Unter atmosphärischen Zirkulationsregimen versteht man bevorzugte quasi-stationäre Zustände der atmosphärischen Zirkulation auf der planetaren Skala, die für eine bis mehrere Wochen persistieren können. Klimaänderungen, ob natürlich entstanden oder anthropogen verursacht, äußern sich in erster Linie durch Änderungen der Auftrittswahrscheinlichkeiten der natürlichen Regime. <br><br> In der vorliegenden Arbeit wurden dynamische Mechanismen des Regimeverhaltens und der dekadischen Klimavariabilität der Atmosphäre bei Abwesenheit zeitlich veränderlicher externer Einflussfaktoren untersucht. Das Hauptwerkzeug dafür war ein quasi-geostrophisches Dreischichtenmodell der winterlichen atmosphärischen Zirkulation auf der Nordhemisphäre, das eine spektrale T21-Auflösung, einen orographischen und einen zeitlich konstanten thermischen Antrieb mit nicht-zonalen Anteilen besitzt. Ein solches Modell vermag großskalige atmosphärische Strömungsvorgänge außerhalb der Tropen mit einiger Genauigkeit zu simulieren. Nicht berücksichtigt werden Feuchteprozesse, die Wechselwirkung der Atmosphäre mit anderen Teilen des Klimasystems sowie anthropogene Einflüsse. <br><br> Für das Dreischichtenmodell wurde ein automatisiertes, iteratives Verfahren zur Anpassung des thermischen Modellantriebs neu entwickelt. Jede Iteration des Verfahrens besteht aus einer Testintegration des Modells, ihrer Auswertung, dem Vergleich der Ergebnisse mit den NCEP-NCAR-Reanalysedaten aus den Wintermonaten Dezember, Januar und Februar sowie einer auf diesem Vergleich basierenden Antriebskorrektur. Nach Konvergenz des Verfahrens stimmt das Modell sowohl bezüglich des zonal gemittelten Klimazustandes als auch bezüglich der zeitgemittelten nicht-zonalen außertropischen diabatischen Erwärmung nahezu perfekt mit den wintergemittelten Reanalysedaten überein. <br><br> In einer 1000-jährigen Simulation wurden die beobachtete mittlere Zirkulation im Winter sowie ihre Variabilität realitätsnah reproduziert, insbesondere die Arktische Oszillation (AO) und ihre vertikale Ausdehnung. Der AO-Index des Modells weist deutliche dekadische Schwankungen auf, die allein durch die interne Modelldynamik bedingt sind. Darüber hinaus zeigt das Modell ein Regimeverhalten, das gut mit den Beobachtungsdaten übereintimmt. Es besitzt ein Regime, das in etwa der negativen Phase der Nordatlantischen Oszillation (NAO) entspricht und eines, das der positiven Phase der AO ähnelt. <br><br> Eine weit verbreitete Hypothese ist die näherungsweise Übereinstimmung zwischen Regimen und stationären Lösungen der Bewegungsgleichungen. In der vorliegenden Arbeit wurde diese Hypothese für das Dreischichtenmodell überprüft, mit negativem Resultat. Es wurden mittels eines Funktionalminimierungsverfahrens sechs verschiedene stationäre Zustände gefunden. Diese sind allesamt durch eine äußerst unrealistische Zirkulation gekennzeichnet und sind daher weit vom Modellattraktor entfernt. Fünf der sechs Zustände zeichnen sich durch einen extrem starken subtropischen Jet in der mittleren und obereren Modellschicht aus. <br><br> Da die Ursache des Regimeverhaltens des Dreischichtenmodells nach wie vor unklar war, wurde auf ein einfacheres Modell, nämlich ein barotropes Modell mit T21-Auflösung zurückgegriffen. Für die Anpassung des Oberflächenantriebs wurde eine modifizierte Form der iterativen Prozedur verwendet. Die zeitgemittelte Zirkulation des barotropen Modells stimmt sehr gut mit der zeitlich und vertikal gemittelten Zirkulation des Dreischichtenmodells überein. Das dominierende räumliche Muster der Variabilität besitzt eine AO-ähnliche Struktur. Zudem besitzt das barotrope Modell zwei Regime, die näherungsweise der positiven und negativen Phase der AO entsprechen und somit auch den Regimen des Dreischichtenmodells ähneln. Im Verlauf der Justierung des Oberflächenantriebs konnte beobachtet werden, dass die zwei Regime des barotropen Modells durch die Vereinigung zweier koexistierender Attraktoren entstanden. Der wahrscheinliche Mechanismus der Attraktorvereinigung ist eine Randkrise eines der beiden Attraktoren, gefolgt von einer explosiven Bifurkation des anderen Attraktors. <br><br> Es wird die Hypothese aufgestellt, dass der beim barotropen Modell vorgefundene Mechanismus der Regimeentstehung für atmosphärische Zirkulationsmodelle mit realitätsnahem Regimeverhalten Allgemeingültigkeit besitzt. Gestützt wird die Hypothese durch vier Experimente mit dem Dreischichtenmodell, bei denen jeweils der Parameter der Bodenreibung verringert und die Antriebsanpassung wiederholt wurde. Bei diesen Experimenten erhöhte sich die Persistenz und die Separiertheit der Regime bei abnehmender Reibung drastisch und damit auch der Anteil dekadischer Zeitskalen an der Variabilität. Die Zunahme der Persistenz der Regime ist charakteristisch für die Annäherung an eine inverse innere Krise, deren Existenz aber nicht nachgewiesen werden konnte. / Preferred quasi-stationary states of the planetary-scale atmospheric circulation, which may persist for one or several weeks, are referred to as atmospheric circulation regimes. Climate variations, either natural or anthropogenic, manifest themselves mainly in changes of the frequencies of occurrence of the natural regimes. <br><br> In the presented work, dynamical mechanisms of regime behavior and decadal climate variability of the atmosphere in absence of time-varying external forcing factors have been examined using a quasi-geostrophic three-level model of the wintertime atmospheric circulation over the northern hemisphere. This model has spectral T21 resolution, an orographic and a time-constant thermal forcing including non-zonal components. Such kind of a model is able to simulate large-scale extratropical atmospheric processes with reasonable accuracy. However, moisture processes, the interaction between the atmosphere and other parts of the climate system, and anthropogenic influences are not accounted for. <br><br> For the three-level model, a novel, automated, iterative procedure for the tuning of the thermal forcing has been developed. Every iteration of the procedure consists of a model test run, its evaluation, the comparison of the results with NCEP-NCAR reanalysis data for the winter months December, January, and February, and a forcing correction based on this comparison. After convergence of the procedure, the model matches the reanalysis data almost perfectly, as far as it concerns the zonal mean climate state and the time-mean non-zonal extratropical diabatic heating. <br><br> In a 1000-year simulation, the observed time-mean circulation in winter as well as its variability have been reproduced with considerable realism, in particular the Arctic Oscillation (AO) and its deep vertical extent. The modeled AO index exhibits pronounced decadal variations, exclusively caused by internal model dynamics. Furthermore, the model's regime behavior is in good agreement with observations. It possesses one regime resembling the negative phase of the North Atlantic Oscillation (NAO) and another resembling the positive phase of the AO. <br><br> A well-known hypothesis is the approximate correspondence between regimes and stationary solutions of the equations of motion. In the presented work, this hypothesis has been checked for the three-level model, but with negative result. Using a functional minimization method, six steady states have been found. All of them correspond to an extremely unrealistic circulation, and thus they are far away from the model's attractor. Five of the six steady states are characterized by a strongly exaggerated subtropical jet in the middle and upper model level. <br><br> As the origin of regime behavior was still unclear, a simpler model, namely a T21 barotropic model, has been reverted to. For the adaptation of the surface forcing, a modified version of the tuning procedure has been applied. The time-mean circulation of the barotropic model matches the temporally and vertically averaged circulation of the three-level model very well. The dominant spatial pattern of variability has an AO-like structure. Furthermore, the barotropic model possesses two regimes which approximately correspond to the positive and negative AO phase and therefore resemble the regimes of the three-level model. During the tuning of the surface forcing it has been observed that the two regimes of the barotropic model have emerged from the unification of two coexisting attractors. The mechanism responsible for this attractor merging is probably a boundary crisis of one of these attractors, followed by an explosive bifurcation of the other attractor. <br><br> It is hypothesized that the mechanism of regime genesis found in the barotropic model is universally valid for atmospheric circulation models with realistic regime behavior. This hypothesis is supported by four experiments with the three-level model, where the surface friction parameter has been decreased and the tuning procedure has been repeated, respectively. In these experiments, the persistence and separation of the regimes increases dramatically with decreasing friction, and thereby the fraction of decadal-scale variability. The increase of regime persistence is characteristic of approaching an inverse interior crisis, the existence of which, however, could not be proven.

A prestudy indicated superior accuracy and convergence properties of apseudo-spectral method compared to a spline-based method implemented byCòrdoba et al. in 2005 when solving the &amp;#945;-patches problem. In this thesis wefurther investigate the numerical properties of the pseudo-spectral method and makeit more robust by implementing the Nonequispaced Fast Fourier Transform. Wepresent a more detailed overview and analysis of the pseudo-spectral method and the&amp;#945;-patches problem in general and conclude that the pseudo-spectral method issuperior in regards to accuracy in periodic settings.

This thesis describes a combined model and laboratory investigation of the generation and mutual interactions of fluid waves whose characteristic scales differ by an order of magnitude or more. The principal aims are to study how waves on one scale can generate waves on another, much shorter scale, and to examine the subsequent nonlinear feedback of the short waves on the long waves. The underlying motive is to better understand such interactions in rotating, stratified, planetary fluids such as atmospheres and oceans. The first part of the thesis describes a laboratory investigation using a rotating, two-layer annulus, forced by imposing a shear across the interface between the layers. A method is developed for making measurements of the two-dimensional interface height field which are very highly-resolved both in space and time. The system's linear normal modes fall into two distinct classes: 'slow' waves which are relatively long in wavelength and intrinsic period, and 'fast' waves which are much shorter and more quickly-evolving. Experiments are performed to categorize the flow at a wide range of points in the system's parameter space. At very small background rotation rates, the interface is completely devoid of waves of both types. At higher rates, fast modes only are generated, and are shown to be consistent with the Kelvin-Helmholtz instability mechanism based on a critical Richardson number. At rotation rates which are higher still, baroclinic instability gives rise to the onset of slow modes, with subsequent localized generation of fast modes superimposed in the troughs of the slow waves. In order to examine the generation mechanism of these coexisting fast modes, and to assess the extent of their impact upon the evolution of the slow modes, a quasi-geostrophic numerical model of the laboratory annulus is developed in the second part of the thesis. Fast modes are filtered out of the model by construction, as the phase space trajectory is confined to the slow manifold, but the slow wave dynamics is accurately captured. Model velocity fields are used to diagnose a number of fast wave radiation indicators. In contrast to the case of isolated fast waves, the Richardson number is a poor indicator of the generation of the coexisting fast waves that are observed in the laboratory, and so it is inferred that these are not Kelvin-Helmholtz waves. The best indicator is one associated with the spontaneous emission of inertia-gravity waves, a generalization of geostrophic adjustment radiation. A comparison is carried out between the equilibrated wavenumbers, phase speeds and amplitudes of slow waves in the laboratory (which coexist with fast modes), and slow waves in the model (which exist alone). There are significant differences between these wave properties, but it is shown that these discrepancies can be attributed to uncertainties in fluid properties, and to model approximations apart from the neglect of fast modes. The impact of the fast modes on the slow modes is therefore sufficiently small to evade illumination by this method of inquiry. As a stronger test of the interaction, a stochastic parameterization of the inertia-gravity waves is included in the model. Consistent with the laboratory/model intercomparison, the parameterized fast waves generally have only a small impact upon the slow waves. However, sufficiently close to a transition curve between two different slow modes in the system's parameter space, it is shown that the fast modes can exert a dominant influence. In particular, the fast modes can force spontaneous transitions from one slow mode to another, due to the phenomenon of stochastic resonance. This finding should be of interest to the meteorological and climate modelling communities, because of its potential to affect model reliability.

Denomina-se Sistema Corrente do Brasil (CB) ao sistema de correntes de contorno oeste formados pela CB, fluindo para sul-sudoeste, e Corrente de Contorno Intermediária (CCI), fluindo para norte-nordeste, associado aos meandros e vórtices. O sistema bordeja a margem continental brasileira sudeste ao longo de 1200-1800 m. A investigação da dinâmica das ondas baroclínicas de vorticidade superpostas ao Sistema Corrente do Brasil é conduzida através exclusivamente de análise de dados hidrográficos de dois cruzeiros de meso-escala (verão e inverno de 1993) do projeto Circulação Oceânica da Região Oeste do Atlântico Sul - COROAS, a componente brasileira do World Ocean Circulation Experiment - WOCE. Estes cruzeiros foram realizados na porção central do Embaiamento de São Paulo (\'23,5 GRAUS\' - \'27 GRAUS\'S). Objetivando-se a aplicação do Método Dinâmico, estimativa quantitativa de um Nível de Referência (NR) é conduzida comparando-se duas metodologias diferentes e independentes. A primeira utiliza o fato de que a CB transporta Água Tropical (AT) e Água Central do Atlântico Sul (ACAS) e de que a CCI transporta dominantemente Água Intermediária Antártica (AIA). Aplica-se então um Critério Termodinâmico, no qual a interface que separa ACAS e AIA é estimada para os dois cruzeiros via aplicação dos Teoremas de Shtokman. A outra metodologia consiste na obtenção de padrões verticais de velocidade baroclínica absoluta a partir de simulações numéricas com a versão seccional do Princenton Ocean Model - POM inicializados com 14 campos termohalinos interpolados a partir dos dados - é o Critério Dinâmico. Os dois critérios apresentam resultado médio que difere apenas cerca de 7 dbar um do outro. Assim, adota-se valor de 480 dbar como NR para os cálculos geostróficos como nível isobárico que demarca a interface média entre CB e CCI. Mapas de função de corrente geostrófica são gerados através de mapeamento objetivo. Tais mapas apresentam evidências inequívocas de que os ciclones e anticiclones, observados nos experimentos de verão e inverno de 1993, são estruturas de vórtices associadas a meandros do Sistema CB. Este aparecem como estruturas vorticais postadas em lados diametralmente opostos ao eixo da CB: ciclones no lado costeiro, e anticiclones no lado oceânico. A variação vertical das estruturas dos meandros e a existência de uma única inversão de sentido permite comprovar e concluir que são ondas baroclínicas de primeiro modo, corroborando especulações presentes na literatura. A construção de um modelo quase-geostrófico de duas camadas para um oceano não-viscoso no plano \'beta\' e de fundo plano permite a realização de análise de vorticidade potencial. Tal análise permite concluir que o campo de vorticidade básico devido à CB suplanta o planetário e que estas ondas baroclínicas são ondas que devem sua existência ao cisalhamento vertical e horizontal da corrente. A variação frontal em vorticidade potencial baroclínica do Sistema CB é de \'1,7x10 POT.-5 s POT. -1\'. A dominãncia do termo da vorticidade de estiramento, que responde por 60% da variação de vorticidade na frente, permite estabelecer que as ondas capturadas na malha hidrográfica são ondas longas dentro da classe de meso-escala. O princípio de conservação de vorticidade potencial é invocado numa análise que envolve a superposição dos campos de vorticidade potencial e função de corrente para a primeira camada. Esta análise apresenta tanto evidências robustas de propagação das ondas baroclínicas quanto indícios de crescimento do meandro ciclônico, ou seja, de processo de instabilidade. Face aos achados das análises anteriores, teoria linear e método das perturbações são utilizados para obter uma relação de dispersão para as ondas baroclínicas da CB. Esta relação é dependente da velocidade da CB e do gradiente de vorticidade potencial através da corrente / The Brazil Current System is formed by two western boundary currents that flow along the Southeast Brazil continental margin from surface to 1200-1800 m deep. These two currents are the southward-flowing Brazil Current (BC) and the northward-flowing Intermediate Western Boundary Current (IWBC). The investigation of the dynamics of the barociinic vorticity waves superimposed to the BC system is conducted in this work solely from hydrographic data anaiysis and manipulation from two oceanographic meso-scale surveys that were part of the COROAS Project, the Brazilian arm of the Worid Ocean Circulation Experiment. These two cruises sampled the central portion of the São Paulo Bight (23,5°- 27°S) in the summer and winter seasons of 1993. As it was intended to appiy the classical Dynamic Method to the data, a quantitative estimate of the reference levei (RL) is conducted through the comparison of two different and independent methodoiogies. The first uses the previous knowiedge that the BC transports Tropical Water and South Atlantic Central Water (SACW) as well as that the IWBC transports mainly Antarctic Intermediate Water (AAIW). This method, referred here as the Thermodynamic Criterion applies the Shtokman theorems to estimate the interface depth between SACW and AAIW. The second methodology, designated here as the Dynamic Criterion, consists of modeiing absolute baroclinic velocities for all 14 hydrographic transects using the sectional version of the Princeton Ocean Model. The results of the two methods differ oniy in 7 dbar and a RL of 480 dbar is adopted as to represent the average interface isobaric level between BC and IWBC in the following geostrophic calculations. Horizontal distributions of geostrophic stream function are generated using objective mapping. These distributions present unequivocal evidences of cyclonic and anticyclonic structures in both Summer and Winter 1993 cruises. These features are associated to meanders of the BC System. They are depicted in opposing sides of the current core. The cyclone is seen in the BC coastal side as the anticyclone is placed in its oceanic side. The vertical variation of these pattems with a single flow direction inversion confirms that these vortical features are part of a first baroclinic mode wave, which corroborates previous speculations found in the literature. In order to pursue a potential vorticity analysis, a data-derived two-layer quasi-geostrophic model is built assuming an invicid flat-bottomed ocean in the 3-plane. This analysis allowed to conclude that the basic vorticity field associated with both horizontal and vertical shear of the boundary currents are responsible for the baroclinic wave existence. The planetary vorticity gradient is one order of magnitude lower. The frontal variation in baroclinic potential vorticity is 1,7 x i0 s1. The dominance of the stretching vorticity, which accounts for 60% of the gradient variation, leads to classify these oscillatory motions as long meso-scale waves. The potential vorticity conservation principle is invoked on an analysis that consists of superimposing the first layer quasi-gesotrophic potential vorticity and geostrophic stream funtion maps. This analysis revealed that the baroclinic waves are propagating as well as evidences of meander growth, an indication of a possible geophysical instability mechanism, are seen. Given the findings of the previous analyses, linear theory and the perturbation method are used to derive a dispersion relation for the BC System first mode baroclinic waves. The wave frequency is function of the BC velocity as well as the potential vorticity cross-stream gradient.

Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasi-geostrophic turbulence.The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of twodimensionaland quasi-geostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascades in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasi-geostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the sensitivity toan infrared Reynolds number in the spectral scaling of the energy spectrumin the inverse energy cascade range, and the validation of Charney’s predictionson the dynamics of quasi-geostrophic turbulence. It has also been shownthat the scaling of the energy spectrum in the enstrophy cascade is insensitiveto intermittency in higher order statistics, but that corrections apply to the”universal” Batchelor-Kraichnan constant, as a consequence of large-scale dissipationanomalies following a classical remark by Landau (Landau &amp; Lifshitz1987). Another finding is that the inverse energy cascade is maintained bynonlocal triad interactions, which is in contradiction with the classical localityassumption. / QC 20101029

Denomina-se Sistema Corrente do Brasil (CB) ao sistema de correntes de contorno oeste formados pela CB, fluindo para sul-sudoeste, e Corrente de Contorno Intermediária (CCI), fluindo para norte-nordeste, associado aos meandros e vórtices. O sistema bordeja a margem continental brasileira sudeste ao longo de 1200-1800 m. A investigação da dinâmica das ondas baroclínicas de vorticidade superpostas ao Sistema Corrente do Brasil é conduzida através exclusivamente de análise de dados hidrográficos de dois cruzeiros de meso-escala (verão e inverno de 1993) do projeto Circulação Oceânica da Região Oeste do Atlântico Sul - COROAS, a componente brasileira do World Ocean Circulation Experiment - WOCE. Estes cruzeiros foram realizados na porção central do Embaiamento de São Paulo (\'23,5 GRAUS\' - \'27 GRAUS\'S). Objetivando-se a aplicação do Método Dinâmico, estimativa quantitativa de um Nível de Referência (NR) é conduzida comparando-se duas metodologias diferentes e independentes. A primeira utiliza o fato de que a CB transporta Água Tropical (AT) e Água Central do Atlântico Sul (ACAS) e de que a CCI transporta dominantemente Água Intermediária Antártica (AIA). Aplica-se então um Critério Termodinâmico, no qual a interface que separa ACAS e AIA é estimada para os dois cruzeiros via aplicação dos Teoremas de Shtokman. A outra metodologia consiste na obtenção de padrões verticais de velocidade baroclínica absoluta a partir de simulações numéricas com a versão seccional do Princenton Ocean Model - POM inicializados com 14 campos termohalinos interpolados a partir dos dados - é o Critério Dinâmico. Os dois critérios apresentam resultado médio que difere apenas cerca de 7 dbar um do outro. Assim, adota-se valor de 480 dbar como NR para os cálculos geostróficos como nível isobárico que demarca a interface média entre CB e CCI. Mapas de função de corrente geostrófica são gerados através de mapeamento objetivo. Tais mapas apresentam evidências inequívocas de que os ciclones e anticiclones, observados nos experimentos de verão e inverno de 1993, são estruturas de vórtices associadas a meandros do Sistema CB. Este aparecem como estruturas vorticais postadas em lados diametralmente opostos ao eixo da CB: ciclones no lado costeiro, e anticiclones no lado oceânico. A variação vertical das estruturas dos meandros e a existência de uma única inversão de sentido permite comprovar e concluir que são ondas baroclínicas de primeiro modo, corroborando especulações presentes na literatura. A construção de um modelo quase-geostrófico de duas camadas para um oceano não-viscoso no plano \'beta\' e de fundo plano permite a realização de análise de vorticidade potencial. Tal análise permite concluir que o campo de vorticidade básico devido à CB suplanta o planetário e que estas ondas baroclínicas são ondas que devem sua existência ao cisalhamento vertical e horizontal da corrente. A variação frontal em vorticidade potencial baroclínica do Sistema CB é de \'1,7x10 POT.-5 s POT. -1\'. A dominãncia do termo da vorticidade de estiramento, que responde por 60% da variação de vorticidade na frente, permite estabelecer que as ondas capturadas na malha hidrográfica são ondas longas dentro da classe de meso-escala. O princípio de conservação de vorticidade potencial é invocado numa análise que envolve a superposição dos campos de vorticidade potencial e função de corrente para a primeira camada. Esta análise apresenta tanto evidências robustas de propagação das ondas baroclínicas quanto indícios de crescimento do meandro ciclônico, ou seja, de processo de instabilidade. Face aos achados das análises anteriores, teoria linear e método das perturbações são utilizados para obter uma relação de dispersão para as ondas baroclínicas da CB. Esta relação é dependente da velocidade da CB e do gradiente de vorticidade potencial através da corrente / The Brazil Current System is formed by two western boundary currents that flow along the Southeast Brazil continental margin from surface to 1200-1800 m deep. These two currents are the southward-flowing Brazil Current (BC) and the northward-flowing Intermediate Western Boundary Current (IWBC). The investigation of the dynamics of the barociinic vorticity waves superimposed to the BC system is conducted in this work solely from hydrographic data anaiysis and manipulation from two oceanographic meso-scale surveys that were part of the COROAS Project, the Brazilian arm of the Worid Ocean Circulation Experiment. These two cruises sampled the central portion of the São Paulo Bight (23,5°- 27°S) in the summer and winter seasons of 1993. As it was intended to appiy the classical Dynamic Method to the data, a quantitative estimate of the reference levei (RL) is conducted through the comparison of two different and independent methodoiogies. The first uses the previous knowiedge that the BC transports Tropical Water and South Atlantic Central Water (SACW) as well as that the IWBC transports mainly Antarctic Intermediate Water (AAIW). This method, referred here as the Thermodynamic Criterion applies the Shtokman theorems to estimate the interface depth between SACW and AAIW. The second methodology, designated here as the Dynamic Criterion, consists of modeiing absolute baroclinic velocities for all 14 hydrographic transects using the sectional version of the Princeton Ocean Model. The results of the two methods differ oniy in 7 dbar and a RL of 480 dbar is adopted as to represent the average interface isobaric level between BC and IWBC in the following geostrophic calculations. Horizontal distributions of geostrophic stream function are generated using objective mapping. These distributions present unequivocal evidences of cyclonic and anticyclonic structures in both Summer and Winter 1993 cruises. These features are associated to meanders of the BC System. They are depicted in opposing sides of the current core. The cyclone is seen in the BC coastal side as the anticyclone is placed in its oceanic side. The vertical variation of these pattems with a single flow direction inversion confirms that these vortical features are part of a first baroclinic mode wave, which corroborates previous speculations found in the literature. In order to pursue a potential vorticity analysis, a data-derived two-layer quasi-geostrophic model is built assuming an invicid flat-bottomed ocean in the 3-plane. This analysis allowed to conclude that the basic vorticity field associated with both horizontal and vertical shear of the boundary currents are responsible for the baroclinic wave existence. The planetary vorticity gradient is one order of magnitude lower. The frontal variation in baroclinic potential vorticity is 1,7 x i0 s1. The dominance of the stretching vorticity, which accounts for 60% of the gradient variation, leads to classify these oscillatory motions as long meso-scale waves. The potential vorticity conservation principle is invoked on an analysis that consists of superimposing the first layer quasi-gesotrophic potential vorticity and geostrophic stream funtion maps. This analysis revealed that the baroclinic waves are propagating as well as evidences of meander growth, an indication of a possible geophysical instability mechanism, are seen. Given the findings of the previous analyses, linear theory and the perturbation method are used to derive a dispersion relation for the BC System first mode baroclinic waves. The wave frequency is function of the BC velocity as well as the potential vorticity cross-stream gradient.

Orientador: Lucas Catão de Freitas Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:31:34Z (GMT). No. of bitstreams: 1 Moitinho_ValterVictorCerqueira_M.pdf: 1171427 bytes, checksum: 9207703fa3477244cb0e004220ae2827 (MD5) Previous issue date: 2015 / Resumo: Nesta dissertação, estudamos o problema de existência de soluções globais suaves para a equação quase-geostrófica em R2 (2DQG) com condições periódicas e no caso de valor crítico para a viscosidade fracionária. Esta equação aparece em estudos de alguns fluidos geofísicos que apresentam altas velocidades de rotação. De um ponto de vista dimensional, a equação é considerada um análogo em 2D das equações de Navier-Stokes em 3D. Primeiramente, estudamos a teoria de soluções fracas com dados iniciais em L2 via o método de Galerkin. Depois mostramos um princípio do máximo em espaços Lp e investigamos a regularidade de soluções para tempos pequenos e dados iniciais nos espaços de Sobolev Hs com s > 1. Finalmente, mostramos que a solução suave localmente no tempo de fato existe globalmente e é suave para todo tempo. Esta dissertação é baseada na Tese de Doutorado de Resnick [36] e no recente trabalho de Kiselev, Narazov e Volberg [33] / Abstract: In this dissertation, we study existence of smooth global solutions for the quasi-geostrophic equation in R2 (2DQG) with periodic conditions and critical value for the fractional viscosity. This equation appears in studies of some geophysical fluids that present high rotational speed. Dimensionally speaking, the equation is the analogue in 2D of the Navier-Stokes equations in 3D. First, we study the theory of weak solutions with initial data in L2 via the Galerkin method. After we show a maximum principle in Lp spaces and investigate regularity of solutions for small times and initial data in Sobolev spaces Hs with s > 1. Finally, we show that local-in-time smooth solutions are indeed global ones. This dissertation is based on the PhD thesis of Resnick [36] and recent work of Kiselev, Narazov e Volberg [33] / Mestrado / Matematica / Mestre em Matemática

La dynamique océanique, notamment dans les régions Australes, se caractérise par d'importantes fluctuations induites par les processus à mésoéchelle (tourbillons, 100-200km) et à sous-mésoéchelle (filaments, <50km). Ces processus sont connus pour stimuler fortement le développement du phytoplancton et avec lui l'ensemble de la chaine trophique. Toutefois les relations entre la distribution des proies et celle des prédateurs sont encore loin d'être bien connues pour la plupart des espèces marines. C'est en particulier le cas pour l'éléphant de mer austral (EDM) dont les proies souvent localisées à grandes profondeurs. Cette thèse s’est intéressée à étudier comment le comportement de plongée et de chasse des EDM est influencé par les variations à fine échelle de l'environnement. Une des originalités de cette thèse a été d’utiliser les mesures à très haute résolution récoltées par les éléphants de mer qui constituent un jeu de données 3-D in-situ unique à sous-mésoéchelle, puis de les combiner aux mesures satellites plus classiques de température et d'altimétrie. Ce travail a montré, pour la première fois à l’aide de données in-situ très haute résolution, l’importance des zones frontales à sous-mésoéchelle dans le comportement alimentaire d’un prédateur supérieur. De plus, elle a permis le développement d’une méthode originale d’identification des zones frontales à fine échelle et confirmé la pertinence de la méthode Quasi-Géostrophique de Surface (SQG) dans l’étude de la dynamique fine échelle, notamment dans les perspectives des futures missions spatiales à hautes résolutions (de type SWOT). / Ocean dynamics, especially in the southern ocean, are caracterized by strong fluctuation due to mesoscale (eddies, 100-200km) and submesoscale (filaments, <50km) processes. Theses processes are known to strongly stimulate primary production and with him the rest of the trophic chain. However, in marine ecosystems, relationship between prey and predator distribution remain challenging to understand. Such complexe link exist within the Southern Elephant Seal (SES) and their deep diving prey.This PhD worked to understand how the SES diving and foraging behaviour is impacted by submesoscale variation of the environment. Two original aspects of this work was first to use the very high resolution measurement from SES as an unique 3-D in-situ submesoscale dataset and then to combine it to, more classic, satellite temperature and altimetry measurement. This work showed, for the first time the in-situ impact of submesoscale frontal regions on one top predator foraging behaviour. Furthermore, during this study, an original method to identify fine scale frontal regions was developped. Finally, this PhD confirm the relevant use of the Surface Quasi-Geostrophic method in the study of fine scale dynamics, especially in the possibility of high resolution spatial missions (such as SWOT).