG (Boutreux and de Gennes) with some modifications., Bien que répandus dans l'environnement et dans l'industrie, les écoulements granulaires possèdent des caractéristiques particulières qui sont différentes de celles des écoulements de liquides ordinaires comme l'eau (fluides newtoniens). L'une de ces caractéristiques est de présenter un seuil d'écoulement, il est donc fréquent qu'une des frontières de l'écoulement soit constituée de grains au repos (frontière érodable). L'échange entre les deux états solide et liquide d'un écoulement granulaire est à l'origine du phénomène d'érosion et de déposition et constitue le cœur de cette thèse. Nous y effectuons à la fois des études expérimentales et des études théoriques en nous basant sur les modèles phénoménologiques concernant le taux d'échange proposés par Bouchaud, Cates, Ravi Prakash et Edwards et modifiés par Boutreux et de Gennes. A l'aide d'un dispositif expérimental permettant de lâcher sans vitesse initiale une colonne de grains sur une pente granulaire, nous avons quantifié l'importance relative des phénomènes d'érosion et de déposition notamment en déterminant l'angle neutre qui définit la pente critique pour laquelle ces deux processus s'équilibrent. Dans un deuxième temps nous avons appliqué le modèle proposé par Boutreux et de Gennes au cas de l'étalement d'une « marche » granulaire (marche du Sinaï).

A flow (continuous real action) on a compact orientable surface M of genus greater than one (a sphere with at least two handles) has sufficient room for orbits to wrap around one of the handles in an exotic fashion. Specifically, an orbit that is wrapping around one handle can, between wraps, spend increasing amounts of time wrapping and unwrapping around a second handle before returning to the first for the next wrap around it. As a result the omega limit set of such an orbit can contain a simple closed curve of fixed points around the second handle in spite of wrapping around the first handle. In an earlier paper (Colloq. Math. 84/85 (2000) 235), the authors constructed such a flow from this perspective and studied its lift to the universal covering space of the surface. In this paper it is shown that many of the properties of the example are consequences of a general theory that extends classical limit cycle theory.

International audience; Models of monodisperse particle flow in partially filled three-dimensional tumblers often assume that flow along the axis of rotation is negligible. We test this assumption, for spherical and double cone tumblers, using experiments and discrete element method simulations. Cross sections through the particle bed of a spherical tumbler show that, after a few rotations, a colored band of particles initially perpendicular to the axis of rotation deforms: particles near the surface drift toward the pole, while particles deeper in the flowing layer drift toward the equator. Tracking of mm-sized surface particles in tumblers with diameters of 8-14 cm shows particle axial displacements of one to two particle diameters, corresponding to axial drift that is 1-3% of the tumbler diameter, per pass through the flowing layer. The surface axial drift in both double cone and spherical tumblers is zero at the equator, increases moving away from the equator, and then decreases near the poles. Comparing results for the two tumbler geometries shows that wall slope causes axial drift, while drift speed increases with equatorial diameter. The dependence of axial drift on axial position for each tumbler geometry is similar when both are normalized by their respective maximum values.

Rotating flows with free surface are commonly observed in everyday-life, the most popular example being the drain vortex observed in bathtubs and sinks. These flows are known to support spectacular patterns arising from breaking of the axial symmetry. A situation which has been particularly investigated through experiments is the case of a partially filled container with a rotating bottom. In this situation, an instability leads to the appearance of rotating polygons along the free surface. The axisymmetric base flow preexisting the instability is rather complex, involving strong recirculations, but includes a region where the rotation is approximately potential, suggesting that the potential vortex may be a relevant model to investigate the instability mechanism. Consequently, we investigate here the linear inviscid stability of the potential swirling flow with a free surface; namely, the flow defined Vθ = Γ/(2πr), with a free surface given by h0 (r) ∼ R2 − r12 , where R1 corresponds to the radius of the dry area. For the study, we use both a global stability approach based on the finite element software Freefem++ and a shallow water approach. Our results show that unstable modes exist in narrow ranges of the Froude number (defined by F r = Γ/2π (gR0 ), R0 being the radius of the cylinder), for all non-zero values of the azimuthal wavenumber m (see figure 1). The instability seems to be related to the ”strato-rotational” instability mechanism existing in stratified rotating fluids.

Polymer processing entails several operations involving the handling of granular materials. We present here a review of some recent advances in the field which are of relevance to polymer processing. The stress distribution in static material is considered with application to particulates in bins and hoppers. A new model for description of the rheology of dense granular flows is reviewed. A model for surface granular flows with application to rotating cylinders is discussed. Finally the mixing and segregation is tumbling mixers is reviewed.

International audience; The flow of a granular material down an incline of finite width with a strain-rate dependent coefficient of friction and a conical yield criterion is semi-analytically obtained using a characteristic method for flows on a deep layer of grains. This analysis leads to a flow field with three distinct zones: a Bagnold-flow zone below the free surface, a dead zone and a matching zone between the two, linked to slippage at the wall. A good agreement between the computed flow field and experimental data is obtained.

Dense granular flows, which are common in nature and industry, have peculiar characteristics that seem to strongly depend on geometries. When the bottom, which supports the flow, can be eroded, the mechanisms determining the position of the liquid-solid interface or the velocity of the grains down the slope are not yet well understood. This case underlines the lack of knowledge about the rheology of dense granular flows. The experimental study of flows on heap is the central part of this thesis.In order to provide a detailed description of flows on heap, we first carried out an experimental study of the stationary flows in a channel. Systematic measurements allowed us to highlight the important role of sidewalls in such systems: the flow properties are completely controlled by the width of the channel. According to this result, we proposed a model based on a recent rheology. This rheology has been then extended to three dimensions and was applied to our configuration. Numerical simulations quantitatively reproduce the properties of steady flows . We finally studied a peculiar avalanche in order to understand the exchange between the flowing layer and the bottom by following the flowing-thickness during the transient regime. In spite of some limits, this work shows the relevance of a local rheology, which opens the way to more complete model of the dense granular flows., Bien qu'assez répandus dans le milieu naturel et dans diverses activités industrielles, les écoulements granulaires denses possèdent des caractéristiques particulières qui semblent dépendre fortement des géométries observées. Lorsque le fond qui supporte la coulée peut être érodé, les mécanismes déterminant la position de l'interface liquide-solide ou la vitesse à laquelle la pente est dévalée ne sont pas encore bien compris. Ceci provient du manque de connaissance de la rhéologie des écoulements granulaires et constitue le coeur de cette thèse.Ce travail s'articule principalement en trois parties. Premièrement, dans le but de fournir une description détaillée des écoulements sur tas, une étude expérimentale systématique des écoulements stationnaires a été menée dans un canal. Nous avons ainsi pu mettre en évidence l'importance des parois latérales du système dans le cadre des écoulements à la surface d'un tas : les propriétés de l'écoulement sont complètement contrôlé par la largeur du canal. Ce constat nous a ensuite conduit à la proposition d'une modélisation fondée sur une rhéologie récemment développée.Cette rhéologie a été ensuite étendue à trois dimensions et appliquée à notre configuration. Des simulations numériques permettent de reproduire correctement les propriétés des écoulements stationnaires. Nous avons enfin étudié un phénomène transitoire particulier afin de comprendre la manière dont l'épaisseur coulante évolue. Malgré la présence de certaines limitations, ce travail montre qu'une description locale des écoulements granulaire est appropriée et que la rhéologie proposée ouvre la voie à des modélisations plus complètes des écoulements granulaires denses.

Particle self-diffusion has a significant effect on mixing and thus on performance of rotating cylinder systems such as rotary kilns and drum mixers. We study experimentally the radial mixing of monodisperse beads of different colors in a quasi-two-dimensional cylinder rotated in the continuous flow regime. In this regime a shallow surface layer of particles flows steadily while the rest of the material rotates as a solid body. The initial distribution of tracer particles is taken to be radially symmetric and cylinder is taken to be half full. Both facilitate estimation of the particle self-diffusivity since the evolving concentration distribution during mixing in this case is radial for most part and the mixing in these conditions is shown to be dominated by diffusion of particles. A qualitative study of the mixing is carried out using digital photography. Radial number fraction profiles of the tracer particles are obtained by bulk sampling. Since mixing occurs only in the flowing layer, mixing is considered in terms of "passes" defined as the number of times the material in the bed entirely flows through the layer. Experimental results indicate that the mixing per pass decreases with increasing rotational speed, increases with increasing particle size, and is nearly independent of cylinder size. The mixed state captured by digital photography and the measured radial concentration profiles are well described by a convective diffusion model, using diffusivity as a fitting parameter. The diffusivity obtained from the model follows the scaling proposed by Savage ["Disorder, diffusion, and structure formation in granular flow," Disorder and Granular Media, edited by A. Hansen and D. Bideau (Elsevier, Amsterdam, 1993), pp. 255-285] and a simple expression for the diffusivity is obtained in terms of the particle diameter and the static and dynamic angles of repose. (C) 2005

The rheology of a granular shear flow is studied in a quasi-2d rotating cylinder. Measurements are carried out near the midpoint along the length of the surface flowing layer where the flow is steady and non-accelerating. Streakline photography and image analysis are used to obtain particle velocities and positions. Different particle sizes and rotational speeds are considered. We find a sharp transition in the apparent viscosity ($\eta$) variation with rms velocity ($u$). In the fluid-like region above the depth corresponding to the transition point (higher rms velocities) there is a rapid increase in viscosity with decreasing rms velocity. Below the transition depth we find $\eta \propto u^{-1.5}$ for all the different cases studied and the material approaches an amorphous solid-like state deep in the layer. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The observed transition appears to be analogous to a glass transition., Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett

We study the statistical properties of population dynamics in 2d turbulent and compressible surface flows. We show that the compressible surface flow leads to a patchiness in the population density that resembles the patchiness of the Plankton population as observed from the satellite images of the ocean surface. The statistical properties of the population concentration are investigated and quantified for different growth rates, diffusivities and for different level of compressibility of the surface flow.

Optimum bitki gelişiminde sulamanın, ayrılmaz bir parçası olan drenaj, yağış miktarının çok, toprak geçirgenliğinin düşük ve boşaltma ağzının yetersiz olduğu tarım alanlarında önem kazanmaktadır. Bu çalışmada, Uludağ Üniversitesi Tarımsal Araştırma ve Uygulama Merkezi Arazisinin drenaj sorunları belirlenmeye çalışılmış, çözüm önerilerinde bulunulmuş ve yüzey drenaj sistemi projelenmiştir. İnceleme alanında KATKAT ve Ark. (1984) tarafından yapılan toprak etüdleri sonucunda 4 farklı toprak grubu bulunmuştur. Bunlar Vertisol, Rendzina, Kahverengi orman ve Aluviyal grubu topraklardır. Bu toprakların büyük bir çoğunluğu Vertisol ve Rendzina grubu topraklardır. Yapılan denemelerde, kanal kapasitesinin hesabında gerekli olan yüzey akışın belirlenmesi için TÜLÜCÜ(1987) 'de esasları belirtilen McMath metodu kullanılmıştır. Hidrolik iletkenlik ölçümleri ise 0?UZER(1981)'de esasları belirtilen Ters Kuyu metoduna göre yapılmıştır. Araştırma ile belirlenen sorunları gidermeye yönelik öneriler; elde edilen veriler ve ilgisi kaynaklar ışığında aşağıdaki biçimde sıralanabilir. 1. İnceleme alanının topoğrafik durumu, çıkış ağzı, mevcut dere ve doğal hendeklerin durumu, arazinin eğimi ve toprak yapısı gözönüne alındığında düşen yağışlar, alanın güney ve kuzey-batı bölgelerinde yüzey su birikintilerine neden olmaktadır. Drenaj sorunu bulunan eğimi %l-5 arasındaki alanlarda yüzey drenaj kanalları açılmalıdır. 2. İnceleme alanının kuzeyinden geçen Nilüfer Çayı, boşaltma ağzı görevini yapmaktadır. Boşaltma ağzının kapasitesini etkileyen faktörler yağışlar ve yağışlardan akışa geçen yüzey akış miktarıdır. Boşaltma ağzı kapasitesi 10 yıl tekerrürlü 1.19 saat süreli en büyük yağış değerine göre-66- 6.4 m3 /s olmalıdır. 3. Haftalık yapılan taban suyu düzeyi ölçüm sonuçlarına göre, alana düşen yağışlar dikkate alındığında sorunun yağışlardan kaynaklandığı belirlenmiştir. 4. Hidrolojik etüdleri sonucunda alana yıllık 713.1 mm düşen yağışın % 39. 2 'si kış aylarında düşmektedir. Alanın düz ve düze yakın bölgelerinde kış yağışları, toprak geçirgenliğinin çok düşük olması nedeniyle yüzey su birikintilerine neden olmaktadır. 5. Kanal kapasitelerini belirlemek amacıyla derelerin yüzey akış kapasiteleri hesaplanmıştır. Ayıcı Pınar Deresi yüzey akış debisi 1.2 m3 /s, Ayıcı Dere yüzey akış debisi 1.32 m3 /s ve Görükle Deresi yüzey akış debisi ise 6.4 m3 /s bulunmuştur. 6. Drenaj sularının analiz sonuçlarına göre, drenaj suyunun tekrar sulamada kullanılması mümkün görünmektedir. Bu nedenle Ayıcı Dere üzerinde bir gölet yapımı uygun olacaktır. 7. Görükle Deresine paralel biçimde uzanan dar ve uzun bir şeritte oluşan ıslaklık ve yüksek taban suyu seviyesinin önlenebilmesi için Görükle Deresine dökülen dere ve doğal hendekler ıslah edilmelidir. 8. Ortalama eğimin % 3 dolaylarında olduğu Görükle yolu ile işletme binaları arasındaki alana tesviye eğrilerine paralel yüzey drenaj kanalları açılmalıdır. 9. İnceleme alanının sıralanan sorunlarını çözmeye yardımcı olmak üzere elde edilen verilerin ışığında bir yüzey drenaj planlaması yapılmış ve Ek 1' ve Ek 2' de verilmiştir. Projenin uygulamaya konulması durumunda sorunların büyük oranda çözülmesi mümkün olacaktır.ALAGÖZ, H., 1967. Kurutma ve Drenaj, E.Ü. Zir. Fak. Yayınları, No: 123, Ankara. AKALAN, t., 1983. Toprak ve Su Muhafazası, A.Ü. Zir. Fak. Yayınları, No: 873, Ankara. ANONYMOUS, 1974. Ortalama ve Ekstrem Kıymetler Meteoroloji Bülteni, Başbakanlık Basımevi, Ankara ANONYMOUS, 1978. Türkiye Arazi Varlığı, TOPRAKSU Genel Müdürlüğü Yayınları, Ankara. ANONYMOUS, 1983. Bursa tli Verimlilik Envanteri ve Gübre İhtiyaç Raporu, Köy İşleri ve Kooperatifler Bakanlığı TOPRAKSU Genel Müdürlüğü Yayınları, No: 724, Ankara. ANONYMOUS, 1987. Köy Hizmetleri Genel Müdürlüğü APK Dairesi Başkanlığı, Toprak ve Su Kaynakları Araştırma Şube Müdürlüğü, Yayın No: 57, Ankara. ANONYMOUS. 1989. tiden İle Tarım Bursa, TOK Dergisi Sayı: 41 s. 41-43. ARICI, i., 1988. örtü malzemelerinin Dik Eğimli Şevlerde Erozyon ve Bitki örtüsü Oluşumuna Etkisi Üzerine Bir Araştırma, U.Ü. Zir. Fak. Yayınları No: 7-015-0175, Bursa. AVCI, K., 1986. Bafra Ovası Kapalı Drenaj Projeleme Kriterleri, T.C. Tarım Orman ve Köy İşleri Bakanlığı Köy Hizmetleri Genel Müdürlüğü Köy Hizmetleri Samsun Araştırma Enstitüsü Müdürlüğü Yayınları, No: 40, Samsun. AYDENtZ, A., 1976. İklim Verimlilik İlişkileri, Topraksu Teknik Dergisi, Sayı: 44, Ankara. AYYILDIZ, M., 1983a. Sulama Suyu Kalitesi ve Tuzluluk Problemleri, A.Ü. Zir. Fak. Yayınları, No: 879, Ankara. ABSTRACT In this study, the drainage problems of university of Uludağ, Agricultural Research and Practice Centre field were determined. The main problems encountered in the study area were high amount of rainfall, low permeability in soil and inadequate capacity of streamlet and natural ditches. These problematic conditions causes inadequate drainage in flat and semi-flat areas. In this study, proposals were introduced for the solution of these problems and surface drainage capacities were calculated and canal sections were designed. KEY WORDS : Surface drainage, surface flows, water table, hydraulic permeability, hydrologic research, topographic research, discharging point 70

Based on the results of Aerogamma spectrometric examination of morphological and geological-structural analysis, for explore the content of natural radionuclides in groundwater and surface water, the basin of Vranje area (Southern Serbia) was selected. On the area of 500 km2, the samples were collected from springs, wells, boreholes and surface flows. The water contents were determined by U, 226Ra, 222Rn, gases (O2, CO2, H2O), anion-cation composition, trace elements, pH value, Eh, Ec, water hardness and mineralization. Data analysis was performed according to the geology, in volcanoclastic sedimentary and metamorphic complex of the area of Vranjska Spa-Leskovac. In the area of Vranje Spa anomalous uranium content in groundwater and surface water, and mineralization in the volcanoclastic sediments have been identified. The warmest water source in borehole with temperature of 91-93 ºC is located in the area of Vranje Spa. The research results will be shown with tables and geochemical map 1: 50000.