15,894 research outputs found

    Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow

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    Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this paper, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time.Comment: 9 pages, 9 figure

    Hydromagnetic Stability of a Slim Disk in a Stationary Geometry

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    The magnetorotational instability originates from the elastic coupling of fluid elements in orbit around a gravitational well. Since inertial accelerations play a fundamental dynamical role in the process, one may expect substantial modifications by strong gravity in the case of accretion on to a black hole. In this paper, we develop a fully covariant, Lagrangian displacement vector field formalism with the aim of addressing these issues for a disk embedded in a stationary geometry with negligible radial flow. This construction enables a transparent connection between particle dynamics and the ensuing dispersion relation for MHD wave modes. The MRI--in its incompressible variant-- is found to operate virtually unabated down to the marginally stable orbit; the putative inner boundary of standard accretion disk theory. To get a qualitative feel for the dynamical evolution of the flow below rmsr_{\rm ms}, we assume a mildly advective accretion flow such that the angular velocity profile departs slowly from circular geodesic flow. This exercise suggests that the turbulent eddies will occur at spatial scales approaching the radial distance while tracking the surfaces of null angular velocity gradients. The implied field topology, namely large-scale horizontal field domains, should yield strong mass segregation at the displacement nodes of the non-linear modes when radiation stress dominates the local disk structure (an expectation supported by quasi-linear arguments and by the non-linear behavior of the MRI in a non-relativistic setting). Under this circumstance, baryon-poor flux in horizontal field domains will be subject to radial buoyancy and to the Parker instability, thereby promoting the growth of poloidal field.Comment: submitted to M.N.R.A.S. (3/29/02), 14 pages, 2 figures v2 accepted paper: clarified text and added discussion on radial flow effects. Added reference

    Hydro-dynamical models for the chaotic dripping faucet

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    We give a hydrodynamical explanation for the chaotic behaviour of a dripping faucet using the results of the stability analysis of a static pendant drop and a proper orthogonal decomposition (POD) of the complete dynamics. We find that the only relevant modes are the two classical normal forms associated with a Saddle-Node-Andronov bifurcation and a Shilnikov homoclinic bifurcation. This allows us to construct a hierarchy of reduced order models including maps and ordinary differential equations which are able to qualitatively explain prior experiments and numerical simulations of the governing partial differential equations and provide an explanation for the complexity in dripping. We also provide a new mechanical analogue for the dripping faucet and a simple rationale for the transition from dripping to jetting modes in the flow from a faucet.Comment: 16 pages, 14 figures. Under review for Journal of Fluid Mechanic

    Lagrangian acceleration statistics in a turbulent channel flow

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    Lagrangian acceleration statistics in a fully developed turbulent channel flow at Reτ=1440Re_\tau = 1440 are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the Lagrangian velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a strong anisotropy at small scales in the near-wall region that remains present in most of the channel. Such statistical properties may be used as constraints in building advanced Lagrangian stochastic models to predict the dispersion and mixing of chemical components for combustion or environmental studies.Comment: accepted for publication in Physical Review Fluid

    Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids

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    We study the spectrum of density fluctuations of Fractional Hall Fluids in the context of the noncommutative hidrodynamical model of Susskind. We show that, within the weak-field expansion, the leading correction to the noncommutative Chern--Simons Lagrangian (a Maxwell term in the effective action,) destroys the incompressibility of the Hall fluid due to strong UV/IR effects at one loop. We speculate on possible relations of this instability with the transition to the Wigner crystal, and conclude that calculations within the weak-field expansion must be carried out with an explicit ultraviolet cutoff at the noncommutativity scale. We point out that the noncommutative dipoles exactly match the spatial structure of the Halperin--Kallin quasiexcitons. Therefore, we propose that the noncommutative formalism must describe accurately the spectrum at very large momenta, provided no weak-field approximations are made. We further conjecture that the noncommutative open Wilson lines are `vertex operators' for the quasiexcitons.Comment: 20 pages, harvma

    Chaotic advection of reacting substances: Plankton dynamics on a meandering jet

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    We study the spatial patterns formed by interacting populations or reacting chemicals under the influence of chaotic flows. In particular, we have considered a three-component model of plankton dynamics advected by a meandering jet. We report general results, stressing the existence of a smooth-filamental transition in the concentration patterns depending on the relative strength of the stirring by the chaotic flow and the relaxation properties of planktonic dynamical system. Patterns obtained in open and closed flows are compared.Comment: 5 pages, 3 figues, latex compiled with modegs.cl
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