On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

We propose a procedure - partly analytical and partly numerical - to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The unsteady Stokes equations for the stream function are decomposed onto normal modes for the angular and temporal variables, leading to a fourth-order linear ordinary differential equation in the radial variable. The forcing terms are dictated by the properties of the membrane, and result into jump conditions at the interface between the internal and external media. The equation can be solved numerically, and an excellent agreement is found with a fully-computational approach we developed in parallel. Comparisons are also shown with the results available in the scientific literature for drops, and a model based on the concept of embarked fluid is presented, which allows for a good representation of the results and a consistent interpretation of the underlying physics.Comment: in press on JF

Point-source scalar turbulence

The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the spectrum, a statistical indicator widely used both in experiments and in numerical simulations. The only source of inhomogeneity/anisotropy is in the injection mechanism, the advecting velocity here being statistically homogeneous and isotropic. Our main results can be summarized as follows. 1) For a very large velocity integral scale, a pure scaling behaviour in the distance between the two points emerges only if their separation is much smaller than their distance from the point source. 2) The value we have found for the scaling exponent suggests the existence of a direct cascade, in spite of the fact that here the forcing integral scale is formally set to zero. 3) The combined effect of a finite inertial-range extension and of inhomogeneities causes the emergence of subleading anisotropic corrections to the leading isotropic term, that we have quantified and discussed.Comment: 10 pages, 1 figure, submitted to Journal of Fluid Mechanic

Kazantsev dynamo in turbulent compressible flows

We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension $d = 3$ is special, since for all other values of $d$ the critical exponent is higher and depends on the compressibility.Comment: 12 pages, 6 figure

Optimal transient growth in an incompressible flow past a backward-slanted step

With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 degrees of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin-Helmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic forcing is tackled by means of variational formulation, adjoint method, penalization scheme and orthogonalization algorithm. Dealing with the transient growth of spanwise-periodic perturbations and inspired by the need of physically-realizable disturbances, we finally provide a procedure attaining a kinetic-energy maximal gain of the order of one million with respect to the power introduced by the external forcing.Comment: 17 figure

La Dependencia Hídrica de Portugal Respecto a España: Cuestiones de Política y Seguridad

El objetivo de este artículo fue el de analizar la dimensión que los impactos directos de las alteraciones climáticas pueden tener sobre los recursos hídricos en Portugal, considerando su posición geográfica río abajo con respecto a España, ya que 2/3 de su territorio continental asientan en cuencas hidrográficas internacionales, y que cerca de 67% de los recursos hídricos a los que Portugal tiene acceso provienen de ellas. A pesar de comprobadas, con algún grado de seguridad, las consecuencias que las alteraciones climáticas podrán acarrear, en un futuro próximo, con profundos cambios en el medio ambiente y la vida humana, es evidente, a lo largo de las últimas décadas, la ausencia de intervención política e inversiones concretas por parte de Portugal para minorar esos impactos previsibles, y asimismo promover una adaptación gradual al conjunto de estas contingencias. Considerando el profundo impacto que la reducción del acceso al agua dulce podrá tener en Portugal, y que, al constituir uno de los propósitos del Estado, la Seguridad Nacional es uno de los fundamentos de la soberanía y garantía de perennidad, parece esencial averiguar si la dependencia hídrica de Portugal constituye una amenaza concreta a dicha Seguridad Nacional, y a qué nivel podrá ser reducida

Tensões e Paradoxos da Desordem Mundial numa Era de Crise

Neste livro examinam-se as problemáticas que constituem a actual época de transição paradigmática no sistema internacional. Através da Ciência Política, Relações Internacionais e Filosofia Política são abordados temas tais como o da natureza do actual sistema internacional, a emergência dos BRICS, conflitos, centros de poder, direitos, natureza do poder na actual ordem mundial, inventariando-se criticamente doutrinas e procede-se à análise da realidade contemporânea