Acoustic Transfer Functions Derived from Finite Element Modeling for Thermoacoustic Stability Predictions of Gas Turbine Engines Design and prediction of thermoacoustic instabilities is a major challenge in aerospace propulsion and the operation of power generating gas turbine engines. This is a complex problem in which multiple physical systems couple together. Traditionally, thermoacoustic models can be reduced to dominant physics which depend only on flame dynamics and acoustics. This is the general approach adopted in this research. The primary objective of this thesis is to describe how to obtain acoustic transfer functions using finite element modeling. These acoustic transfer functions can be coupled with flame transfer functions and other dynamics to predict the thermoacoustic stability of gas turbine engines. Results of this research effort can go beyond the prediction of instability and potentially can be used as a tool in the design stage. Consequently, through the use of these modeling tools, better gas turbine engine designs can be developed, enabling expanded operating conditions and efficiencies. This thesis presents the finite element (FE) methodology used to develop the acoustic transfer functions of the Combustion System Dynamics Laboratory (CSDL) gaseous combustor to support modeling and prediction of thermoacoustic instabilities. In this research, several different areas of the acoustic modeling were addressed to develop a representative acoustics model of the hot CSDL gaseous combustor. The first area was the development and validation of the cold acoustic finite element model. A large part of this development entailed finding simple but accurate means for representing complex geometries and boundary conditions. The cold-acoustic model of the laboratory combustor was refined and validated with the experimental data taken on the combustion rig. The second stage of the research involved incorporating the flame into the FE model and has been referred to in this thesis as hot-acoustic modeling. The hot-acoustic model also required the investigation and characterization of the flame as an acoustic source. The detailed mathematical development for the full reacting acoustic wave equation was investigated and simplified sufficiently to identify the appropriate source term for the flame. It was determined that the flame could be represented in the finite element formulation as a volumetric acceleration, provided that the flame region is small compared to acoustic wavelengths. For premixed gas turbine combustor flames, this approximation of a small flame region is generally a reasonable assumption. Both the high temperature effects and the flame as an acoustic source were implemented to obtain a final hot-acoustic FE model. This model was compared to experimental data where the heat release of the flame was measured along with the acoustic quantities of pressure and velocity. Using these measurements, the hot-acoustic FE model was validated and found to correlate with the experimental data very well. The thesis concludes with a discussion of how these techniques can be utilized in large industrial-size combustors. Insights into stability are also discussed. A conclusion is then presented with the key results from this research and some suggestions for future work. / Master of Science

Yes / Cancer-causing mutations often arise from inappropriate DNA repair, yet acute exposure to DNA damage is widely used to treat cancer. The challenge remains in how to specifically induce excessive DNA damage in cancer cells while minimizing the undesirable effects of genomic instability in noncancerous cells. One approach is the acute exposure to hyperthermia, which suppresses DNA repair and synergizes with radiotherapy and chemotherapy. An exception, however, is the protective effect of hyperthermia on topoisomerase targeting therapeutics. The molecular explanation for this conundrum remains unclear. Here, we show that hyperthermia suppresses the level of topoisomerase mediated single- and double-strand breaks induced by exposure to topoisomerase poisons. We further uncover that, hyperthermia suppresses hallmarks of genomic instability induced by topoisomerase targeting therapeutics by inhibiting nuclease activities, thereby channeling repair to error-free pathways driven by tyrosyl-DNA phosphodiesterases. These findings provide an explanation for the protective effect of hyperthermia from topoisomerase-induced DNA damage and may help to explain the inverse relationship between cancer incidence and temperature. They also pave the way for the use of controlled heat as a therapeutic adjunct to topoisomerase targeting therapeutics.

We use hydrographic and direct velocity observations from two quasi-synoptic cruises in conjunction with a primitive equation linear instability model, to investigate the Brazil Current (BC) downstream change effect between 23°S-30°S on the temporal mixed instabilities properties. The quasi-synoptic data revealed that the BC is ∼400-500 m deep to the north of the so-called Santos Bifurcation (26°S-28°S) and extends down to 1000 m to the south of it. We estimated that the BC receives at least 7 Sv from the Santos Bifurcation, which drastically alters the BC\'s velocity vertical structure and meanders characteristics as it flows poleward. Based on direct velocity measurements, we computed the mixed-instability properties at three different latitudes (24°S, 26°S and 30°S). The instability analysis revealed unstable current systems to mesoscale perturbations with maximum growth rates of 0.12, 0.19 and 0.06 day-1 at 24°S, 26°S and 30°S respectively. The corresponding downstream phase speeds are -0.19, -0.24 and -0.26 m s-1. The analysis of the mean-to-eddy energy conversion terms show that the barotropic instability drains 60-90% less energy from the background state than the baroclinic instability. Nevertheless, the maximum growth rates are at least the double in magnitude when both instabilities occur simultaneously. The topography presents a stabilizing effect for both kind of instabilities along all the BC path. At the vicinities of the Cape Santa Marta (28°S), we explored the the recurrent cyclonic meanders of the BC. Combining a wide range of observations, we provided a overview of such features and the relations between its velocity patterns, the water properties (temperature, salinity, nutrients), chlorophyll-a distribution and the BC variability. The top-bottom quasi-synoptic velocity measurements depicted cyclonic meanders over the continental slope with diameters larger than 100 km and vertically extending to approximately 1500 m depth. Moreover, the observed eddies seems to trap and recirculate a small portion (∼1.5 to 4 Sv) of the BC main flow (-13.16 to -17.89 Sv), which is consisted of Tropical Water (TW), South Atlantic Central Water (SACW), Antarctic Intermediate Water (AAIW) and Upper Circumpolar Deep Water (UCDW). Additionally, we presented observational evidence that the meanders actively influence the transport of nutrient-rich shelf waters to the open ocean enhancing the primary productivity at the photic zone over the continental slope. Satellite imagery show that these cyclonic events occur 5-6 times per year and are generally associated with wave-like perturbations on the flow with mean wavelength of ∼219 km. Finally, Empirical Orthogonal Functions (EOF) analysis computed from an array of mooring lines show that more than half of the along-isobath velocity variance on the continental slope is explained by the BC mesoscale activity. / As propriedades de instabilidade temporal mista da Corrente do Brasil (CB), entre 23°S-30°S, foram investigadas combinando dados hidrográficos e medições diretas de velocide com modelagem numérica. As observações revelaram uma CB com ∼400-500 m de profundidade ao norte da Bifurcação de Santos (26°S-28°S). Em contrapartida, a CB ao sul da bifurcação se mostrou muito mais profunda (> 1000 m) devido ao aporte de aproximadamente 7 Sv de águas em profundidades intermediárias (∼500-1500 m) oriundas do ramo sul da Bifurcação de Santos. Baseado-se nas observações, experimentos numéricos foram conduzidos em três latitudes (24°S, 26°S and 30°S), com o intuito de se estudar as propriedades da instabilidade geofísica da CB. Tais experimentos mostraram que o sistema de correntes é instável para perturbações de mesoescala com taxas de crescimento máximas de 0,12, 0,19 and 0,06 dia-1 nas latitudes de 24°S, 26°S and 30°S, respectivamente. A análise das taxas de transferências de energia das correntes médias para as pertubações revelou que a instabilidade barotrópica é de 60 a 90% menor que a instabilidade baroclínica. No entanto observou-se que as propriedades das instabilidades da BC são altamente sensíveis à presença de instabilidade barotrópica. A topografia demonstrou possuir um efeito estabilizador ao longo de toda trajetória da CB. Ao largo do Cabo de Santa Marta (28°S) os meandros ciclônicos da CB tiveram suas características exploradas do ponto de vista observacional. Combinando uma grande variedade de observações, foi obtido uma visão geral de tais feições, assim como as relações entre seus padrões de velocidade, propriedades da água do mar (temperatura, salinidade, nutrientes), distribuição de clorofila A e a variabilidade da BC. As observações quasi-sinóticas de velocidade em toda a coluna mostraram que os meandros possuem diâmetro superiores à 100 km e extensão vertical de aproximadamente 1500 m. Desta forma, observou-se feições que recirculam uma pequena parte (∼1.5 à 4 Sv) do eixo principal da CB (-13.16 à -17.8 Sv) composta por Água Tropical, Água Central do Atlântico Sul, Água Intermediária Antártica e Água Circumpolar Superior. Além disso, evidências de que tais meandros influenciam ativamente no transporte de águas da Plataforma Continental, ricas em nutrientes, para regiões profundas do Talude Continental foram encontradas. A análise de imagens de satelitárias indicaram que essas feições são efetivamente recorrentes na região e ocorrrem entre 5 a 6 vezes por ano. Para concluir, registros correntográficos indicaram que aproximadamente metade da variância da componente da velocidade ao logo das isóbatas, sobre o talude continental, é devido à atividade de mesoescala da CB.

We use hydrographic and direct velocity observations from two quasi-synoptic cruises in conjunction with a primitive equation linear instability model, to investigate the Brazil Current (BC) downstream change effect between 23°S-30°S on the temporal mixed instabilities properties. The quasi-synoptic data revealed that the BC is ∼400-500 m deep to the north of the so-called Santos Bifurcation (26°S-28°S) and extends down to 1000 m to the south of it. We estimated that the BC receives at least 7 Sv from the Santos Bifurcation, which drastically alters the BC\'s velocity vertical structure and meanders characteristics as it flows poleward. Based on direct velocity measurements, we computed the mixed-instability properties at three different latitudes (24°S, 26°S and 30°S). The instability analysis revealed unstable current systems to mesoscale perturbations with maximum growth rates of 0.12, 0.19 and 0.06 day-1 at 24°S, 26°S and 30°S respectively. The corresponding downstream phase speeds are -0.19, -0.24 and -0.26 m s-1. The analysis of the mean-to-eddy energy conversion terms show that the barotropic instability drains 60-90% less energy from the background state than the baroclinic instability. Nevertheless, the maximum growth rates are at least the double in magnitude when both instabilities occur simultaneously. The topography presents a stabilizing effect for both kind of instabilities along all the BC path. At the vicinities of the Cape Santa Marta (28°S), we explored the the recurrent cyclonic meanders of the BC. Combining a wide range of observations, we provided a overview of such features and the relations between its velocity patterns, the water properties (temperature, salinity, nutrients), chlorophyll-a distribution and the BC variability. The top-bottom quasi-synoptic velocity measurements depicted cyclonic meanders over the continental slope with diameters larger than 100 km and vertically extending to approximately 1500 m depth. Moreover, the observed eddies seems to trap and recirculate a small portion (∼1.5 to 4 Sv) of the BC main flow (-13.16 to -17.89 Sv), which is consisted of Tropical Water (TW), South Atlantic Central Water (SACW), Antarctic Intermediate Water (AAIW) and Upper Circumpolar Deep Water (UCDW). Additionally, we presented observational evidence that the meanders actively influence the transport of nutrient-rich shelf waters to the open ocean enhancing the primary productivity at the photic zone over the continental slope. Satellite imagery show that these cyclonic events occur 5-6 times per year and are generally associated with wave-like perturbations on the flow with mean wavelength of ∼219 km. Finally, Empirical Orthogonal Functions (EOF) analysis computed from an array of mooring lines show that more than half of the along-isobath velocity variance on the continental slope is explained by the BC mesoscale activity. / As propriedades de instabilidade temporal mista da Corrente do Brasil (CB), entre 23°S-30°S, foram investigadas combinando dados hidrográficos e medições diretas de velocide com modelagem numérica. As observações revelaram uma CB com ∼400-500 m de profundidade ao norte da Bifurcação de Santos (26°S-28°S). Em contrapartida, a CB ao sul da bifurcação se mostrou muito mais profunda (> 1000 m) devido ao aporte de aproximadamente 7 Sv de águas em profundidades intermediárias (∼500-1500 m) oriundas do ramo sul da Bifurcação de Santos. Baseado-se nas observações, experimentos numéricos foram conduzidos em três latitudes (24°S, 26°S and 30°S), com o intuito de se estudar as propriedades da instabilidade geofísica da CB. Tais experimentos mostraram que o sistema de correntes é instável para perturbações de mesoescala com taxas de crescimento máximas de 0,12, 0,19 and 0,06 dia-1 nas latitudes de 24°S, 26°S and 30°S, respectivamente. A análise das taxas de transferências de energia das correntes médias para as pertubações revelou que a instabilidade barotrópica é de 60 a 90% menor que a instabilidade baroclínica. No entanto observou-se que as propriedades das instabilidades da BC são altamente sensíveis à presença de instabilidade barotrópica. A topografia demonstrou possuir um efeito estabilizador ao longo de toda trajetória da CB. Ao largo do Cabo de Santa Marta (28°S) os meandros ciclônicos da CB tiveram suas características exploradas do ponto de vista observacional. Combinando uma grande variedade de observações, foi obtido uma visão geral de tais feições, assim como as relações entre seus padrões de velocidade, propriedades da água do mar (temperatura, salinidade, nutrientes), distribuição de clorofila A e a variabilidade da BC. As observações quasi-sinóticas de velocidade em toda a coluna mostraram que os meandros possuem diâmetro superiores à 100 km e extensão vertical de aproximadamente 1500 m. Desta forma, observou-se feições que recirculam uma pequena parte (∼1.5 à 4 Sv) do eixo principal da CB (-13.16 à -17.8 Sv) composta por Água Tropical, Água Central do Atlântico Sul, Água Intermediária Antártica e Água Circumpolar Superior. Além disso, evidências de que tais meandros influenciam ativamente no transporte de águas da Plataforma Continental, ricas em nutrientes, para regiões profundas do Talude Continental foram encontradas. A análise de imagens de satelitárias indicaram que essas feições são efetivamente recorrentes na região e ocorrrem entre 5 a 6 vezes por ano. Para concluir, registros correntográficos indicaram que aproximadamente metade da variância da componente da velocidade ao logo das isóbatas, sobre o talude continental, é devido à atividade de mesoescala da CB.

Reduction of the pollutant emissions is a challenge for the gas turbine industry. A solution to this problem is to employ the low swirl burner which can operate at lower equivalence ratios than a conventional swirl burner. However, flames in the lean regime of combustion are susceptible to flow perturbations and combustion instability. Combustion instability is the coupling between unsteady heat release and combustor acoustic modes where one amplifies the other in a feedback loop. The other method for significantly reducing NOx and CO2 is increasing fuel reactivity, typically done through the addition of hydrogen. This helps to improve the flammability limit and also reduces the pollutants in products by decreasing thermal NOx and reducing CO2 by displacing carbon. In this work, the flammability limits of a low swirl burner at various operating conditions, is studied and the effect of pressure, bulk velocity, burner shape and percent of hydrogen (added to the fuel) is investigated. Also, the flame structure for these test conditions is measured using OH planar laser induced fluorescence and assessed. Also, the OH PLIF data is used to calculate Rayleigh index maps and to construct averaged OH PLIF intensity fields at different acoustic excitation frequencies (45-155, and 195Hz). Based on the Rayleigh index maps, two different modes of coupling between the heat release and the pressure fluctuation were observed: the first mode, which occurs at 44Hz and 55Hz, shows coupling to the flame base (due to the bulk velocity) while the second mode shows coupling to the sides of the flame. In the first mode, the flame becomes wider and the flame base moves with the acoustic frequency. In the second mode, imposed pressure oscillations induce vortex shedding in the flame shear layer. These vortices distort the flame front and generate locally compact and sparse flame areas. The local flame structure resulting from these two distinct modes was markedly different.

High explosive charges when detonated ensue in a flow field characterized by several physical phenomena that include blast wave propagation, hydrodynamic instabilities, real gas effects, fluid mixing and afterburn effects. Solid metal particles are often added to explosives to augment the total impulsive loading, either through direct bombardment if inert, or through afterburn energy release if reactive. These multiphase explosive charges, termed as heterogeneous explosives, are of interest from a scientific perspective as they involve the confluence and interplay of various additional physical phenomena such as shock-particle interaction, particle dispersion, ignition, and inter-phase mass, momentum and energy transfer. In the current research effort, chemical explosions in multiphase environments are investigated using a robust, state-of-the-art Eulerian-gas, Lagrangian-solid methodology that can handle both the dense and dilute particle regimes. Explosions into ambient air as well as into aluminum particle clouds are investigated, and hydrodynamic instabilities such as Rayleigh- Taylor and Richtmyer-Meshkov result in a mixing layer where the detonation products mix with the air and afterburn. The particles in the ambient cloud, when present, are observed to pick up significant amounts of momentum and heat from the gas, and thereafter disperse, ignite and burn. The amount of mixing and afterburn are observed to be independent of particle size, but dependent on the particle mass loading and cloud dimensions. Due to fast response times, small particles are observed to cluster as they interact with the vortex rings in the mixing layer, which leads to their preferential ignition/ combustion. The total deliverable impulsive loading from heterogeneous explosive charges containing inert steel particles is estimated for a suite of operating parameters and compared, and it is demonstrated that heterogeneous explosive charges deliver a higher near-field impulse than homogeneous explosive charges containing the same mass of the high explosive. Furthermore, particles are observed to introduce significant amounts of hydrodynamic instabilities in the mixing layer, resulting in augmented fluctuation intensities and fireball size, and different growth rates for heterogeneous explosions compared to homogeneous explosions. For aluminized explosions, the particles are observed to burn in two regimes, and the average particle velocities at late times are observed to be independent of the initial solid volume fraction in the explosive charge. Overall, this thesis provides useful insights on the role played by solid particles in chemical explosions.

A spectacular instability has been observed in low density round jets when the density ratio of jet fluid to ambient fluid falls below a threshold of approximately 0.6. This phenomenon has been observed in non-buoyant jets of helium in air, heated air jets and heated buoyant jets. The oscillation of the flow near the nozzle is extremely regular and periodic and consists of ring vortices. Even the smaller scale structures that appear downstream exhibit similar regularity. A theory for predicting the onset of this oscillation is based on finding regions of absolute instability from linear stability analysis of parallel flow. However, experiments suggest that the theory is at least incomplete and fortuitous as the oscillation is not a linear process. The present work is to observe and understand the process of regeneration of these oscillations by conducting numerical simulations. Here, two-dimensional, plane jets were simulated because they undergo a qualitatively similar process. A spatial and temporal picture of a heated jet has been obtained numerically. A perturbation expansion was used to obtain a system of conservation laws for compressible flows which is valid for low Mach numbers. The low Mach number approximation removes the high frequency acoustic waves from the flow field. This enables a larger time step to be taken without making the calculation unstable. To ensure that all the scales of motion are properly resolved, calculations were done at a low Reynolds number. The governing equations were discretized in space using second-order finite difference formulas on a staggered grid. Velocity fields were advanced using a second-order Adams-Bashforth explicit scheme and then corrected by solving for pressure such that continuity is satisfied at every time step. The Poisson problem for pressure requires the time derivative of the density which was approximated by a third-order backward difference formula. Gauss-Siedel iteration was used to find the pressure. Several numerical tests were conducted prior to simulations of variable density jets to check the stability and accuracy of the code. Two dimensional driven cavity flow calculations were done as a first test. Then a calculation of a forced, spatially developing, incompressible, plane mixing layer was done to check the time accuracy of the code. After obtaining satisfactory performance of the code for the different test cases, two-dimensional, variable density jets were simulated. Since the plane jet extends ad infinitum in the streamwise direction, a sufficiently large domain was used to capture all the relevant physics in the downstream regions of the jet. An advective boundary condition was imposed at the exit plane. Rigid, slipwall conditions were employed to prescribe lateral boundary conditions. A 2-D, incompressible plane jet was simulated first. The jet profile was approximated by two hyperbolic tangent shear layers. The most unstable mode of the inviscid shear layer for this profile, along with its first and second harmonics, was imposed on the velocity profile at the inlet plane. The amplitude of oscillation of the harmonics was chosen so as to provide sufficient energy in the perturbation to accelerate the growth of the layer. No explicit phase lag was introduced in the perturbation. The flow was allowed to develop long enough to wash out the effect of the initial condition. The results obtained for this case indicate that experimentally realized phenomena such as vortex pairing were captured in this simulation. Furthermore, to check the convective nature of instability of the incompressible jet, the forcing at the inlet plane was turned off. The disturbances were gradually convected downstream, out of the computational domain. Next, two-dimensional heated, non-buoyant jets were studied numerically. The effects of the ratio of jet density to ambient density S, the velocity ratio R, and jet width W, on the near field behavior of an initial laminar jet and the regeneration mechanism of the self-sustaining vortices were explored. The theory based on domain of absolute/convective instability identifies these three parameters. No initial perturbation was necessary to start roll-up of the shear layer. For certain choices, e.g., S= 0.75, R = 20, W =10.5, self-sustaining oscillations appeared spontaneously, and these cycles repeated for very long simulation intervals. Waviness on the jet shear layers grow and roll-up into vortices as in constant density shear layers. But unlike the incompressible plane jet, these vortices grow much larger and mixes more with the surrounding fluid. As these vortices evolve, packets of fluid break away as trailing legs similar to side jet expulsions observed in round jets and plumes. The growing vortices disturb the upstream shear layer. Consistently with linear theory, which predicts absolute instability for these parameters, these disturbances are able to grow and roll up. If these disturbances travelled faster than the downstream vortices, it would not be possible for the cycle to repeat. With sufficient shear between the co-flowing streams (R not too small), the entire regeneration process was found to begin from roughly the same streamwise location. Furthermore, it is the symmetric, varicose mode which occurs. At a slightly larger density ratio (S = 0.8, R = 10), self-sustaining oscillations appeared, but each new cycle began slightly farther downstream. It seems likely that these values are close to the boundary in parameter space between self-sustained oscillatory and convectively unstable behaviors. Jet width also influences the selection of these two behaviors. When jet width was reduced, W = 6, even for S = 0.75,R = 20, each new cycle began to shift downstream. For larger jet width (W = 12.3), self-sustaining oscillations occur but the response is now as an asymmetric sinuous mode after a short initial varicose mode. The detailed processes that have now been revealed in plane jets should serve as guidelines for the study of such processes in the technologically more important round jets.

A lot has changed since that day on December 17, 1903 when the Wright brothers made the first powered manned flight. Even though the concepts behind flying are unaltered, appearance of stat-of-the-art modern aircrafts has undergone a massive evolution. This is mainly owed to our deeper understanding of how to harness and optimize the interaction between fluid flows and aircraft bodies. Flow passing over wings and different junctions on an aircraft faces numerous local features, for instance, acceleration or deceleration, laminar or turbulent state, and interacting boundary layers. In our study we aim to characterize some of these flow features and their physical roles. Primarily, stability characteristics of flow over a wing subject to a negative pressure gradient are studied. This is a common condition for flows over swept wings. Part of the current numerical study conforms to existing experimental studies where a passive control mechanism has been tested to delay laminarturbulent transition. The same flow type has also been considered to study the receptivity of three-dimensional boundary layers to freestream turbulence. The work entails investigation of effects of low-level freestream turbulence on crossflow instability, as well as interaction with micron-sized surface roughness elements. Another common three-dimensional flow feature arises as a resultof stream-lines passing through a junction, the so-calledcorner-flow. For instance, thisflow can be formed in the junction between the wing and fuselage on aplane.A series of direct numerical simulations using linear Navier-Stokes equationshave been performed to determine the optimal initial perturbation. Optimalrefers to perturbations which can gain the maximum energy from the flow overa period of time. In other words this method seeks to determine theworst-casescenario in terms of perturbation growth. Here, power-iterationtechnique hasbeen applied to the Navier-Stokes equations and their adjoint to determine theoptimal initial perturbation. Recent advances in super-computers have enabled advance computational methods to increasingly contribute to design of aircrafts, in particular for turbulent flows with regions of separation. In this work we investigate theturbulentflow on an infinite wing at a moderate chord Reynolds number of Re= 400,000 using a well resolved direct numerical simulation. A conventional NACA4412 has been chosen for this work. The turbulent flow is characterizedusing statistical analysis and following time history data in regions with interesting flow features. In the later part of this work, direct numerical simulation has been chosen as a tool to mainly investigate the effect of freestream turbulence on the transition mechanism of flow from laminar to turbulent around a turbine blade. / <p>QC 20151125</p>

Thesis (MScEng (Industrial Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Any growing system is by definition in a transient phase, and consequently exhibits transient-, non-steady state-, unstable behaviour. Accordingly, this form of instability (systemic growth) is by and large conducive to the prosperity of said system. From a Control Systems perspective, transient behaviour that is not subjected to an adequate damping mechanism, does however lead to unavoidable adverse instability. Within the context of business systems, four distinct, yet interconnected entities (raw material, market demand, internal capability to deliver, and cash funds) serve as the damping mechanism to protect companies as a whole, against variation in any of the aforementioned entities. The level of damping afforded by the aforementioned entities is governed by its ability to decouple variation in one entity from undue variation in other entities. The higher the level of instability, the higher the associated level of damping required. The Thesis focuses on core instigators of negative instability within the context of Fast Growing Manufacturing Companies (FGMCs), and ultimately proposes a solution to prevent the regression from positive instability towards negative instability. / AFRIKAANSE OPSOMMING: Enige groeiende stelsel is per definisie in ’n oorgangsfase en vertoon gevolglik verbygaande-, niestabiele oorgangsgedrag. Dienooreenkomstig is hiérdie vorm van onstabiliteit (sistemiese groei) in die algemeen bevorderlik vir die welvaart van genoemde stelsel. Vanuit ’n Beheerstelsels oogpunt, lei oorgangsgedrag wat nie onderworpe is aan ’n voldoende dempingsmeganisme nie, egter tot onafwendbare negatiewe onstabiliteit. Binne ’n besigheidstelsel konteks dien vier afsonderlike, tog onderlingverbonde entiteite (roumateriaal, markaanvraag, interne bekwaamheid om te lewer, en kontantfondse) as die dempingsmeganisme om besighede holisties te beskerm teen variasie in enige van die voorgenoemde entiteite. Die dempingsvlak wat deur die voorgenoemde entiteite gegun word, word bepaal deur dié se vermoë om variasie in een entiteit te ontkoppel van variasie in ander entiteite. Hoe hoër die vlak van onstabiliteit, hoe hoër die vereiste vlak van demping. Die Tesis fokus op kern aanstigters van negatiewe onstabiliteit binne die konteks van VinnigGroeiende Vervaardigingsbesighede en stel uiteindelik ’n oplossing voor om die regressie vanaf positiewe onstabiliteit na negatiewe onstabiliteit te verhoed.

La finalité de cette thèse est de fournir une meilleure compréhension de la turbulence homogène anisotrope soumise à un forçage barocline. À cette fin, nous utilisons une approche numérique pseudo-spectrale basée sur la transformation de Rogallo. L’utilisation d’un tel algorithme nous permet de considérer une asymétrie des fonctions de probabilité en faveur des évènements négatifs est observée. Le lien entre la distribution de vorticité potentielle et celle d’un scalaire passif est également étudié. Il est montré qu’à faible nombre de Richardson, c’est le mode vortex (à vorticité potentielle nulle) qui contient les plus importantes fuctuations de scalaire. Un écoulement homogène dans les trois directions de l’espace. Plusieurs simulations numériques directes (DNS) sont effectuées dans un contexte assez proche des écoulements géophysiques que l’on retrouve entre autre dans la stratosphère, où un gradient constant de vitesse zonale vient se coupler à un gradient constant de densité dans un repère tournant. Les résultats obtenus s’articulent autour de quatre axes principaux. Tout d’abord, une étude linéaire à temps fini est présentée en vue de compléter les résultats existants sur la dynamique linéaire asymptotique. La solution linéaire est décomposée en une partie ‘onde’ (qui se propage) et une partie dite ‘vortex’(stationnaire). L’étude analytique est complétée par un modèle synthétique de turbulence (Kinematic Simulation ou KS) basé sur la théorie de la distorsion rapide(RDT). Nous montrons qu’une distribution initiale non nulle de vorticité potentielle linéarisée peut conduire à d’importantes croissances transitoires. Ce résultat pourrait s’étendre à des modélisations du climat ou météorologique, où la distribution initiale de vorticité potentielle semble avoir autant d’importance que la distribution initiale de température ou de vitesse. Ensuite, nous consacrons une partie de notre étude à l’analyse paramétrique et à la stabilité de l’écoulement. Plusieurs DNS sont effectuées pour différents taux de rotation et stratification. Le diagramme de stabilité obtenu montre que pour de faibles taux de rotation, la limite de stabilité est identique à celle connue des écoulements sans rotation. À plus faible nombre de Rossby — lorsque la baroclinicité devient importante — la limite linéaire de stabilité Ri = 1 relative à l’instabilité symétrique est confirmée. La coexistance de l’instabilité barocline avec l’instabilité symétrique est également clarifiée. Une analyse énergétique détaillée mène à la conclusion suivante : la stratification doit être suffisamment importante (Ri ' 1) pour que l’instabilité barocline soit dominante i.e. que la conversion d’énergie potentielle soit la source principale d’énergie cinétique turbulente. Dans le cas contraire, l’instabilité symétrique — qui tire son énergie de l’énergie cinétique de l’écoulement moyen et non de son énergie potentielle — domine la dynamique de l’écoulement. Le troisième axe d’étude concerne la turbulence à proprement parler. En conséquence de l’ajustement géostrophique, le vent thermique force la turbulence d’une manière naturelle, en opposition à d’autres méthodes de forçage stochastique. L’émergence de structures dans le contexte barocline est approfondie. Des statistiques Euleriennes sont présentées afin de fournir une caractérisation fine de l’anisotropie de l’écoulement. Enfin, nous étendons notre étude à la caractérisation de la vorticité potentielle turbulente. Les fonctions de probabilité de la vorticité potentielle d’Ertel montrent que des anomalies sont présentes dans les configurations instables. En particulier, une asymétrie des fonctions de probabilité en faveur des évènements négatifs est observée. Le lien entre la distribution de vorticité potentielle et celle d’un scalaire passif est également étudié. Il est montré qu’à faible nombre de Richardson, c’est le mode vortex (à vorticité potentielle nulle) qui contient les plus importantes fuctuations de scalaire. / The main objective of this thesis is to provide a better understandingof homogeneous turbulence dynamics under an external baroclinic forcing.To achieve this goal, we use a pseudo-spectral code based on the Rogallo transformation.The use of such an algorithm allows to assume homegeneity in the threespatial directions. Direct Numerical Simulations (DNS) are done in a context representativeof geophysical baroclinic flows in the middle atmosphere: superpositionof a uniform mean zonal flow with stable vertical stratification and frame rotation.The results we obtained are then presented along four axes.First, a finite-time linear analysis is done to complete previous asymptotic results.The linearized flow is decomposed into a propagating (wave) and stationary (vortex)part. The analytical work is completed by a Kinematic Simulation (KS) modelbased on Rapid Distortion Theory (RDT). It is shown that the linearized potentialvorticity mode can produce dramatic transient growth of the kinetic energy if nonzeroinitially. The consequence of such a result is then of capital interest in climatemodelling, where the initial distribution of potential vorticity seems to have moreimportance than other eulerian quantities (temperature or velocity).The second axis is dedicated to a parametric analysis of the flow stability. SeveralDNS are done for different rotation and stratification rates. The derived stabilitydiagram shows that at low rotation rates, the stability bound for purely shearedstratifiedflows is recovered. At higher rotation rates — when baroclinicity is dominant— the linear bound for the so-called symmetric instability is confirmed. Thecoexistence of baroclinic and symmetric instabilies is also clarified. A complete energeticanalysis leads to the conclusion that stratification must be sufficiently highto enhance potential energy release through baroclinic instability. If not, symmetricinstability — driving its energy from the kinetic energy of the mean flow and notfrom the potential energy of the mean flow — is found to dominate the dynamics.The third axis is devoted to a characterisation of homogeneous turbulence submittedto an external baroclinic forcing. As coming from the geostrophic adjustment,the thermal shear allows an organic forcing of turbulence, in opposition to ad-hocarticificial forcing. The structures associated with the simultaneous presence of rotation,stratification and shear are investigated. Eulerian statistics are gathered togive a sharp characterisation of the spatial anisotropy of the flow.Finally, we open our work to the study of turbulent potential vorticity. Probabilitydensity functions of Ertel’s potential vorticity show that potential vorticityanomalies are present in unstable configurations. In particular, an asymmetry ofthe probability density functions toward negative events is observed. An attemptto link potential vorticity dynamics with scalar mixing in baroclinic flows is donethrough joint probability functions analysis.