Instabilities of the flow around a cylinder and emission of vortex dipoles

Instabilities and long-term evolution of two-dimensional circular flows around a rigid circular cylinder (island) are studied analytically and numerically. For that we consider a base flow consisting of two concentric neighbouring rings of uniform but different vorticity, with the inner ring touching the cylinder. We first study the inviscid linear stability of such flows to perturbations of the free edges of the rings. For a given ratio of the vorticity in the rings, the governing parameters of the problem are the radii of the inner and outer rings scaled on the cylinder radius. In this two-dimensional parameter space, we determine analytically the regions of linear stability/instability of each azimuthal mode m=1, 2, .... In the physically most meaningful case of zero net circulation, for each mode m > 1, two regions are identified: a regular instability region where mode m is unstable along with some other modes, and a unique instability region where only mode m is unstable. After the conditions of linear instability are established, inviscid contour-dynamics and high-Reynolds-number finite-element simulations are conducted. In the regular instability regions, simulations of both kinds typically result in the formation of vortical dipoles or multipoles. In the unique instability regions, where the inner vorticity ring is much thinner than the outer ring, the inviscid contour-dynamics simulations do not reveal dipole emission. In the viscous simulation, because viscosity has time to widen the inner ring, the instability develops in the same manner as in the regular instability regions

Instability of a shear flow around a circular island and emission of vortex dipoles

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Kramers-Kronig Relations For The Dielectric Function And The Static Conductivity Of Coulomb Systems

The mutual influence of singularities of the dielectric permittivity e(q,w) in a Coulomb system in two limiting cases w tends to zero, q tends to zero, and opposite q tends to zero, w tends to zero is established. It is shown that the dielectric permittivity e(q,w) satisfies the Kramers-Kronig relations, which possesses the singularity due to a finite value of the static conductivity. This singularity is associated with the long "tails" of the time correlation functions.Comment: 9 pages, 0 figure

The break-up of Ekman theory in a flow subjected to background rotation and driven by a non-conservative body force

We present an experimental/numerical study of a dipolar flow structure in a shallow layer of electrolyte driven by electromagnetic forcing and subjected to background rotation. The aim of this study is to determine the influence of a non-conservative body force on the range of applicability of the classical Ekman boundary layer theory in rapidly rotating systems. To address this question, we study the response of the flow to the three control parameters: the magnitude of the forcing, the rotation rate of the system, and the shallowness of the layer. This response is quantified taking into account the magnitude of the flow velocity (represented by the Reynolds number), the symmetry between both vortex cores, and the vertical profile of the horizontal velocity. As in the case without background rotation, the response of the flow exhibits two scaling regimes (a linear and a nonlinear regime) in which the flow exhibits different vertical profiles of velocity. The transition between the two regimes occurs when the convective acceleration becomes of the same order as the viscous damping. This suggests that the applicability of the Ekman theory depends on the existence of a balance between the forcing and the damping due to the Ekman layers and does not depend solely on the value of the Rossby number as for decaying flows. On the other hand, the cyclone/anticyclone asymmetry is governed exclusively by the Rossby number. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4766818

Analysis of linear and nonlinear conductivity of plasma-like systems on the basis of the Fokker-Planck equation

The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular chains, lattices, conducting polymers and semiconductor layers. Exploring the role of noise we introduce the generalized Fokker-Planck equation. Second, one-dimensional models are considered on the basis of the Fokker-Planck equation with active and passive velocity-dependent friction including an external electrical field. On this basis it is possible to find the linear and nonlinear conductivities for electrons and other charged particles in a homogeneous external field. It is shown that the velocity dependence of the friction coefficient can lead to an essential increase of the electron average velocity and the corresponding conductivity in comparison with the usual model of constant friction, which is described by the Drude-type conductivity. Applications including novel forms of controlled charge transfer and non-Ohmic conductance are discussed.Comment: 14 pages with 6 figure

Developmental motor problems and health-related quality of life in 5-year-old children born extremely preterm: A European cohort study

Aim To measure the association between cerebral palsy (CP) and non-CP-related movement difficulties and health-related quality of life (HRQoL) among 5-year-old children born extremely preterm (<28 weeks gestational age). Method We included 5-year-old children from a multi-country, population-based cohort of children born extremely preterm in 2011 to 2012 in 11 European countries (n = 1021). Children without CP were classified using the Movement Assessment Battery for Children, Second Edition as having significant movement difficulties (<= 5th centile of standardized norms) or being at risk of movement difficulties (6th-15th centile). Parents reported on a clinical CP diagnosis and HRQoL using the Pediatric Quality of Life Inventory. Associations were assessed using linear and quantile regressions. Results Compared to children without movement difficulties, children at risk of movement difficulties, with significant movement difficulties, and CP had lower adjusted HRQoL total scores (beta [95% confidence interval] = -5.0 [-7.7 to -2.3], -9.1 [-12.0 to -6.1], and - 26.1 [-31.0 to -21.2]). Quantile regression analyses showed similar decreases in HRQoL for all children with CP, whereas for children with non-CP-related movement difficulties, reductions in HRQoL were more pronounced at lower centiles. Interpretation CP and non-CP-related movement difficulties were associated with lower HRQoL, even for children with less severe difficulties. Heterogeneous associations for non-CP-related movement difficulties raise questions for research about mitigating and protective factors.Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Grant/Award Number: SFRH/BPD/117597/2016; Horizon 2020 Framework Programme, Grant/Award Number: No 633724 and No 733280; Seventh Framework Programme, Grant/Award Number: No 25988