In this study we investigate the interactions between two co-rotating vortices. These vortices are subject to rapid rotation and stable stratification such as are found in planetary atmospheres and oceans. By conducting a large number of simulations of vortex interactions, we intend to provide an overview of the interactions that could occur in geophysical turbulence. We consider a wide parameter space covering the vortices height-to-width aspect-ratios, their volume ratios and the vertical offset between them. The vortices are initially separated in the horizontal so that they reside at an estimated margin of stability. The vortices are then allowed to evolve for a period of approximately 20 vortex revolutions. We find that the most commonly observed interaction under the quasi-geostrophic (QG) regime is partial-merger, where only part of the smaller vortex is incorporated into the larger, stronger vortex. On the other hand, a large number of filamentary and small scale structures are generated during the interaction. We find that, despite the proliferation of small-scale structures, the self-induced vortex energy exhibits a mean `inverse-cascade' to larger scale structures. Interestingly we observe a range of intermediate-scale structures that are preferentially sheared out during the interactions, leaving two vortex populations, one of large-scale vortices and one of small-scale vortices. We take a subset of the parameter space used for the QG study and perform simulations using a non-hydrostatic model. This system, free of the layer-wise two-dimensional constraints and geostrophic balance of the QG model, allows for the generation of inertia-gravity waves and ageostrophic advection. The study of the interactions between two co-rotating, non-hydrostatic vortices is performed over four different Rossby numbers, two positive and two negative, allowing for the comparison of cyclonic and anti-cyclonic interactions. It is found that a greater amount of wave-like activity is generated during the interactions in anticyclonic situations. We also see distinct qualitative differences between the interactions for cyclonic and anti-cyclonic regimes.

O escoamento estratificado óleo-água é bastante comum na indústria do petróleo, especialmente em poços direcionas offshore, oleodutos e gasodutos. Entretanto, existem poucos trabalhos na literatura sobre a natureza da estrutura ondulatória observada no escoamento em dutos ascendentes ou descendentes a partir da horizontal. O objetivo deste trabalho foi estudar as propriedades geométricas e cinemáticas da onda interfacial, i.e, forma média, comprimento, amplitude e celeridade, e assim contribuir para a compreensão do papel da onda interfacial na dinâmica do escoamento estratificado. Um software baseado em plataforma Labview® possibilitou a automação para obtenção dos dados das ondas interfaciais extraídas de imagens de vídeos de alta resolução. Além das propriedades das ondas, também se coletaram valores de fração volumétrica in situ e de gradiente de pressão bifásico para cinco ângulos de inclinação (-20°, -10°, 0°, 10° e 20°) em diferentes pares de vazões de óleo e água. Desenvolveu-se um modelo fenomenológico considerando os termos ondulatórios do escoamento para o cálculo da fração volumétrica in situ e do gradiente de pressão bifásico, sendo comparado com modelos disponíveis na literatura e dados experimentais. A concordância do modelo proposto com os dados coletados neste trabalho se mostrou muito boa, o que sugere um avanço em comparação ao existente na literatura. O estudo da equação da onda de perturbação interfacial para o escoamento estratificado óleo-água indicou que a natureza da onda observada é cinemática e não dinâmica; e baseado na equação da celeridade da onda cinemática pode-se confrontar a celeridade experimental com a teórica, revelando boa concordância. / The oil-water stratified flow is quite common in the oil industry, especially in offshore directional wells and pipelines. However, there are few studies on the physics of the wavy structure observed in upward and downward stratified flow. The goal of this work was to study the geometric and kinematic properties of interfacial waves, i.e., the average shape, wavelength, amplitude and celerity. A homemade Labview®-based software enabled the automatic acquisition of data extracted from frames obtained via high resolution video recording. In situ volume fraction and two-phase pressure gradient data for five inclination angles (-20°, -10°, 0°, 10° and 20°) at several pairs of oil and water flow rates were also collected. A phenomenological model that takes into account the wavy structure is proposed to calculate volume fractions and two-phase pressure gradient and it was compared with available models from the literature and experimental data. The good agreement of the proposed model with the data collected in this study is promising and suggests that it may provide better predictions in comparison with models from the literature. The study of the interfacial perturbation wave equation for stratified flow indicates that the observed waves nature is kinematic and not dynamic; and based on the kinematic wave velocity equation we could compare the experimental celerity with the theoretical one, with good agreement.

Embora o escoamento estratificado óleo-água seja comum na indústria do petróleo, existem poucos trabalhos na literatura sobre a estrutura ondulatória encontrada no escoamento em dutos ascendentes ou descendentes. O objetivo deste trabalho é entender e caracterizar as estruturas interfaciais ondulatórias em escoamentos estratificados óleo e água em dutos levemente inclinados e comparar com os resultados retirados da modelagem proposta. Uma primeira tentativa de modelar a onda interfacial óleo-água através da equação da energia bifásica unidimensional para regime permanente é apresentada e comparada aos resultados obtidos experimentalmente. Valores de comprimento de onda foram coletados para quatro ângulos de inclinação a partir da horizontal (-5º, -2º, 2º e 5º) e diversos pares de vazão de óleo e água. Os dados foram extraídos de frames de vídeos de alta resolução através de uma técnica manual. Um software baseado em LabView foi desenvolvido para possibilitar a automação da obtenção do comprimento de onda e amplitude. Os comprimentos de onda obtidos com a técnica automática foram comparados com os dados obtidos através da técnica manual. O mensuramento é bem satisfatório e sugere que a ferramenta experimental proposta possa ser aplicada para o estudo de qualquer padrão de escoamento óleo-água, onde uma estrutura ondulatória possa ser identificada. A validade da modelagem da onda interfacial proposta foi avaliada através da comparação entre os resultados teóricos e dados experimentais. A concordância observada é encorajadora. / Even though the oil-water stratified flow pattern has a common occurrence in the upstream oil industry, quite often in directional wells, there are only a few works in the literature dealing with its interfacial wavy structure. This work has the mean goal of comprehending a characterizing the interfacial wave structure in inclined water-oil stratified pipe flow, comparing it with the proposed model. A model, based on the steady-state one-dimensional two-phase flow energy equation is presented and compared to our experimental data. Wave lengths and amplitude data were collected at four inclinations from the horizontal (-5º, -2º, 2º and 5º) and several oil and water flow rates. The data were extracted form high-resolution video images through a manual technique. A LabView based software was developed in order to obtain the lengths and amplitude automatically. Wave length obtained from it were compared to the manual technique data. The satisfactory measurement suggests the applicability of the experimental tool to any water-oil pipe flow pattern, where a wave structure can be identified. The validity by the comparison between theoretical and experimental data. The agreement observed is promising.

[Truncated abstract] The lake boundaries are an important source of sediment, nutrients and chemicals. For life inside the lake, the exchange between the lake boundaries (littoral) and lake interior (pelagic) is of central importance to Limnology as the net flux of nutrients into the water column is both the driving force and limiting factor for most algae blooms found during the stratification period. Consequently, the understanding of the relevant processes defining such an exchange is a further step toward a sound basis for future decisions by lake managers in order to ensure high water quality. The objective of this research was to investigate the physical processes responsible for the exchange of water and particles between the lake boundaries and the lake interior. An integrated approach using field experiments and 3D modelling as applied to Lake Kinneret (Israel) is presented. The field data revealed large-scale metalimnion oscillations with amplitudes up to 10 m in response to westerly diurnal winds, the existence of a well-defined suspended particle intrusion into the metalimnion of the lake, characterized by high concentrations of organic matter, and a well-mixed benthic boundary layer (BBL). The changes in the thermal structure explained the observed vertical and horizontal movements of the suspended particle intrusion. The horizontal advective transport via the metalimnion, associated with the velocities induced by the basin-scale mode-two Poincare wave, controlled the exchange between the lake boundaries and lake interior on daily time scales. The observed BBL over the lake slope varied markedly with time and space. Detailed comparison of simulation results with field data revealed that the model captured the lake hydrodynamics for time scales from hours to days. The model could then be used to extract the residual motions in the various regions of the lake. The residual motions below the surface layer were predominantly forced by the basin-scale internal wave motions, but the residual motion in the surface layer was found to be very sensitive to the curl of the wind field. The residual circulation was responsible for redistributing mass throughout the lake basin on time scales from days to weeks. A clear connection of dynamics of the BBL with the large-scale features of the flow was addressed. The time history of the mixing in the BBL and the resulting cross-shore flux was shown to vary with the phase of the basin-scale internal waves.

[Truncated abstract] The process of selective withdrawal has, over many years, been used as an effective tool for extraction of water of particular quality from stratifed reservoirs. While the formation and steady-state theory of selective withdrawal in a stratifed fluid at rest has been extensively studied, little is known how vertical displacements of stratifcation due to long internal waves affect the water quality of the outflows. The first part of this study investigates the effect of basin-scale internal waves on the water quality parameters in Lake Burragorang, a large water supply reservoir for the city of Sydney, Australia. It is shown from field observations how the steady-state formulation of selective withdrawal can be used to predict the outflow water quality in reservoirs where internal waves are present, with a temperature prediction accuracy within 0.2 oC. . . In order to explain fluctuations in water quality parameters of the outflows, such as turbidity, it is important to know not only the stratifcation conditions in front to the offtake, but also to understand the dynamics of suspended particles in the upper reaches of the reservoir. In the third part of this study, transport and settling of suspended particles was investigated in the Wollondilly arm of Lake Burragorang by combination of direct and inverse methods. The inverse method was modifed to enable the separation of advective and diffusive transport of suspended particles from Stokes settling controlled by gravity, yielding twodimensional fields of particle velocities and settling fluxes in the upper reaches of the reservoir. These estimates are compared to the direct measurements of sedimentation fluxes made by the sediment traps and LISST-100.

[Truncated abstract] Internal waves redistribute energy and momentum in stratified lakes and constitute the path through which the energy that is introduced at the lake scale is cascaded down to the turbulent scales where mixing and dissipation take place. This research, based on intensive field data complemented with numerical simulations, covers several aspects of the energy flux path ranging from basin-scale waves with periods of several hours to high frequency waves with periods of few minutes. It was found that, at the basin-scale level, the horizontal shape of the lake at the level of the metalimnion controls the period and modal structure of the basin-scale natural modes, conforming to the dispersion relationship of internal waves in circular basins. The sloping bottom, in turn, produces local intensification of the wave motion due to focusing of internal wave rays over near-critical slopes, providing hot spots for the degeneration of the basin-scale waves due to shear instabilities, nonlinear processes and dissipation. Different types of high-frequency phenomena were observed in a stratified lake under different forcing conditions. The identification of the generation mechanisms revealed how these waves extract energy from the mean flow and the basin-scale waves. The changes to the stratification show that such waves contribute to mixing in different ways . . . Detailed field observations were used to develop a comprehensive description of an undocumented energy flux mechanism in which shear-instabilities with significant amplitudes away from the generation level are produced in the surface layer due to the shear generated by the wind. The vertical structure of these instabilities is such that the growing wave-related fluctuations strain the density field in the metalimnion triggering secondary instabilities. These instabilities also transport energy vertically to the thermocline where they transfer energy back to the mean flow through interaction with the background shear.

Embora o escoamento estratificado óleo-água seja comum na indústria do petróleo, existem poucos trabalhos na literatura sobre a estrutura ondulatória encontrada no escoamento em dutos ascendentes ou descendentes. O objetivo deste trabalho é entender e caracterizar as estruturas interfaciais ondulatórias em escoamentos estratificados óleo e água em dutos levemente inclinados e comparar com os resultados retirados da modelagem proposta. Uma primeira tentativa de modelar a onda interfacial óleo-água através da equação da energia bifásica unidimensional para regime permanente é apresentada e comparada aos resultados obtidos experimentalmente. Valores de comprimento de onda foram coletados para quatro ângulos de inclinação a partir da horizontal (-5º, -2º, 2º e 5º) e diversos pares de vazão de óleo e água. Os dados foram extraídos de frames de vídeos de alta resolução através de uma técnica manual. Um software baseado em LabView foi desenvolvido para possibilitar a automação da obtenção do comprimento de onda e amplitude. Os comprimentos de onda obtidos com a técnica automática foram comparados com os dados obtidos através da técnica manual. O mensuramento é bem satisfatório e sugere que a ferramenta experimental proposta possa ser aplicada para o estudo de qualquer padrão de escoamento óleo-água, onde uma estrutura ondulatória possa ser identificada. A validade da modelagem da onda interfacial proposta foi avaliada através da comparação entre os resultados teóricos e dados experimentais. A concordância observada é encorajadora. / Even though the oil-water stratified flow pattern has a common occurrence in the upstream oil industry, quite often in directional wells, there are only a few works in the literature dealing with its interfacial wavy structure. This work has the mean goal of comprehending a characterizing the interfacial wave structure in inclined water-oil stratified pipe flow, comparing it with the proposed model. A model, based on the steady-state one-dimensional two-phase flow energy equation is presented and compared to our experimental data. Wave lengths and amplitude data were collected at four inclinations from the horizontal (-5º, -2º, 2º and 5º) and several oil and water flow rates. The data were extracted form high-resolution video images through a manual technique. A LabView based software was developed in order to obtain the lengths and amplitude automatically. Wave length obtained from it were compared to the manual technique data. The satisfactory measurement suggests the applicability of the experimental tool to any water-oil pipe flow pattern, where a wave structure can be identified. The validity by the comparison between theoretical and experimental data. The agreement observed is promising.

O escoamento estratificado óleo-água é bastante comum na indústria do petróleo, especialmente em poços direcionas offshore, oleodutos e gasodutos. Entretanto, existem poucos trabalhos na literatura sobre a natureza da estrutura ondulatória observada no escoamento em dutos ascendentes ou descendentes a partir da horizontal. O objetivo deste trabalho foi estudar as propriedades geométricas e cinemáticas da onda interfacial, i.e, forma média, comprimento, amplitude e celeridade, e assim contribuir para a compreensão do papel da onda interfacial na dinâmica do escoamento estratificado. Um software baseado em plataforma Labview® possibilitou a automação para obtenção dos dados das ondas interfaciais extraídas de imagens de vídeos de alta resolução. Além das propriedades das ondas, também se coletaram valores de fração volumétrica in situ e de gradiente de pressão bifásico para cinco ângulos de inclinação (-20°, -10°, 0°, 10° e 20°) em diferentes pares de vazões de óleo e água. Desenvolveu-se um modelo fenomenológico considerando os termos ondulatórios do escoamento para o cálculo da fração volumétrica in situ e do gradiente de pressão bifásico, sendo comparado com modelos disponíveis na literatura e dados experimentais. A concordância do modelo proposto com os dados coletados neste trabalho se mostrou muito boa, o que sugere um avanço em comparação ao existente na literatura. O estudo da equação da onda de perturbação interfacial para o escoamento estratificado óleo-água indicou que a natureza da onda observada é cinemática e não dinâmica; e baseado na equação da celeridade da onda cinemática pode-se confrontar a celeridade experimental com a teórica, revelando boa concordância. / The oil-water stratified flow is quite common in the oil industry, especially in offshore directional wells and pipelines. However, there are few studies on the physics of the wavy structure observed in upward and downward stratified flow. The goal of this work was to study the geometric and kinematic properties of interfacial waves, i.e., the average shape, wavelength, amplitude and celerity. A homemade Labview®-based software enabled the automatic acquisition of data extracted from frames obtained via high resolution video recording. In situ volume fraction and two-phase pressure gradient data for five inclination angles (-20°, -10°, 0°, 10° and 20°) at several pairs of oil and water flow rates were also collected. A phenomenological model that takes into account the wavy structure is proposed to calculate volume fractions and two-phase pressure gradient and it was compared with available models from the literature and experimental data. The good agreement of the proposed model with the data collected in this study is promising and suggests that it may provide better predictions in comparison with models from the literature. The study of the interfacial perturbation wave equation for stratified flow indicates that the observed waves nature is kinematic and not dynamic; and based on the kinematic wave velocity equation we could compare the experimental celerity with the theoretical one, with good agreement.

In this thesis is presented mathematical model of stratified 2D flow of viscous incopressible fluid and its program realization. Basic equations of fluid flow in Boussinesq approximation were solved by finite volume method on structured nonortogonal grid. Discretization was done by the principle of semi-discretisation. The space derivative was solved by AUSM me- thod with MUSCL velocity reconstruction. The viscid terms were solved through auxiliary grids. During time discretization artificial compressibility method was used in dual time. The resulting system of ODEs is integrated in time by a suitable Runge-Kutta multistage scheme. Numerical experiments were calculated for flow with Reynolds number equals 1000. Further 3 numerical experiments are presented with different boundary conditions. 1

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