The dynamics of the world's oceans occur at a vast range of length scales. Although there are theories that aid in understanding the dynamics at planetary scales and microscales, the motions in between are still not yet well understood. This work discusses a numerical model to study barotropic wind-driven gyre flow that is capable of resolving dynamics at the synoptic, O(1000 km), mesoscale, O(100 km) and submesoscales O(10 km). The Quasi-Geostrophic (QG) model has been used predominantly to study ocean circulations but it is limited as it can only describe motions at synoptic scales and mesoscales. The Rotating Shallow Water (SW) model that can describe dynamics at a wider range of horizontal length scales and can better describe motions at the submesoscales. Numerical methods that are capable of high-resolution simulations are discussed for both QG and SW models and the numerical results are compared. To achieve high accuracy and resolve an optimal range of length scales, spectral methods are applied to solve the governing equations and a third-order Adams-Bashforth method is used for the temporal discretization. Several simulations of both models are computed by varying the strength of dissipation. The simulations either tend to a laminar steady state, or a turbulent flow with dynamics occurring at a wide range of length and time scales. The laminar results show similar behaviours in both models, thus QG and SW tend to agree when describing slow, large-scale flows. The turbulent simulations begin to differ as QG breaks down when faster and smaller scale motions occur. Essential differences in the underlying assumptions between the QG and SW models are highlighted using the results from the numerical simulations.

The dynamics of the world's oceans occur at a vast range of length scales. Although there are theories that aid in understanding the dynamics at planetary scales and microscales, the motions in between are still not yet well understood. This work discusses a numerical model to study barotropic wind-driven gyre flow that is capable of resolving dynamics at the synoptic, O(1000 km), mesoscale, O(100 km) and submesoscales O(10 km). The Quasi-Geostrophic (QG) model has been used predominantly to study ocean circulations but it is limited as it can only describe motions at synoptic scales and mesoscales. The Rotating Shallow Water (SW) model that can describe dynamics at a wider range of horizontal length scales and can better describe motions at the submesoscales. Numerical methods that are capable of high-resolution simulations are discussed for both QG and SW models and the numerical results are compared. To achieve high accuracy and resolve an optimal range of length scales, spectral methods are applied to solve the governing equations and a third-order Adams-Bashforth method is used for the temporal discretization. Several simulations of both models are computed by varying the strength of dissipation. The simulations either tend to a laminar steady state, or a turbulent flow with dynamics occurring at a wide range of length and time scales. The laminar results show similar behaviours in both models, thus QG and SW tend to agree when describing slow, large-scale flows. The turbulent simulations begin to differ as QG breaks down when faster and smaller scale motions occur. Essential differences in the underlying assumptions between the QG and SW models are highlighted using the results from the numerical simulations.

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.

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.

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.