L’océan et l’atmosphère sont des environnements fluides stratifiés en densité, en référentiel tournant : la force de Coriolis due à la rotation de la planète influence l’écoulement. De grands tourbillons lenticulaires évoluent dans ces environnements, avec parfois de grandes durées de vie comme les Meddies de l’Océan Atlantique.Dans la continuité des expériences de Griffiths & Linden (1981) et Hedstrom & Armi (1988), ces tourbillons sont reproduits en laboratoire en injectant ou aspirant localement du fluide dans une couche d’eau salée tournante, linéairement stratifiée en densité. A l’ordre dominant, les tourbillons sont à l’équilibre cyclo-géostrophique et hydrostatique, d’où l’on dérive la loi de leur rapport d’aspect, validée par les expériences et les observations. Un modèle complet de tourbillon à l’équilibre incluant les recirculations internes est proposé, en partant d’un profil Gaussien pour la vitesse azimutale, puis validé numériquement. A partir de ce modèle, un bilan d’énergie permet alors de décrire la décroissance des tourbillons.Certains tourbillons naturels comme les Meddies présentent des structures fines associées à de forts gradients de densité à leur frontière, que l’on reproduit en laboratoire autour de tourbillons entretenus par une injection continue de fluide. Ces structures en couches sont la manifestation de l’instabilité de McIntyre, instabilité qui apparaît lorsque les diffusivités visqueuse et moléculaire sont sensiblement différentes. L’analyse de stabilité linéaire de McIntyre appliquée au modèle Gaussien de tourbillon permet de retrouver les tailles et temps d’apparition associés au couches qui entourent les Meddies. / The ocean and the atmosphere are density stratified fluid environments in a rotating frame: the Coriolis force, due to the rotation of the planet, influences the flow. Huge lenticular vortices evolve in these environments, sometimes with very long lifetimes as the Meddies of the Atlantic Ocean.Based on Griffiths & Linden (1981) and Hedstrom & Armi (1988) experiments, such vortices are experimentally reproduced by locally injecting or sucking up fluid in a rotating layer of salty water, linearly density stratified. At dominant order, the vortices are in cyclo-geostrophic and hydrostatic balance, from which the law for their vertical aspect ratio is derived, validated by experiments and observations. A more complete model of vortex in equilibrium is proposed from a Gaussian profile for the azimuthal velocity, including internal secondary circulations, and then numerically validated. From this model, an energy balance allows us to describe the vortices decay.Some natural vortices, as the Meddies, have fine-structures associated to high density gradients at their frontier, that we experimentally reproduce around vortices maintained through a continuous injection of fluid. This layered structure is the expression of McIntyre's instability, which appears when viscous and molecular diffusivities are significantly different. The linear stability analysis of McIntyre applied to the Gaussian model of vortex allows us to recover the sizes and duration of appearance of the layers that surround the Meddies when eddy viscosities measured in the ocean are used.

Sejam K um corpo algebricamente fechado, A uma K-álgebra básica conexa de dimensão finita sobre K e ê=(e_1,e_2,... ,e_n) um conjunto completo de idempotentes ortogonais, primitivos e ordenados de A. O conjunto dos módulos estandares é o conjunto Delta ={ D_1, ..., D_n }, onde D_i é o quociente maximal do A-módulo projetivo P_i com fatores de composição simples S_j, com j\\leq i, F(Delta) é a subcategoria plena de mod A dos módulos têm uma Delta-filtração. Se A_A esta em F(Delta) diz-se que A é uma álgebra estandarmente estratificada. Se, além disso, para cada elemento em Delta vale que End_A(D_i) é isomorfo a K diz-se que A é uma álgebra álgebra quase-hereditária. Nesta dissertação estudamos as propriedades de F(Delta), especialmente quando A é estandarmente estratificada, e algumas condições necessárias e suficientes para que A seja quase-hereditária. / Let K be an algebraically closed field, A a basic, connected, finite dimensional K-algebra and ê=(e_1,e_2,...,e_n) a complete set of ordered primitive orthogonal idempotents of A. The set of standard modules is the set Delta={D_1, ..., D_n}, where D_i is the maximal factor submodule of P_i whose composition factors are isomorphic to S_j, for j\\leq i. We denote by F(Delta) the full subcategory of mod A containing the modules which are filtered by modules in Delta. If iA_A is in F(Delta) we say that A is standardly stratified. Moreover, if End_A(D_i) is isomorphic with K, for each element in Delta we say that A is quasi hereditary. In this work we study the properties of the category F(Delta), especially when A is stardardly stratified, and some necessary and sufficient conditions to A be quasi hereditary.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Ph.D.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Mechanical Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / M.S.

abstract: A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations. The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation. / Dissertation/Thesis / Supplemental Materials Description File / zip file containing 10 mp4 formatted video animations, as well as a text readme and the previously submitted Supplemental Materials Description File / Doctoral Dissertation Mathematics 2019

abstract: The dynamics of a fluid flow inside 2D square and 3D cubic cavities under various configurations were simulated and analyzed using a spectral code I developed. This code was validated against known studies in the 3D lid-driven cavity. It was then used to explore the various dynamical behaviors close to the onset of instability of the steady-state flow, and explain in the process the mechanism underlying an intermittent bursting previously observed. A fairly complete bifurcation picture emerged, using a combination of computational tools such as selective frequency damping, edge-state tracking and subspace restriction. The code was then used to investigate the flow in a 2D square cavity under stable temperature stratification, an idealized version of a lake with warmer water at the surface compared to the bottom. The governing equations are the Navier-Stokes equations under the Boussinesq approximation. Simulations were done over a wide range of parameters of the problem quantifying the driving velocity at the top (e.g. wind) and the strength of the stratification. Particular attention was paid to the mechanisms associated with the onset of instability of the base steady state, and the complex nontrivial dynamics occurring beyond onset, where the presence of multiple states leads to a rich spectrum of states, including homoclinic and heteroclinic chaos. A third configuration investigates the flow dynamics of a fluid in a rapidly rotating cube subjected to small amplitude modulations. The responses were quantified by the global helicity and energy measures, and various peak responses associated to resonances with intrinsic eigenmodes of the cavity and/or internal retracing beams were clearly identified for the first time. A novel approach to compute the eigenmodes is also described, making accessible a whole catalog of these with various properties and dynamics. When the small amplitude modulation does not align with the rotation axis (precession) we show that a new set of eigenmodes are primarily excited as the angular velocity increases, while triadic resonances may occur once the nonlinear regime kicks in. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019

Thermal stratification occurs in shallow water bodies because solar energy separates the water column into an upper warm layer, a lower cold layer, and an intermediate layer between the upper and lower layers. In general the intermediate layer exhibits a significant thermal gradient over depth. Because cold water is heavier than warm water, this temperature structure produces a stable stratification, thereby inhibiting circulation from the bottom to the surface. This stable stratification results in a deficit of dissolved oxygen in the lower layer leading to water quality problems. Hence understanding the thermal structure and vertical circulation in shallow water bodies is important for water quality and its management. In this research, a numerical code is developed to examine the three-dimensional flow structure in shallow water bodies. This numerical code is used to solve the governing equations : the Reynolds averaged Navier-Stokes equations for three velocities and pressure, the depth-averaged continuity equation for free surface movement, the equations for turbulence closure, the scalar transport equation for temperature, and the international equation of state for density variation due to temperature. These equations are solved simultaneously using a finite difference method. The mathematical equations are transformed into a generalised coordinate system which allows flexibility for irregular boundaries and the allocation of vertical grid points every time step depending on free surface movements. In order to overcome possible numerical instabilities because of the small vertical length scale in shallow water bodies, an implicit method is used in the vertical direction. Several test cases involving free surface movement are used to verify the numerical code, and numerical solutions compare favourably against analytical solutions and measured data. The numerical code has been applied to the Torrens Lake in Adelaide, South Australia, where algal blooms occur frequently in summer due to thermal stratification. Typical thermal structures have been obtained from the model and these are compared with field data. The current code has been developed to improve upon existing commercial models which may not adequately address shallow water flows because of the high computational burden required to resolve free surface movements and consequential difficulties encountered for models with a small vertical length scale. / Thesis (Ph.D.)--School of Mathematical Sciences, 2007.

<p>For papermakers, an understanding of the development of strength properties in the paper is of uttermost importance. Strong papers are desirable both in the traditional paper industry as well as in new fields of application, such as fibre-based packaging and light-weight building material. In this study, the effects of adding abaca (Musa textilis) as a reinforcement fibre for softwood pulp was investigated. Moreover, the LB Multilayer Handsheet Former for the production of stratified sheets was evaluated and used to study the effects of placing selected fibres in separate layers, rather than by making homogeneous sheets from a mixture of the pulps.</p><p>Handsheets of a softwood sulphate pulp with the addition of abaca fibres were made in a conventional sheet former. It was seen that the addition of abaca fibres can increase the tearing resistance, fracture toughness, folding endurance and air permeance. Tensile strength, tensile stiffness and tensile energy absorption, however, decreased somewhat.</p><p>It was shown that the LB Multilayer Handsheet Former is suitable for studying the effects of stratification of paper. The sheet former produces sheets with good formation and the variation of paper properties of the sheets is retained at a fairly constant level when the number of layers in the stratified sheets is increased. The uniformity of the sheets produced in the LB Multilayer Handsheet Former are generally at the same level as of those produced in conventional sheet formers.</p><p>Homogeneous and stratified sheets were produced in the LB Multilayer Handsheet Former and it was found that by stratifying a sheet, so that pulp with a high tear index and pulp with a high tensile index are placed in separate layers, it was possible to increase the tear index by approximately 25%, while the tensile index was decreased by 10-20%.</p>

We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference “Elliptic and Hyperbolic Equations on Singular Spaces”, October 27 - 31, 2008, at the MSRI, University of Berkeley.

For papermakers, an understanding of the development of strength properties in the paper is of uttermost importance. Strong papers are desirable both in the traditional paper industry as well as in new fields of application, such as fibre-based packaging and light-weight building material. In this study, the effects of adding abaca (Musa textilis) as a reinforcement fibre for softwood pulp was investigated. Moreover, the LB Multilayer Handsheet Former for the production of stratified sheets was evaluated and used to study the effects of placing selected fibres in separate layers, rather than by making homogeneous sheets from a mixture of the pulps. Handsheets of a softwood sulphate pulp with the addition of abaca fibres were made in a conventional sheet former. It was seen that the addition of abaca fibres can increase the tearing resistance, fracture toughness, folding endurance and air permeance. Tensile strength, tensile stiffness and tensile energy absorption, however, decreased somewhat. It was shown that the LB Multilayer Handsheet Former is suitable for studying the effects of stratification of paper. The sheet former produces sheets with good formation and the variation of paper properties of the sheets is retained at a fairly constant level when the number of layers in the stratified sheets is increased. The uniformity of the sheets produced in the LB Multilayer Handsheet Former are generally at the same level as of those produced in conventional sheet formers. Homogeneous and stratified sheets were produced in the LB Multilayer Handsheet Former and it was found that by stratifying a sheet, so that pulp with a high tear index and pulp with a high tensile index are placed in separate layers, it was possible to increase the tear index by approximately 25%, while the tensile index was decreased by 10-20%.