15,894 research outputs found
Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow
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
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 , 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
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
Lagrangian acceleration statistics in a fully developed turbulent channel
flow at 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
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
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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