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A steady-state barotropic model, linearized about a GCM-derived 500 hPa basic state, is driven by a sample of \"observed\" forcing fields. lt tums out that the leading mode (LEOF) obtained from the sample of linear solutions matches weil with the leading EOF of low-frequency atmospheric variability actually occurring in the GCM. The response ofthe linear model is analysed in tenns of the singular modes of the model\'s linear operator. lt is found that about 50 percent ofthe spatial variance of the LEOF can be explained in tenns of the leading two singular modes. This finding is reflected also in the linear barotropic energy balance of the LEOF which shows that the mode is maintained through nearly equal contributions from i) the kinetic energy conversion of basic state kinetic energy (which is primarily due to the action of the singular modes) and ii) the forcing. The linear simulation of the GCM EOF fails if the linear model is linearized about a 300 hPa basic. This is explained by the fact that in this case the structure of the leading singular modes, which have a strong impact on the linear response, is much more dissimilar to the structure of the GCM EOF than in the 500 hPa case. / Ein stationäres barotropes Modell, das bezüglich eines (aus einem GCM Experiment abgeleiteten) 500 hPa Grundzustandes linearisiert ist, wird für einen Satz von "beobachteten" Antriebsfeldern gelöst. Dabei zeigt sich, daß die führende Mode der langperiodischen atmosphärischen Variabilität (EOF) im GCM Experiment durch das lineare Modell sehr gut simuliert wird. Weiterhin stellt sich heraus, daß hierfür die Antriebsfelder und die singulären Moden des linearen Modelloperators die gleiche Bedeutung besitzen. Auf die Wichtigkeit der Anwendung des Modells bezüglich des äquivalentbarotropen Niveaus wird hingewiesen.

The movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model, using a previously developed non-oscillatory balanced scheme. The model of TC used here takes an exponential form, and its size and strength are selected to be of a middle scale. Without a background flow, TCs move in the northwest direction due to the beta effect. The amplitudes of high wavenumber modes of the asymmetric flow, that are believed to be responsible for the TC drift, are computed using Fourier analysis. The amplitude of wavenumber one and two modes are dominant, so they are indicators of beta conversion of energy. Also, the effect of the monsoon trough on the TC movement is investigated. The results show a sudden change of the TC propagation path, consistent with earlier work. These two studies correspond to previous works. Here, the effect of equatorially trapped waves such as Kelvin, Rossby, and Mixed Rossby Gravity, on the TC path is newly studied by varying the wavenumber and wave speed of the underlying waves. The effect of the waves is considered because they are believed to contribute to cyclogenesis. For studying the effect, the barotropic flow induced by these waves via momentum transport and its variation were simulated for 50 days, and some patterns are found in the change of maximum wind speed. At a given time during the simulation, a TC is injected and the effect of the background wave is analyzed. Using the wavefield of 11 cases from 10 days to 30 days, the trajectories are calculated, and their patterns appear to be stochastic. So, the patterns are identified by calculating the mean path and its spread. The trajectories of TCs are different for different time of the waves. Kelvin waves make small variations on the length and direction of the trajectory of TCs. On the contrary, Rossby waves cause a dramatic change in the TC path and yield longer trajectories. Meanwhile, TCs in MRG waves keep fairly the same direction and usually have longer traveling distance. These changes vary by wave conditions. Therefore, the three kinds of waves have different effects on the trajectories of the TC. For some peculiar cases, the movements are explained based on wavefields. / Graduate

The exchange flow through tidal inlets generates two-dimensional large coherent vortical structures (2DLCS), that are much broader than the water depth and exist because of the inherent instability of shallow shear flows. These vortical starting jets are critical to the mixing that occurs in the inlet area. Depending on the tidal period T, the width of the inlet W, and the maximum velocity in the inlet UMAX, the mixing will vary from poor exchange to efficient exchange. Here, we present laboratory and numerical experiments that study the formation of the 2DLCS at the mouth of the inlets. Experiments were conducted at large scale, in the shallow flat-bottomed water basin at the Institute of Hydromechanics of the University of Karlsruhe, Germany, which has the capability to generate a sinusoidal flow that simulates a series of tidal cycles. A set of idealized inlets were arranged in the tank, and by varying the tidal period and the maximum velocity, three different types of life-history were obtained (stationary dipole, dipole entrains, and dipole escapes). These types of life-history are defined by the mixing number depending if KW is equal, less or greater than a critical value. The experiments were visualized using color dye tracers. To quantify the shallow water velocity field, the Particle Image Velocimetry (PIV) technique was used. From the PIV data the vorticity field was obtained, and the regions where the vortex formed were identified. Then, a vortex time-evolution analysis was developed using iv physical parameters such as the position on the basin of the vortex, the equivalent diameter, and the maximum vorticity among others. The mixing number accurately predicts the behavior of the vortex for the first cycle on idealized inlets for the subsequent cycles; the structures behave differently than predicted by KW, because the blocking effect of the vortex /formed in the previous cycle. For characteristic times t*  tUWless than about 2, the dipole is attached to the inlet and forms rapidly. For later times, the dipole advects downstream, and slowly dissipates. Numerical experiments are also presented. Comparing the numerical data with the laboratory data, good agreement is reached, but important limitations are identified for the grid resolution and domain size.

Divergence structures associated with the spectrum of precipitating systems in the subtropics and midlatitudes are not well documented. A mesoscale model (MM5) is employed to quantify the relative importance different baroclinic environments have on divergence profiles for common storm types in southeast Texas, a subtropical region. Divergence profiles averaged over a 100 x 100 nested grid with 3-km grid spacing are calculated from the model-derived wind fields for each storm. The divergence profiles simulated for selected storms are consistent with those calculated from an S-band radar using the velocity-azimuth display (VAD) technique. Divergence profiles from well-modeled storms vary in magnitude and structure across the spectrum of baroclinicities and storm types common in southeast Texas. Barotropic storms more characteristic of the Tropics generate the most elevated divergence (and thus diabatic heating) structures with the largest magnitudes. As the degree of baroclinicity increases, stratiform area fractions increase while the levels of non-divergence (LNDs) decrease. However, some weakly baroclinic storms contain stratiform area fractions and divergence profiles with magnitudes and LNDs that are similar to barotropic storms, despite having lower tropopause heights and less deep convection. Additional convection forms after the passage of some of the modeled barotropic and weakly baroclinic storms that contain elevated divergence signatures, circumstantially suggesting that heating at upper-levels may cause diabatic feedbacks that help drive regions of persistent convection in the subtropics. Applying a two-dimensional stratiform-convective separation algorithm to MM5 reflectivity data generates realistic stratiform and convective divergence signals. Stratiform regions in barotropic storms contain thicker, more elevated mid-level convergence structures with larger magnitudes than strongly baroclinic storms, while weakly baroclinic storms have LNDs that fall somewhere in between with magnitudes similar to barotropic storms. Divergence profiles within convective regions typically become more elevated as baroclinicity decreases, although variations in magnitude are less coherent. These simulations suggest that MM5 adequately captures mass field perturbations within convective and stratiform regions, the latter of which produces diabatic feedbacks capable of generating additional convection. As a result, future research determining the climatological dynamic response caused by divergence profiles in MM5 may be feasible.

Two basins separated by a strait often have different densities due to environmental factors, resulting in a situation in the strait where fluids of different densities are essentially side-by-side, causing an exchange flow due to gravitational forces. Dense fluid is pulled below light fluid and the light fluid is pushed above the dense, creating an opposing flow in the two layers. This exchange is often “controlled” at the point in the strait where cross-sectional area is minimized due to a constriction, either horizontal or vertical. Exchange in the strait can control the dynamics, and in turn energy, nutrient, pollutant and biological transport between the basins. Since strait dynamics are often not resolved in regional or global models, it is useful to parameterize the exchange based on external variables such as the density difference in the basins, the level of the dense water in the dense basin, and the tidal forcing. Exchange flow can be “maximal” or “sub-maximal”. The flow is “maximal” if raising the interface in the dense basin (presumably by modifying light water to be dense) does not further increase the exchange flow through the strait. While many ocean straits are usually “maximal”, there are also many that are “sub-maximal,” and thus require separate theoretical treatment. Time-dependent external barotropic forcing (i.e. the tide) modifies the time-averaged exchange flow in a strait. The relationship between tidal forcing and the average exchange flow in a channel has been examined for maximal exchange (Helfrich, 1995). In the present study, that effort is extended to include tidal forcing on a sub-maximal exchange flow. A strait with a sill is simulated numerically, using a two layer hydrostatic approximation. Time-averaged exchange flow increases with tidal amplitude depending on three factors: the physical dimensions of the problem, the tidal amplitude, and the relative strength of flow of the density layers. Results show that all exchange flows increase at a similar rate with tidal forcing, after being normalized by a parameter relating physical dimensions of the strait to the interfacial wave speed. This result quantifies the exchange increase due to tidal forcing for all degrees of “maximality” in this simple sill-only geometry. This relates time-dependent sub-maximal flows to the maximal case that has already been studied in depth. / Graduate / 0415 / ryanpc@uvic.ca

In this work, we studied three selected problems in FRW spacetime. In the first part, we analysed the motion of a test particle in the homogeneous and isotropic universe. We presented a framework in which one can derive the uniformly accelerated trajectory and geodesic motion if a scale factor for a given spacetime is provided as a function of coordinate time. By applying the confomal time transformation, we were able to convert second order differential equations of motion in FRW spacetime to first order differential equations. From this, we managed to obtain a formalism to derive the uniformly accelerated trajectory of a test particle in spatially curved FRW spacetime. The second part of this work is devoted to dynamical cosmology. In particular, we analyse the cases of barotropic fluids and non-minimally coupled scalar field in spatially curved FRW spacetime. First, we set up the dynamical systems for an unspecified EoS of a barotropic fluid case and an unspecified positive potential for a non-minimal coupled scalar field case. For both of these systems, we determined well-defined dynamical variables valid for all curvatures. In the framework of these general setups we discovered several characteristic features of the systems, such as invariant subsets, symmetries, critical points and their...

A Corrente do Brasil é formada na bifurcação do ramo sul da Corrente Sul Equatorial e flui meridionalmente para sul ao largo das costas leste, sudeste e sul do Brasil, apresentando intensa atividade de mesoescala entre a Cadeia Vitória-Trindade (20oS) e o Cabo de Santa Marta Grande (28oS). O conhecimento de tal atividade, construído ao longo do tempo, se refere principalmente aos meandros e vórtices frontais, sendo os vórtices de borda na configuração de dipolos vorticais relatados apenas através de imagens AVHRR. Dessa forma, objetivamos caracterizar a estrutura dinâmica de um dipolo vortical, observado na Bacia de Santos, a partir de dados quase-sinóticos de velocidade e hidrográficos oriundos do Cruzeiro Dinâmica do Ecossistema da Plataforma da Região Oeste do Atlântico Sul V. O mapeamento objetivo das estruturas capturadas pela grade amostral quase-sinótica do cruzeiro foi o ponto de partida para a descrição do dipolo e avaliação de sua geostrofia. Os campos de função de corrente apresentaram um padrão clássico de dipolo vortical, com vórtices ciclônico e anticiclônico posicionados em lados opostos ao eixo da corrente, que se enfraquece após a estrutura. Em média, o diâmetro de ambos os vórtices ficou em torno de 110 km, em seus maiores eixos. Em seguida, como o número de Rossby máximo foi de 0,27, para avançar nas questões dinâmicas envolvendo a estrutura, aproximamos o oceano a um modelo quase-geostrófico de 11/2-camadas derivado das observações e dinamicamente calibrado. A análise dos campos modelados, utilizando o número de Burger, revelou que a vorticidade relativa compete com a vorticidade de estiramento pela dinâmica do sistema. Ao compararmos os campos modelados de função de corrente e vorticidade potencial, observamos que o dipolo e o escoamento da CB não se encontram em um cenário estacionário. Finalmente, evidências de retroalimentação mútua entre os vórtices do dipolo foram obtidas através da interação entre o campo de função de corrente de uma estrutura com o campo de vorticidade potencial da outra. Logo, concluímos que o dipolo capturado encontrava-se em processo de crescimento barotrópico. / The Brazil Current (BC) is formed at the bifurcation of the southern branch of the South Equatorial Current and flows south-southeastward off the east, southeast and southern Brazilian continental margin, exhibiting intense meso-scale activity between the Vitória-Trindade Ridge (20oS) and Cape Santa Marta Grande (28oS). The knowledge of such activity, built over time, refers mainly to the frontal meanders and eddies. The edge vortical structures as a dipole configuration are reported only through AVHRR images. Thus, we aimed to characterize the dynamical structure of a BC vortical dipole, observed in the Santos Basin, with a quasi-synoptic velocity (vessel-mounted ADCP) and hydrographic (CTD) dataset from DEPROAS V cruise. The objective mapping of structures captured by the cruise sampling grid was the departing point for the description of the dipole and evaluation of its degree of geostrophy. The fields of the stream function showed a classic pattern of a dipole with cyclonic and anticyclonic eddies positioned on opposite sides of the current axis. On average, the diameter of the two eddies was around 110 km in their largest axes. Then, as the Rossby number was 0.27, we advanced in investigating the issues involving the dynamic structure by we approximating the ocean to a 11/2 layer quasi-geostrofic model derived from the observations and dynamically calibrated. Burger number revealed that both relative and stretching vorticity were competing for the dynamics of the system. The comparison between the modeled stream function and potential vorticity fields showed that both the dipole and the BC flow were not in a stationary state. Finally, evidences of reinforcement between the eddies of the dipole were obtained through the interaction between the field of the stream function of vortical structure with the field of potential vorticity of the other one, and vice-versa. Therefore, we conclude that the dipole were in a barotropic growth process.