La presente ricerca è volta a indagare le proprietà idrotermodinamiche dei laghi alpini, con particolare riferimento al caso del lago di Tovel (Trentino, Italia). Tale lago era noto a livello internazionale a causa di unospettacolare fenomeno di arrossamento che si verificava ogni anno fino al 1964, quando il fenomeno è improvvisamente cessato. Parte del presente lavoro è stato sviluppato nell'ambito del progetto di ricerca "SALTO" finanziato dalla "Provincia Autonoma di Trento", orientato allo studio dei diversi aspetti ecologici, biologici e fisici del lago, insieme al suo sviluppo storico. La presente tesi è divisa in tre parti. Nella prima parte si riassumono i processi fondamentali che caratterizzano l' idrotermodinamica dei laghi e di tutti quei specifici aspetti che sono poi stati indagati anche sperimentalmente. Nella seconda parte si riporta una dettagliata descrizione della campagna di misure effettuata nel 2003 sul lago di Tovel. In particolare vengono illustrate le tecniche sperimentali e le procedure di post-processing dei dati. L'analisi dei dati di temperatura misurati dalle catene di termistori e dei dati di velocità raccolti attraverso profilatori e correntometri fornisce un significativo contributo alla comprensione delle principali circolazioni che possono svilupparsi nel lago. La terza parte è dedicata alla modellazione numerica: vengono riportati i risultati di un 1-D modello verticale e un modello 3-D. Il primo modello (DYRESM), sviluppato in Western Australia University, è stato utilizzato per studiare l'evoluzione stagionale del lago mentre il secondo modello 3-D è stato specificamente sviluppato nel quadro di questo progetto per studiare il comportamento idrodinamica su scala temporale breve. I risultati della simulazione mostrano notevole accordo con i dati della campagna di misura. [ENGLISH ABSTRACT] The present research is aimed at investigating the hydrothermodynamic properties of small alpine lakes, with specific reference to the case of lake Tovel (Trentino, Italy). The lake was subject to a spectacular reddening which had been occurring each year until 1964, when the phenomenon suddenly ceased. The work has been developed within the framework of the multidisciplinary research project "SALTO", funded by "Provincia Autonoma di Trento" which is oriented to the study of different ecological, biological and physical aspects of lake Tovel, along with his historical development. The present thesis is divided in three parts. In the first part we summarize the fundamental processes which characterize the physical limnology, which specific reference to those aspects that we have also investigated through field easurements. In the second part a detailed report is given on the procedures and results of the field campaign performed during the year 2003 on lake Tovel. In particular, the experimental techniques are illustrated along with the data post-processing procedures. The temperature data measured by thermistor chains and velocity data collected through current meter and profiler are then analysed to provide a quantitative estimate of the main circulations that may develop within the lake, due to different meteorological conditions. Finally, the third part is devoted to numerical modelling. Results of a 1-D vertical model and of a 3-D model are discussed. The former model (DYRESM), developed in Western Australia University, has been used to study the seasonal evolution of the lake; the latter has been specifically developed in the framework of this project to investigate the hydrodynamic behaviour of small lakes on short time scale.

Alpine rivers have been regulated to claim productive land in valley bottoms since the last two centuries. Width reduction and rectification often induced the development of regular scour-deposition sequences, called alternate bars, with implications for flood protection, river navigation, environmental integrity. Understanding how alternate bars evolves in rivers and defining the key aspects that influence the development of these regular deposits of sediments represents a challenge that is not fully described. Most studies on alternate bars are in fact based on mathematical theories, laboratory experiments and recently numerical simulations, but only few studies on field cases have been performed so far. The goals of this work are: i) to quantify the morphodynamics of alternate bars in the Alpine Rhine River, with a particular emphasis on bar migration; ii) to assess to what extent the predictions of analytical bar theories are consistent with field observations and to explore how theories may help interpret observed alternate bars dynamics; iii) to determine the ability of a numerical model to simulate correctly the formation and the length scale of alternate bars and influence of different multi-decadal inflow conditions. The 42-km chosen reach is located along the border between Austria and Switzerland, between the confluences of Landquart and Ill rivers. The whole reach has been completely embanked starting from the 19th century, so alternate bars are present for more than a century. Moreover the simplification of the cross section, together with the presence of only few bends, puts the Alpine Rhine in the ideal position to be compared with analytical theories of alternate bars in straight channels. The goals are achieved by analyzing a dataset of freely available Landsat imagery, which combine unprecedented temporal length (3 decades), spatial length (more than 400 channel widths) and temporal resolution (around 3 images per year). Bars show a spatially selective behavior, with short, bars occurring in distinct straight reaches with respect to longer bars. The same evidence is found in terms of bar migration, so that short bars are shown to migrate more than longer bars, in agreement with theoretical predictions. A full range of bar wavelengths and more complex patterns occur in reaches with bends and ramps. Bar height, obtained from cross section monitoring, was found to be much more uniform. The temporally long dataset, including approximately 30 floods with different magnitude and duration, allowed the investigation of bar migration as a function of discharge, showing that bars migrate faster for intermediate foods. Predicted values of linear theories for free and forced bars in straight channels are in good general agreement with field observations, when considering conditions of bar formation and bar wavelength. Comparing theories and observations suggests that theoretical outcomes may represent the boundaries of the actual, wide range of bars’ behaviour, which likely reflects non-linear interactions, flow unsteadiness, sediment size hetero- geneity and finite length of straight reaches, which are not retained in linear theories. Non-linear interactions are investigated through the 2D numerical morphodynamic model Basement, developed at the Swiss Federal Institute of Technology of Zurich. Preliminary investigations focus on the role of the transversal sediment transport, that behaves as a diffusive term. The numerical diffusion can be indirectly evaluated starting from the calibration of the coefficient of the diffusive term and a benchmark methodology to evaluate the lateral and numerical diffusion is defined. The results are used in the morphological calibration of the model. The spatial trend of wavelengths is in general agreement with the field data, and the migration take place mainly in correspondence of short bars, while long bars tend to elongate with time. The choice of a constant discharge or a real hydrograph influences the time scale of bar evolution. The present analysis results in the longest spatial and temporal field case study of river bars in channelized rivers with a temporal survey resolution that allows the investigation of the effect of individual flood events, and provides new quantitative data on bar wavelength and migration. The dataset provides useful information to assess the applicability of analytical bar theories, so far mainly tested against flume experiments, and following recent attempts in French and Dutch streams. Moreover, a novel two-dimensional morphological benchmark to access the role of numerical diffusion is proposed. The new insights are crucial to design future management scenarios accounting for hydraulic safety and environmental quality.

Alpine rivers have been regulated to claim productive land in valley bottoms since the last two centuries. Width reduction and rectification often induced the development of regular scour-deposition sequences, called alternate bars, with implications for flood protection, river navigation, environmental integrity. Understanding how alternate bars evolve in rivers and defining the key aspects that influence the development of these regular deposits of sediments represents a challenge that is not fully described. Most studies on alternate bars are in fact based on mathematical theories, laboratory experiments and since 1990s numerical simulations, but only few studies on field cases have been performed so far. The goals of this work are: i) to quantify the morphodynamics of alternate bars in the Alpine Rhine River, with a particular emphasis on bar migration; ii) to assess to what extent the predictions of analytical bar theories are consistent with field observations and to explore how theories may help interpret observed alternate bars dynamics; iii) to determine the ability of a numerical model to simulate correctly the formation and the length scale of alternate bars and the influence of different multi-decadal inflow conditions. The 42 km chosen reach is located along the border between Austria and Switzerland, between the confluences of Landquart and Ill rivers. The whole reach has been completely embanked starting from the 19th century, so alternate bars have been present for more than a century. Moreover the simplification of the cross section, together with the presence of only few bends, puts the Alpine Rhine in the ideal position to be compared with analytical theories of alternate bars in straight channels. The goals are achieved by analyzing a dataset of freely available Landsat imagery, which combine unprecedented temporal length (3 decades), spatial length (more than 400 channel widths) and temporal resolution (around 3 images per year). Bars show a spatially selective behavior, with short bars occurring in distinct straight reaches with respect to longer bars. The same evidence is found in terms of bar migration, so that short bars are shown to migrate more than longer bars, in agreement with theoretical predictions. A full range of bar wavelengths and more complex patterns occur in reaches with bends and ramps. Bar height, obtained from cross section monitoring, was found to be much more uniform. The temporally long dataset, including approximately 30 floods with different magnitude and duration, allowed the investigation of bar migration as a function of discharge, showing that bars migrate faster for intermediate floods. Predicted values of linear theories for free and forced bars in straight channels are in good general agreement with field observations, when considering conditions of bar formation and bar wavelength. Comparing theories and observations suggests that theoretical outcomes may represent the boundaries of the actual, wide range of bar behavior, which likely reflects non-linear interactions, flow unsteadiness, sediment size heterogeneity and finite length of straight reaches, which are not retained in linear theories. Non-linear interactions are investigated through the 2D numerical morphodynamic model Basement, developed at the Swiss Federal Institute of Technology of Zurich. Preliminary investigations focus on the role of the transverse sediment transport, that behaves as a diffusive term. The numerical diffusion can be indirectly evaluated starting from the calibration of the coefficient of the diffusive term. A benchmark methodology to evaluate the lateral and numerical diffusion is defined. The results are used in the morphological calibration of the model. The spatial trend of wavelengths is in general agreement with the field data, and the migration takes place mainly in correspondence to short bars, whereas long bars tend to elongate with time. The choice of a constant discharge or a real hydrograph influences the time scale of bar evolution. The present analysis results in the longest spatial and temporal field case study of river bars in channelized rivers with a temporal survey resolution that allows the investigation of the effect of individual flood events, and provides new quantitative data on bar wavelength and migration. The dataset provides useful information to assess the applicability of analytical bar theories, so far mainly tested against flume experiments, and following recent attempts in French and Dutch streams. Moreover, a novel two-dimensional morphological benchmark to access the role of numerical diffusion is proposed.

The presence of aquatic vegetation on riverbed and embankments influences flow structure and consequently flow resistance, sediment transport, morphology, and ecology. These influences would lead to a hydraulic diversity, which is a key ingredient of physical habitat in streams. According to this fact, vegetation is commonly incorporated within stream restoration. Although significance of vegetation as an inseparable part of riverine systems is recognized, but yet it is still difficult to predict how the associated influences will respond to the introduction of vegetation and how advantages of vegetation can be optimized to a multitude of different processes. The primary impact of vegetation is slower flow velocity and thus, reduction in conveyance capacity. In addition to affecting the velocity profile over the full depth, vegetation affects turbulence intensity and diffusion. When mean kinetic energy converts to turbulent kinetic energy within the area planted with stems, turbulence intensity will begin to intensify. As a result of velocity and turbulence changes, aquatic vegetation can affect sediment movement and consequently bed form shapes could be stabilized with new patterns. Bed form characteristics (length, shape, structure, dimensions, stability, etc.) also depend on flow structure and can be divided into different categories according to the bed load materials. Locations and extension of vegetation in river channels is a fundamental factor should be considered besides the general impacts of vegetation in rivers. Isolated patches of vegetation are more common in practical applications rather than uniform vegetated channels in which the mean properties of the vegetation canopy are independent of the location. The present study considered the changes in bed forms through semi-circular patches of emergent vegetation, which are located at the banks of the channel. One of the goals is to find out how an island of vegetation modifies the morphology of rivers and mass transport. In particular, this research focuses on the physics of sediment transport and its effect on bed forms, and flow resistance in the presence of a patch of vegetation, by using experimental data and numerical modeling. Providing a physically based model for estimating the effects of vegetation on flow parameters, turbulence dispersion, and sediment transportation, the results of the present study contribute to extending the knowledge of morphology and mass transport in vegetated streams.

Reservoir sediment flushing is increasingly considered beneficial to reduce sedimentation of reservoirs and maintain sediment supply downstream of impounded rivers. Nevertheless, flushing of the accumulated sediments downstream of the dam also bears numerous negative impacts. In this study, first the most important downstream impacts of fine sediment releases of flushing were identified based on previously published research of twenty case studies in eleven countries. The results showed that the long-term as well as short term biological and physical impacts decreased with distance from the dam. The temporal scale of impacts on macro-invertebrates could span from few weeks or a month to several months while the effect on fish could last for a number of years. The impacts on downstream vegetation dynamics is driven by many years of flushing activities. The study also enabled proposing generic management strategies aimed to reduce the impacts. Second, fine sediment transport in coarse immobile bed, which is a common phenomenon downstream of dams during flushing releases, dam removal and also in many mountain and canyon rivers, was investigated. Particularly, the dynamics of the downstream erosion and transport of fine sediments released during sediment flushing was investigated based on a series of flume experiments that were carried out in immobile gravel bed and using a one-dimensional (1-D) suspended sediment transport model developed in the present study. In the framework of the flume experiment, firstly gravel bed roughness, porosity and roughness density were exclusively extracted from gravel surface elevation data in which developing a spatial filter to overcome elevation errors was carried out. Secondly a new technique to acquire fine sediment erosion in immobile coarse bed in running water condition was developed. The method proved to be the back bone of all fine sediment erosion experiments conducted in the present study and could be used for similar studies. This study presents a first work of direct measurement of erosion rate and characterizing its spatial heterogeneity in gravel bed. The experimental data of erosion rate of fine sediments showed that it varied spatially with high erosion rate on the stoss side of gravels and less on the lee side conforming to sweeps and ejections characteristics in coherent flow structure of gravel bed flows. Erosion rate was significantly affected by increase in roughness of immobile gravel bed with high erosion rate noticed when sand level was reduced although the effect on stream-wise velocity was not significant. The vertical profile of erosion rate was found to decrease linearly and showed an exponential decay in time in the gravel matrix. Third, a new non-equilibrium erosion rate relation is proposed. Drag force profile in the interfacial sublayer of clean gravel bed was found to be scaled well with roughness density and allowed predicting the effective shear stress distribution available for fine sediment entrainment with an empirical equation. The new relation is a modified version of the pick-up rate function of van Rijn (1984b) in which the predicted shear stress in the roughness layer was implemented. The most important finding was that if the shear stress distribution in the interfacial sublayer is predicted, a relation for sand bed condition can be applied to predict fine sediment erosion rate in immobile gravel bed. This approach is conceptually superior to previous approaches where erosion rate in sand bed condition was scaled empirically for various fine sediment bed level within the interfacial sublayer. Finally, the effect of the interaction between hydrodynamic and sediment wave dynamics of sediment flushing on spatial pattern of sediment deposition was investigated. The 1-D model was developed to include major processes observed in sediment flushing: sediment wave celerity correction, variable bed roughness, bed exchange in immobile bed, hindered settling velocity and rough bed porosity. The proposed erosion rate relation showed encouraging results when implemented in the 1-D model. The wave celerity factor did not show significant effect on the spatial lag in immobile bed condition although was significant in sand bed condition. Variable bed roughness modified both the flow field and sediment deposition in which larger length of sediment deposit was noted. The immobile bed porosity allowed modelling clogged depth of fine sediments. The model was also found to be very valuable to investigate flushing scenarios that reduce significant deposition through the analysis of the dependence of deposition on peak-to-base flow and intermittence of releases. The highest peak-to-base flows produced the longest and thickest region of deposition while those with the lowest ratio produced the shortest and thinnest. A single flushing release followed by clear water release reduced area or length of sediment deposition more than intermittent flushing followed by inter- and post-flushing clear water releases. In the latter case, the peak of concentration reduced but remained higher for longer duration than the former, which suggests that a large quantity of clear water release has to be available. Overall, the present research represents a step forward in understanding relevant processes involved in the downstream transport of fine sediments released during sediment flushing and the associated impacts that can help the development of better management strategies and predictive tools.

The present study deals with the morphodynamics of rivers and estuaries. The morphodynamic behaviour of natural systems has been investigated using numerical tools. As a first step the hydrodynamics and morphodynamics of both convergent and non-convergent tidal channels have been studied. The analysis has been made using a second order numerical scheme, solving the 1D flow equations and the continuity equation for the bed evolution in order to point out the main characteristics of the phenomenon. Numerical results show that the behaviour is non-linear also for relatively small values of the ratio between tidal amplitude and mean flow depth. The morphodynamic behaviour of tidal dominated estuaries is characterised by the formation of a rising landward bed profile. This trend is due to the flood dominated character of the convergent estuaries with horizontal bed profile, which induces a landward net sediment flux. Due to this sediment flux the channel is filled in with sediment and a beach can form, whose position depends on the geometrical characteristics (channel length, flow depth, convergence degree) and on the hydrodynamic characteristic (tidal amplitude, friction factor). The equilibrium conditions are characterised by symmetrical flood and ebb phases. The second step is the developments of a three-dimensional numerical model for the comprehension of the altimetric behaviour of almost straight channels. Bed forms can form spontaneously starting from a configuration with a plane bed profile. The research activity concerns in particular the geometrical characterisation of the bed forms: wavelength, Fourier composition, mean celerity, maximum scour and deposition and the time scale of the formation phenomenon. The investigation is oriented to the characterisation of the equilibrium geometry, to the description of the dynamical behaviour, of the flow field and of the concentration field. This goal has been obtained using a fully non-linear 3D numerical model, which takes into account sediment transported as bed load and the suspended load. The numerical scheme is that proposed by Casulli & Cattani (1994) suitably modified for this particular problem; the advection-diffusion equation for the sediments transported into suspension , is solved using an original semi-analytical conservative scheme. Results are in agreement with those obtained through analytical linearized theories (see Tubino et al., 1999 for a review). Numerical results suggest that in fine sediment channels, when the suspended load is dominant over the bed load, the instability process is different with respect to the gravel bed case. When suspended load is dominant the model predicts the tendency of free bars to emerge from the free surface, forming islands. A similar behaviour is observed also in gravel bed rivers at relatively high value of the width to depth ratio, while under suspended load dominated conditions the maximum deposits are relatively large also for values of the aspect ratio close to the threshold for bar formation. Finally the analysis and the results for the formation of alternate bars in uniform flow have been extended to the tidal context, adopting a suitable basic flow. In the tidal case the bed forms show vanishing celerity, therefore the altimetric and the planimetric morphological responses might interact. Numerical simulation under tidal conditions are very long until a month of computational time, because the time step for the computation must be mush shorter respect to the tidal period. Therefore we have looked for a suitable 2D approximate formulation for the suspended flux, in order to reduce the number of computational nodes and so also the computational time. In the literature there are many approaches for the evaluation the suspended load through analytical perturbative methods. Here a comparison has been made between the numerical solution and an analytical solution, showing that the latter can be applied for a range of the parameters relatively small.

The present study deals with air pollution modelling over complex topography, both from the phenomenological and numerical point of view. The theme of air pollution modelling has been faced at first from a phenomenological point of view. Then a numerical approach for the resolution of the diffusion-advection equation has been followed. Two different methods have been explored: puff-models and lagrangian particle models. The eulero-lagrangian puff-model CALPUFF (released by Earth Tech) has been used as a reference: closures and parametrizations adopted by this software have been tested over complex terrain and some minor changes have been introduced into the original code. A further step was the development of a lagrangian particle-tracking program, suitable for not homogenous not stationary flows, and also adapted to complex terrain cases, accounting for vertical skewed turrbulence in any atmospheric stability class. Langevin equation were solved following Thomson's (1987) approach. Special attention was put on near field dispersion processes. In fact, lagrangian models turn out to be the most advanced numerical schemes for pollutant transport simulations but at now only suitable for short term simulations, at least in complex errain where high spatial resolution is needed. An extension for the lagrangian model has been then developed, using the so called "kernel method"; this feature improves considerably the calculation performance, dramatically reducing computation time, so that simulations also become praticable for longer temporal scales; nevertheless it seems the kernel method seems to lead to unreliable results for narrow valleys or very steep slopes, so results cannot be generalized. Moreover, the problem of the determination of vertical profiles of turbulent diffusivity on complex orography has been faced. Both a local approach and a global one (suitable for compact valleys) for the estimate of eddy diffusivity in valley have been investigated. The first one has been adopted in the lagrangian problem previously developed. Since atmospheric turbulence is mostly generated by solar thermal flux, a procedure for the calculation of the effective solar radiation was developed. The method, which can be introduced into meteorological models which use complex orography as input, takes into account for shadowed areas, soil coverage and the possible precense of clouds which filter and reduce the incoming solar radiation. Tests have been carried out using a modified version of model CALMET (EarthTech Inc.). Results are in agreement with turbulence data acquired by means of a sonic anemometer during a field campain performed by the Department. Finally, the analysis of near field dispersion over complex terrain has been extended to the urban context, adopting, basically, the same conceptual tools on a smaller scale. A finite volume three-dimensional numerical model has been developed and tested in simulating dispersion of traffic derived pollutants in the town of Trento. For ground level sources geometry of the domain and emission condition turn out to be very important with respect to meteorological conditions (especially atmospheric stability). The roughness, i.e. the buildings of the study area has been therefore explicitely considered, using a high resolution deigital elevation map of the urban area. This approach has turned out to be necessary for near field dispersion, when the emission source is located inside the roughness and the impact area entirely fall inside the near field. Here a comparison has been made between the predicted numerical solution and data measured by air quality stations which are present in the urban area, showing a good agreement. A further refinement of the study has lead to the development of a two-dimensional x-z lagrangian model at the "street scale", for the study of canyon effects which tends to trap pollutant inside an urban canyon with behaviours which typically depends on geometric features, atmospheric turbulence and wind speed.

The gravitational granular flows (e.g. debris flows or snow avalanches) are catastrophic and destructive phenomena affecting many areas in the world, and especially the mountain areas of Europe. Proper design criteria are required in order to improve protection structures and prevention strategies. Due to their complex nature, these phenomena present many aspects still unsolved in the research field. This research addresses some aspects of the mechanics of dry granular flows: a 1D depth integrated model has been developed, based on a two phase approach. The system of equations consists of three partial differential equations, derived from the mass balances for the solid and fluid phase and from the momentum balance for the solid phase, and two rheological relations determined through experimental tests and particle numerical simulations. The experimental investigation hes been conducted in a laboratory channel, by recording through high speed cameras the motion of polystyrene spherical particles. Within this research, it has been developed an ad hoc optical method to analyze and process the images recorded, with the aim of defining the main flow characteristics. From a numerical point of view, a path conservative finite volume scheme has been adopted to solve the system of equations previously described: the numerical solution is compared to the experimental results for different configurations, in order to verify the effectiveness of the mode

The vegetation is an important factor of quality of the river ecosystem, given its capability to contribute to the chemical, biological and physical quality of water. On the other hand, the presence of vegetation in riverbed modifies flow structure, flow resistance, sediment transport and morphology. Each single modification has been largely studied, but the knowledge on the mutual relationships are still limited. This project faces a part of these still-unknown aspects by considering the case of rigid and emergent vegetation and the relationships with sediment transport, flow field, flow resistance and bed forms at small scale. The thesis is based on experimental approach coupled with theoretical analysis. In particular, the research contributes with a rational approach (ballistic approach) to the formulation of sediment transport capacity of a vegetated riverbed as a function of hydrodynamic conditions, types of sediments, dimension and distribution of plants. The validity of the ballistic approach is proved by the comparison with a large number of experimental results obtained in a laboratory channel, in which the vegetation was modeled with cylindrical and rigid elements. The experimental results were carried out for different flow conditions, arrangement of cylinders and cylinder dimensions. For the tests, three different sediments were used, at different densities and grain sizes. The comparison allows the determination of some empirical parameters related with the velocity of movement of particles, characteristics of sediments and plants incumbrance. A partially rational approach for the determination of the empirical parameters comes from the analysis of the flow field through the cylinders. The experimental data highlight bed areas in which the contribution to the sediment discharge is smaller, and bed areas in which is larger, with respect to an unvegetated riverbed at the same flow conditions. The flow field analysis shows also the physical mechanisms which rule the formation of bed forms induced by plants. Height and length of vegetation bed forms are measured and related with the density of vegetation, with the plant diameters and with the average distance between the cylinders interaxis. In particular, the experimental data show the linearity between length of bed forms and average distance between stems. Finally, measurements of the drag force exerted by the cylinders to the flow were carried out by means a load cell fixed to the cylinders in staggered configuration. The measurements were done in a channel with fixed bed, both plane and with bed forms. The experimental measurements of drag show that the drag coefficient depends on the density of vegetation and on the presence of bed forms. This dependence is confirmed by comparing the indirect measurements of the drag coefficient with the measurements done with the load cell and fixed bed. The indirect measurements were done in the flume with mobile bed and sediment transport, for both the staggered and random distribution of cylinders. The direct measurements in the different experimental setup and the comparison between direct and indirect measurements put in evidence that the vegetation bed forms give a contribution to global resistance that, in particular cases, is comparable with the contribution due to the rigid stems, demonstrating that to consider negligible their effect can be sometimes a rough approximation.

In the mountain territory the majority of the population and of the productive activities are concentrated in the proximity of torrents or over alluvial fans. Here, when intense rainfall occurs, debris flow or hyper-concentrated flow events can produce serious problems to the population with possible casualties. On the other hand, the majority of these problems could be overcome with accurate hazard mapping, disaster prevention planning and mitigation structures (e.g. silt check dams, paved channels, weirs ...). Good and reliable mathematical and numerical models, able to accurately describe these phenomena are therefore necessary. Debris flows and hyper-concentrated flows can be adequately represented by means of a mixture of a fluid (usually water) and a solid phase (granular sediment, e.g. sand, gravel ...), flowing over complex and composite topography. Complex topography is related to complicated bed elevation variety inasmuch as there are slopes, channels, human artifacts and so on. On the other hand, topography is composite because every type of flow can encounter two different bed behaviors: the mobile bed and the fixed bed. In the first case, mass can be exchanged between the bed and the flow, so the bottom elevation can change in time. In the second case (fixed bed case), this mass transfer is inhibited, due to the presence of a rigid bottom, such as bedrock or concrete, and the bottom cannot change in time. The first objective of the work presented in this thesis concerns the development of a new type of hyperbolic mathematical model for free-surface two-phase hyper-concentrated flows able to describe in a single way the fixed bed, the mobile bed and also the transition between them. The second objective, strictly connected with the first, is the development of a numerical scheme that implements this mathematical model in an accurate and efficient way. In the framework of finite-volume methods with Godunov approach, the fluxes are evaluated solving a Riemann Problem (RP). A RP is an initial value problem related to a set of PDEs equations wherein, in a certain point, there is a discontinuity separating different left and right initial constant states. However, if the topography is composite, a new type of Riemann problem, called Composite Riemann Problem (CRP), occurs. In a CRP, not only the initial constant states, but also the relevant PDEs systems change across the discontinuity. This additional complexity makes the general solution of the CRP quite challenging to obtain. The first part of the work is devoted to the derivation of the PDEs systems describing the fixed- and mobile-bed behaviors. Starting from the 3D discrete equations valid for each phase (continuous fluid and solid granular) and using suitable average processes the 3D continuous equations (continuous fluid and solid) are obtained. Introducing the shallow water approximation and performing the depth average process, the 2D fully two-phase models for free-surface flow over fixed- and mobile-bed are derived. The isokinetic approximation, which states the equality between the velocity of the solid phase and the liquid phase, is then used, ending up with the so-called two-phase isokinetic models. Finally, an exhaustive comparison between the fixed- and the mobile-bed fully two-phase models, the two-phase isokinetic models and others models proposed in the literature is presented. The second part of the work concerns the definition and, mainly, the solution of the CRP from a mathematical point of view. Firstly, a general strategy for the CRP solution is developed. It allows to couple different hyperbolic systems that are physically compatible (e.g. fixed-bed with mobile-bed systems, free-surface flow with pressurized flow), also if they have a different number of equations. The resulting CRP solution is composed of a single PDEs system, called Composite PDEs system, whose properties, under some assumptions, degenerate to the properties of the original PDEs systems. The general strategy is developed using the simplest 1D isokinetic models for the fixed bed and the mobile bed (i.e. PDEs systems valid only for low concentration). Coherently with the generality of the CRP solution method, the low concentration constraint is then relaxed, ending up with a Composite PDEs system describing also high concentrated flows. From the numerical point of view, all the developed Composite systems are integrated using the finite-volume method with Godunov fluxes. These fluxes are evaluated using three different approximated Riemann solvers: the Generalized Roe solver, the LHLL solver and the Universal Osher solver. All the solvers are analyzed and an exhaustive comparison between them is performed, highlighting pros and cons. The schemes are second order accurate in space and time, and this has been achieved by means of the MUSCL approach. Finally numerical schemes have been parallelized using OpenMP standard. All the models are then tested comparing analytical and numerical solutions. The results are satisfactory, with an accurate agreement between the two solutions in the majority of the physically-based test cases. There is only some small issue when the simulations are performed in a few resonant cases. However, these problems arise in not realistic situations, so it is impossible to encounter them in real situations. Also a realistic application is presented (i.e. the evolution of a trench over partially paved channel), proving the capabilities of both the mathematical approach and the numerical scheme.