Asymptotic behaviour of a rapidly rotating fluid with random stationary surface stress

The goal of this paper is to describe in mathematical terms the effect on the ocean circulation of a random stationary wind stress at the surface of the ocean. In order to avoid singular behaviour, non-resonance hypotheses are introduced, which ensure that the time frequencies of the wind-stress are different from that of the Earth rotation. We prove a convergence result for a three-dimensional Navier-Stokes-Coriolis system in a bounded domain, in the asymptotic of fast rotation and vanishing vertical viscosity, and we exhibit some random and stationary boundary layer profiles. At last, an average equation is derived for the limit system in the case of the non-resonant torus.Comment: 45 page

Método de avaliação de manifestações patológicas pós-restaurações em prédios históricos

A Cidade de Pelotas/RS Brasil, é reconhecida pelo seu significativo patrimônio histórico e arquitetônico. Nos últimos anos, muitas iniciativas foram tomadas para resgatar, preservar e valorizar esta arquitetura. Em 2007, a Universidade Federal de Pelotas incorporou à sua área o prédio que pertencia a Família Assumpção, restaurando-o assim como recuperou a edificação que abrigou o antigo Lyceu Rio-Grandense de Agronomia e Veterinária, que possuem elevado valor cultural da cidade. As restaurações destes prédios envolveram a recuperação de estruturas, coberturas, fachadas, esquadrias, forros, pisos, reforço e consolidação de paredes, elementos de ornamentação tais como molduras, pilastras e frontões, adequação de instalações elétricas, paisagismos e adaptações de acessos para pessoas portadoras de deficiência motora. Após algum tempo da entrega das obras e utilização desses espaços com os fins propostos em projeto percebem-se indícios de manifestações patológicas. A pesquisa tem como objetivo analisar e diagnosticar as manifestações patológicas desses prédios de uso público, pertencentes ao Centro Histórico de Pelotas, que sofreram processo de restauração nos últimos anos. Um levantamento cadastral será realizado, resgatando projeto arquitetônico e histórico dos prédios para identificação das intervenções que os edifícios sofreram ao longo dos anos e dos dados referentes ao recente processo de restauração, tais como técnicas utilizadas e materiais empregados, bem como identificar e mapear as patologias existentes, que se manifestaram após a restauração dos mesmos. Esse levantamento será realizado com observação in loco das anomalias, identificação, mapeamento e registro fotográfico, além de estabelecer as possíveis causas, diagnosticar e definir a terapia mais adequada para cada ocorrência. No processo de identificação das anomalias podemos destacar a grande concentração de eflorescência encontrada no prédio do antigo Lyceu Rio-Grandense de Agronomia e Veterinária, assim como a grande variedade de anomalias encontradas no prédio da Família Assumpção como, por exemplo, trincas, fissuras, descolamento de revestimento, manchas nos diferentes revestimentos, umidades, entre outras, as quais serão verificadas as suas possíveis causas. O presente trabalho apresenta a metodologia adotada e alguns resultados parciais, visto que a pesquisa está em andamento.Tópico 6: Patrimonio Urbano de los siglos XVIII al XX. Técnicas de Limpieza y de Conservación

Large time existence for 3D water-waves and asymptotics

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and remarks added) To appear in Inventione

Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime

In the regime of weakly transverse long waves, given long-wave initial data, we prove that the nondimensionalized water wave system in an infinite strip under influence of gravity and surface tension on the upper free interface has a unique solution on [0,{T}/\eps] for some \eps independent of constant $T.$ We shall prove in the subsequent paper \cite{MZZ2} that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D capillary-gravity waves) into two parts, this is the first on

Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

We investigate here the ability of a Green-Naghdi model to reproduce strongly nonlinear and dispersive wave propagation. We test in particular the behavior of the new hybrid finite-volume and finite-difference splitting approach recently developed by the authors and collaborators on the challenging benchmark of waves propagating over a submerged bar. Such a configuration requires a model with very good dispersive properties, because of the high-order harmonics generated by topography-induced nonlinear interactions. We thus depart from the aforementioned work and choose to use a new Green-Naghdi system with improved frequency dispersion characteristics. The absence of dry areas also allows us to improve the treatment of the hyperbolic part of the equations. This leads to very satisfying results for the demanding benchmarks under consideration

Three-manifold invariant from functional integration

We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1- forms. The result of the functional integration is compared with the abelian U(1) Reshetikhin-Turaev surgery invariant

Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a disturbance moving at constant speed on top of two layers of fluids of different densities. Starting from the full Euler equations, we present several nonlinear asymptotic models, in the long wave regime. These models are rigorously justified by consistency or convergence results. A careful theoretical and numerical analysis is then provided, in order to predict the behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit