Flow separation and reattachment happens in many fluid mechanical situations occurring in engineering applications as well as in nature. The flow over a backward-facing step represents a geometrically simple flow situation exhibiting both flow separation and reattachment. Broadly speaking there are only two important parameters in the problem, the Reynolds number(Re) based on the step height(h),and a geometrical parameter, referred to as the Expansion ratio(ER), defined as the downstream channel height to the upstream channel height. In spite of the relative simplicity of this geometry, the flow downstream is quite complex. The main focus of the present work is to elucidate the unsteady three-dimensional coherent structures present in this flow at large Re, Re>36,000,based on the step height(h). For this, we use velocity field measurements from Particle Image Velocimetry (PIV)in conjunction with hotwire anemometry measurements. The time-averaged structure of this flow is first studied in detail, including the effect of Reynolds number(Re) and Expansion Ratio(ER), on it. These studies show that at sufficiently large Re (Re>20,000), the reattachment length becomes independent of Re. The detailed internal structure of the separation bubble is also found to be independent of Re, but for Revalues that are relatively larger(Re>36,000). At large Re, the main effect of ER ,is found to be on the reattachment length, which increases with ER and saturates for ER values greater than about 1.8. The detailed internal structure of the separation bubble has been mapped at high Re and is found to be nearly the same for all ER, when the streamwise length is normalized by the reattachment length. In order to elucidate the unsteady coherent vortical structures, PIV measurements are done in two orthogonal planes downstream of the backward-facing step. These measurements are done for ER= 1.50 at large Re(Re=36,000) and in a large aspect ratio facility(AR= span length/step height= 24); the latter being important to avoid any effects due to span-wise confinement. In the spanwise plane parallel to the lower wall(x-z plane),instantaneous velocity fields show counter rotating vortex pairs, which is a signature of the three-dimensional vortical structures in this plane. Using conditional averaging, this counter-rotating vortex pair signature is captured right from upstream of the step, to well after reattachment. Spatial correlations are used to get the length scale of these coherent vortical structures, which varies substantially from the attached boundary layer before separation to the region after reattachment. The variation of these structures in the cross-stream (vertical) direction at reattachment and beyond gives an idea about their three dimensional shape. The circulation of these counter-rotating pairs is measured from the conditionally aver-aged fields, and is found to increase with streamwise distance reaching normalized circulation values (Γ/Uoh) of about 0.5 around reattachment. Velocity spectra downstream of the step show peaks corresponding to both the shear layer frequency(Stsl)and a relatively lower frequency that corresponds to large-scale shedding from the separation bubble (Stb); the latter in particular being quasi-periodic. Small amplitude sinusoidal forcing at the shedding frequency(Stb) is applied close to the step, by blowing and suction, to make the quasi-periodic shedding more regular. Measurements show that this has a very small effect on both the mean separation bubble and on the counter-rotating structures in the x-z plane. This mild forcing however enables phase locked PIV measurements to be made which shows the bubble shedding phenomenon in the cross-stream plane(side view or x-y plane). The phase-averaged velocity fields show significant variations from phase to phase. Although there is some hint of structures being shed, from these phase-averaged fields, it is not very clear. One of the primary reasons is the fact that the flow is effectively spanwise averaged, as the three-dimensional structures are not locked in the spanwise direction. To get a three dimensional view of the sheddin gphenomenon, it is necessary to lock the spanwise location with respect to the three-dimensional vortical structures before averaging across the different phases. We use the condition, u’<- urms, to locate the central plane between the counter-rotating structures, which in effect are the “legs” of the three-dimensional structure. With this condition, we effectively get a slice of the shedding cycle cutting through the “head” of the three-dimensional structure. Apart from this cut, we also get a cut between adjacent structures from the weak sweep events, with the condition u’<- urms. Using these conditions, on the phase-locked velocity fields, we effectively lock the structures in time, as well as in the spanwise direction. With this ,a clearer picture of the shedding process emerges. The flow is highly three-dimensional near reattachment and the shedding of the separation bubble is modulated in the spanwise direction owing to the three-dimensional hairpin like vortical structures in the flow. The separation bubble is seen bulged out and lifted high at locations where the head of the hairpin vortex passes, owing to the strong ejection of fluid caused by the vortical structure. On the other hand, outside the hairpin vortices, weak sweep events push the flow towards the wall and make it shallow and less prominent, with the shedding being very weak in this plane. From these observations, a three-dimensional picture of the flow is proposed.

In this study, two major internal erosion initiation processes, suffusion and concentrated leak mechanisms, which lead to both defect formation in a dam’s body and its foundation and high throughflow in dams subjected to internal erosion were studied. This understanding has the potential to facilitate numerical modelling and expedite dam safety assessment studies.  The throughflow properties of coarse rockfill material were studied by; analysing filed pump test data, performing extensive laboratory experiments with a large-scale apparatus and numerically simulating the three-dimensional flow through coarse rock materials, replicating the material used in the laboratory experiments. Results from the tests demonstrate that the parameters of the nonlinear momentum equation of the flow depend on the Reynolds number for pore Reynolds numbers lower than 60000.  Numerical studies were also carried out to conduct numerical experiments. By applying a Lagrangian particle tracking method, a model for estimating the lengths of the flow channels in the porous media was developed.  The shear forces exerted on the coarse particles in the porous media were found to be significantly dependent on the inertial forces of the flow. Suffusion and concentrated leak mechanisms were also studied by means of laboratory experiments to develop a theoretical framework for continuum-based numerical modelling. An erosion apparatus was designed and constructed with the capability of applying hydraulic and mechanical loading. Results were then used to develop constitutive laws of the soil erosion as a function of the applied hydromechanical load for both suffusion and concentrated leak mechanisms. Both the initiation and mass removal rate of were found to be dependent on the soil in-situ stresses. A three-dimensional electrical-resistivity-based tomography method was also adopted for the internal erosion apparatus and was found to be successful in visualising the porosity evolution due to suffusion. / <p>QC 20161006</p>

A simulação computacional de escoamentos incompressíveis multifásicos tem avançado continuamente e é uma área extremamente importante em Dinâmica de Fluidos Computacional (DFC) por suas várias aplicações na indústria, em medicina e em biologia, apenas para citar alguns exemplos. Apresentamos modelos matemáticos e métodos numéricos tendo em vista simulações computacionais de fluidos bifásicos newtonianos e viscoelásticos (não newtonianos), em seus regimes transiente e estacionário de escoamento. Os ingredientes principais requeridos são o Modelo de Um Fluido e o Método da Fronteira Imersa em malhas adaptativas, usados em conjunto com os métodos da Projeção de Chorin-Temam e de Uzawa. Tais metodologias são obtidas a partir de equações a derivadas parciais simples as quais, naturalmente, são resolvidas em malhas adaptativas empregando métodos multinível-multigrid. Em certas ocasiões, entretanto, para escoamentos modelados pelas equações de Navier-Stokes (e.g. em problemas onde temos altos saltos de massa específica), tem-se problemas de convergência no escopo destes métodos. Além disso, no caso de escoamentos estacionários, resolver as equações de Stokes em sua forma discreta por tais métodos não é uma tarefa fácil. Verificamos que zeros na diagonal do sistema linear resultante impedem que métodos de relaxação usuais sejam empregados. As dificuldades mencionadas acima motivaram-nos a pesquisar por, a propor e a desenvolver alternativas à metodologia multinível-multigrid. No presente trabalho, propomos métodos para obter explicitamente as matrizes que representam os sistemas lineares oriundos da discretização daquelas equações a derivadas parciais simples que são a base dos métodos de Projeção e de Uzawa. Ter em mãos estas representações matriciais é vantajoso pois com elas podemos caracterizar tais sistemas lineares em termos das propriedades de seus raios espectrais, suas definições e simetria. Muito pouco (ou nada) se sabe efetivamente sobre estes sistemas lineares associados a discretizações em malhas compostas bloco-estruturadas. É importante salientarmos que, além disso, ganhamos acesso ao uso de bibliotecas numéricas externas, como o PETSc, com seus pré-condicionadores e métodos numéricos, seriais e paralelos, para resolver sistemas lineares. Infraestrutura para nossos desenvolvimentos foi propiciada pelo código denominado ``AMR2D\'\', um código doméstico para problemas em DFC que vem sendo cuidado ao longo dos anos pelos grupos de pesquisa em DFC do IME-USP e da FEMEC-UFU. Estendemos este código, adicionando módulos para escoamentos viscoelásticos e para escoamentos estacionários modelados pelas equações de Stokes. Além disso, melhoramos de maneira notável as rotinas de cálculo de valores fantasmas. Tais melhorias permitiram a implementação do Método dos Gradientes Bi-Conjugados, baseada em visitas retalho-a-retalho e varreduras da estrutura hierárquica nível-a-nível, essencial à implementação do Método de Uzawa. / Numerical simulation of incompressible multiphase flows has continuously of advanced and is an extremely important area in Computational Fluid Dynamics (CFD) because its several applications in industry, in medicine, and in biology, just to mention a few of them. We present mathematical models and numerical methods having in sight the computational simulation of two-phase Newtonian and viscoelastic fluids (non-Newtonian fluids), in the transient and stationary flow regimes. The main ingredients required are the One-fluid Model and the Immersed Boundary Method on dynamic, adaptive meshes, in concert with Chorin-Temam Projection and the Uzawa methods. These methodologies are built from simple linear partial differential equations which, most naturally, are solved on adaptive grids employing mutilevel-multigrid methods. On certain occasions, however, for transient flows modeled by the Navier-Stokes equations (e.g. in problems where we have high density jumps), one has convergence problems within the scope of these methods. Also, in the case of stationary flows, solving the discrete Stokes equations by those methods represents no straight forward task. It turns out that zeros in the diagonal of the resulting linear systems coming from the discrete equations prevent the usual relaxation methods from being used. Those difficulties, mentioned above, motivated us to search for, to propose, and to develop alternatives to the multilevel-multigrid methodology. In the present work, we propose methods to explicitly obtain the matrices that represent the linear systems arising from the discretization of those simple linear partial differential equations which form the basis of the Projection and Uzawa methods. Possessing these matrix representations is on our advantage to perform a characterization of those linear systems in terms of their spectral, definition, and symmetry properties. Very little is known about those for adaptive mesh discretizations. We highlight also that we gain access to the use of external numerical libraries, such as PETSc, with their preconditioners and numerical methods, both in serial and parallel versions, to solve linear systems. Infrastructure for our developments was offered by the code named ``AMR2D\'\' - an in-house CFD code, nurtured through the years by IME-USP and FEMEC-UFU CFD research groups. We were able to extend that code by adding a viscoelastic and a stationary Stokes solver modules, and improving remarkably the patchwise-based algorithm for computing ghost values. Those improvements proved to be essential to allow for the implementation of a patchwise Bi-Conjugate Gradient Method which ``powers\'\' Uzawa Method.

A simulação computacional de escoamentos incompressíveis multifásicos tem avançado continuamente e é uma área extremamente importante em Dinâmica de Fluidos Computacional (DFC) por suas várias aplicações na indústria, em medicina e em biologia, apenas para citar alguns exemplos. Apresentamos modelos matemáticos e métodos numéricos tendo em vista simulações computacionais de fluidos bifásicos newtonianos e viscoelásticos (não newtonianos), em seus regimes transiente e estacionário de escoamento. Os ingredientes principais requeridos são o Modelo de Um Fluido e o Método da Fronteira Imersa em malhas adaptativas, usados em conjunto com os métodos da Projeção de Chorin-Temam e de Uzawa. Tais metodologias são obtidas a partir de equações a derivadas parciais simples as quais, naturalmente, são resolvidas em malhas adaptativas empregando métodos multinível-multigrid. Em certas ocasiões, entretanto, para escoamentos modelados pelas equações de Navier-Stokes (e.g. em problemas onde temos altos saltos de massa específica), tem-se problemas de convergência no escopo destes métodos. Além disso, no caso de escoamentos estacionários, resolver as equações de Stokes em sua forma discreta por tais métodos não é uma tarefa fácil. Verificamos que zeros na diagonal do sistema linear resultante impedem que métodos de relaxação usuais sejam empregados. As dificuldades mencionadas acima motivaram-nos a pesquisar por, a propor e a desenvolver alternativas à metodologia multinível-multigrid. No presente trabalho, propomos métodos para obter explicitamente as matrizes que representam os sistemas lineares oriundos da discretização daquelas equações a derivadas parciais simples que são a base dos métodos de Projeção e de Uzawa. Ter em mãos estas representações matriciais é vantajoso pois com elas podemos caracterizar tais sistemas lineares em termos das propriedades de seus raios espectrais, suas definições e simetria. Muito pouco (ou nada) se sabe efetivamente sobre estes sistemas lineares associados a discretizações em malhas compostas bloco-estruturadas. É importante salientarmos que, além disso, ganhamos acesso ao uso de bibliotecas numéricas externas, como o PETSc, com seus pré-condicionadores e métodos numéricos, seriais e paralelos, para resolver sistemas lineares. Infraestrutura para nossos desenvolvimentos foi propiciada pelo código denominado ``AMR2D\'\', um código doméstico para problemas em DFC que vem sendo cuidado ao longo dos anos pelos grupos de pesquisa em DFC do IME-USP e da FEMEC-UFU. Estendemos este código, adicionando módulos para escoamentos viscoelásticos e para escoamentos estacionários modelados pelas equações de Stokes. Além disso, melhoramos de maneira notável as rotinas de cálculo de valores fantasmas. Tais melhorias permitiram a implementação do Método dos Gradientes Bi-Conjugados, baseada em visitas retalho-a-retalho e varreduras da estrutura hierárquica nível-a-nível, essencial à implementação do Método de Uzawa. / Numerical simulation of incompressible multiphase flows has continuously of advanced and is an extremely important area in Computational Fluid Dynamics (CFD) because its several applications in industry, in medicine, and in biology, just to mention a few of them. We present mathematical models and numerical methods having in sight the computational simulation of two-phase Newtonian and viscoelastic fluids (non-Newtonian fluids), in the transient and stationary flow regimes. The main ingredients required are the One-fluid Model and the Immersed Boundary Method on dynamic, adaptive meshes, in concert with Chorin-Temam Projection and the Uzawa methods. These methodologies are built from simple linear partial differential equations which, most naturally, are solved on adaptive grids employing mutilevel-multigrid methods. On certain occasions, however, for transient flows modeled by the Navier-Stokes equations (e.g. in problems where we have high density jumps), one has convergence problems within the scope of these methods. Also, in the case of stationary flows, solving the discrete Stokes equations by those methods represents no straight forward task. It turns out that zeros in the diagonal of the resulting linear systems coming from the discrete equations prevent the usual relaxation methods from being used. Those difficulties, mentioned above, motivated us to search for, to propose, and to develop alternatives to the multilevel-multigrid methodology. In the present work, we propose methods to explicitly obtain the matrices that represent the linear systems arising from the discretization of those simple linear partial differential equations which form the basis of the Projection and Uzawa methods. Possessing these matrix representations is on our advantage to perform a characterization of those linear systems in terms of their spectral, definition, and symmetry properties. Very little is known about those for adaptive mesh discretizations. We highlight also that we gain access to the use of external numerical libraries, such as PETSc, with their preconditioners and numerical methods, both in serial and parallel versions, to solve linear systems. Infrastructure for our developments was offered by the code named ``AMR2D\'\' - an in-house CFD code, nurtured through the years by IME-USP and FEMEC-UFU CFD research groups. We were able to extend that code by adding a viscoelastic and a stationary Stokes solver modules, and improving remarkably the patchwise-based algorithm for computing ghost values. Those improvements proved to be essential to allow for the implementation of a patchwise Bi-Conjugate Gradient Method which ``powers\'\' Uzawa Method.

Este trabalho é dedicado à análise e implementação de esquemas "upwind" de alta ordem modernos e o modelo de turbulência k-epsilon padrão no Freeflow-2D; um ambiente integrado para simulação numérica em diferenças finitas de problemas de escoamentos incompressíveis com superfícies livres. O propósito do estudo é a simulação de escoamentos de fluidos newtonianos incompressíveis, bidimensionais, confinados e/ou com superfícies livres e a altos valores do número de Reynolds. O desempenho do código Freeflow-2D atual é avaliada na simulação do escoamento numa expansão brusca e de um jato livre incidindo perpendicularmente sobre uma superfície rígida impermeável. O código é então aplicado na simulação de um jato planar turbulento em uma porção de fluido com superfície livre e estacionário. Os resultados numéricos obtidos são comparados com dados experimentais, soluções analíticas e soluções numéricas de outros trabalhos. / This work is devoted to the analysis and implementation of modern high-order upwind schemes and the standard k-epsilon turbulence model into the Freeflow-2D; a finite difference integrated environment for the numerical simulation of incompressible free surface flow problems. The purpose of this study is the two-dimensional simulation of high-Reynolds incompressible newtonian confined and/or free surface flows. The performance of the current Freeflow-2D code is assessed by applying it to the simulation of flow over a backward facing step and of an impinging free jet onto an impermeable rigid surface. The code is then applied to a turbulent planar jet into a pool. The numerical results are compared with experimental data, analytical solution, and numerical simulations of other works.

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.

This thesis deals with the near-field of confluent jets, which can be of interest in many engineering applications such as design of a ventilation supply device. The physical effect of interaction between multiple closely spaced jets is studied using experimental and numerical methods. The primary aim of this study is to explore a better understanding of flow and turbulence behavior of multiple interacting jets. The main goal is to gain an insight into the confluence of jets occurring in the near-field of multiple interacting jets. The array of multiple interacting jets is studied when they are placed on a flat and a curved surface. To obtain the boundary conditions at the nozzle exits of the confluent jets on a curved surface, the results of numerical prediction of a cylindrical air supply device using two turbulence models (realizable 𝑘 − 𝜖 and Reynolds stress model) are validated with hot-wire anemometry (HWA) near different nozzles discharge in the array. A single round jet is then studied to find the appropriate turbulence models for the prediction of the three-dimensional flow field and to gain an understanding of the effect of the boundary conditions predicted at the nozzle inlet. In comparison with HWA measurements, the turbulence models with low Reynolds correction (𝑘 − 𝜖 and shear stress transport [SST] 𝑘 − 𝜔) give reasonable flow predictions for the single round jet with the prescribed inlet boundary conditions, while the transition models (𝑘 − 𝑘l − 𝜔𝜔 and transition SST 𝑘 − 𝜔) are unable to predict the flow in the turbulent region. The results of numerical prediction (low Reynolds SST 𝑘 − 𝜔 model) using the prescribed inlet boundary conditions agree well with the HWA measurement in the nearfield of confluent jets on a curved surface, except in the merging region. Instantaneous velocity measurements are performed by laser Doppler anemometry (LDA) and particle image velocimetry (PIV) in two different configurations, a single row of parallel coplanar jets and an inline array of jets on a flat surface. The results of LDA and PIV are compared, which exhibit good agreement except near the nozzle exits. The streamwise velocity profile of the jets in the initial region shows a saddle back shape with attenuated turbulence in the core region and two off-centered narrow peaks. When confluent jets issue from an array of closely spaced nozzles, they may converge, merge, and combine after a certain distance downstream of the nozzle edge. The deflection plays a salient role for the multiple interacting jets (except in the single row configuration), where all the jets are converged towards the center of the array. The jet position, such as central, side and corner jets, significantly influences the development features of the jets, such as velocity decay and lateral displacement. The flow field of confluent jets exhibits asymmetrical distributions of Reynolds stresses around the axis of the jets and highly anisotropic turbulence. The velocity decays slower in the combined regio  of confluent jets than a single jet. Using the response surface methodology, the correlations between characteristic points (merging and combined points) and the statistically significant terms of the three design factors (inlet velocity, spacing between the nozzles and diameter of the nozzles) are determined for the single row of coplanar parallel jets. The computational parametric study of the single row configuration shows that spacing has the greatest impact on the near-field characteristics.

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.

L'approche de simulation numérique directe est utilisée pour la simulation d'un écoulement en canal pleinement turbulent afin d'étudier l'influence des grandes échelles de l'écoulement ainsi que la dynamique du transport des contraintes de Reynolds et de la vorticité. Les simulations sont réalisées sur un domaine de calcul de grande taille afin de pouvoir capturer l'intégralité des grandes structures de l'écoulement, et portent sur une gamme relativement étendue de nombres de Reynolds (Reτ =180, 395, 590 et 1100) allant des écoulements faiblement turbulents à des écoulements modérément turbulents. L'invariance remarquable des fluctuations de vorticité normale est expliquée à travers une analyse spectrale de la vorticité. L'étude des différents termes du transport de l'intensité turbulente de la vorticité révèle par ailleurs que le pic de production de la vorticité transverse est situé à proximité immédiate de la paroi et pourrait ouvrir la voie à des stratégies de réduction de la traînée basées sur la réduction de la vorticité transverse. Le transport des contraintes de Reynolds dans la couche interne et dans la couche de recouvrement est également étudié. A proximité des parois, la dépendance des termes de transport avec le nombre de Reynolds dans les échelles internes montre que ces dernières ne suffisent pas à caractériser la dynamique des contraintes de Reynolds dans cette zone. Cette insuffisance des échelles internes nous a amenés à nous intéresser plus particulièrement au processus de production à travers les statistiques de la production conditionnées par le passage par niveau des fluctuations de la vitesse normale ou longitudinale. Cette étude nous a permis d'identifier les fluctuations qui contribuent le plus à la production et celles qui sont à l'origine de la dépendance avec le nombre de Reynolds. / The direct numerical simulations of a fully turbulent channel flow are investigated to study the large scales effects on the flow quantities such as the Reynolds stresses and vorticity transport processes. Large computational domains are used so as to cover the largest scales of the flow. The simulations are performed in a wide range of Reynolds numbers (Reτ=180, 395, 590 and 1100) going from weakly to moderately high Reynolds number turbulent flows. The invariance of the wall-normal vorticity fluctuations scaled in wall variables in the inner layer versus the Reynolds number is analyzed using a spectral analysis. The vorticity transport equations are investigated in detail, presumably for the first time. The transport mechanism of the Reynolds shear stresses are subsequently analyzed in the inner layer and the overlapping zone. In the wall layer, different terms of the Reynolds stresses transport expressed in inner scales depend on the Reynolds number. This scaling failure lead us to focus on the statistics of the production when the streamwise or normal velocity fluctuations cross a given level, through the conditional Palm statistics. The main aim is to identify those amplitudes of the fluctuations that contribute more to the production and those which are responsible for the production Reynolds dependence.

Co-location of offshore wind turbines at sites being developed for tidal stream arrays has been proposed as a method to increase capacity and potentially reduce the cost of electricity compared to operating either technology independently. This research evaluates the cost of energy based on capital expenditure and energy yield. It is found that, within the space required around a single 3 MW wind turbine, co-location provides a 10-16% cost saving compared to operating the same size tidal-only array without a wind turbine. Furthermore, for the same cost of electricity, a co-located farm could generate 20% more yield than a tidal-only array. These results are based on analysis of a case-study site in the Pentland Firth. Wind energy is assessed using an eddy viscosity wake model in OpenWind, with a 3 MW rated power curve and thrust coefficient from a Vestas V90 turbine. Three years of wind resource data is from the UK Met Office UK Variable (UKV) 1.5 km numerical model and corrected against a 400 m Weather Research and Forecasting (WRF) model run over the site. Tidal stream energy is modelled using a semi-empirical superposition of self-similar plane wakes, with a generic 1 MW rated power curve and thrust based on a full-scale, fixed-pitch turbine. Coincident tidal resource data is from the Forecasting Ocean Assimilation Model (FOAM) at 7.5 km resolution and correlated with a 150 m ADvanced CIRCulation model (ADCIRC). Wave parameters are corrected from ERA-Interim data with six months of wave buoy data. Multiple tidal turbine array layouts are considered, with maximum tidal energy generated for a staggered array with spacing of 20 tidal turbine diameters, Dt , streamwise and 1.5Dt cross-stream. However, cheapest cost of electricity from the tidal-only array, was found for a single row of turbines, due to minimal wake effects. Laboratory experiments were undertaken to validate the superposition wake model for use with large, shared support structures. Two rotors mounted either side of a central tower generate a peak wake velocity deficit 70% greater than predicted by superposition. This was due to high local blockage and a complex near-wake structure, with a corresponding increase in tower drag of 9%. Further experiments evaluated the impact of oblique inflow on turbines yawed at +/-15 degrees. These results validated a theoretical cosine correction for thrust coefficient and characterised the centreline wake drift with downstream distance. Extreme environmental loads for a shared support structure, compared to structures for wind-only and tidal-only, have also been modelled. A non-linear wave model was used to represent a single wave form with 1% occurrence for each hour of time-series data. Overturning moment about the base of a shared support, with one wind and two tidal turbines, was found to be 4.5% larger than for a wind-only turbine in strong current and with turbines in different operational states. Peak loads across the tidal array were found to vary by 2.5% and so little load reduction benefit could be gained by locating a shared support in a more sheltered area of the array.