10,923 research outputs found
Addendum to "Coherent Lagrangian vortices: The black holes of turbulence"
In Haller and Beron-Vera (2013) we developed a variational principle for the
detection of coherent Lagrangian vortex boundaries. The solutions of this
variational principle turn out to be closed null-geodesics of the Lorentzian
metric associated with a generalized Green-Lagrange strain tensor family. This
metric interpretation implies a mathematical analogy between coherent
Lagrangian vortex boundaries and photon spheres in general relativity. Here we
give an improved discussion on this analogy.Comment: Revised 27 June 201
Coherent Lagrangian vortices: The black holes of turbulence
We introduce a simple variational principle for coherent material vortices in
two-dimensional turbulence. Vortex boundaries are sought as closed stationary
curves of the averaged Lagrangian strain. Solutions to this problem turn out to
be mathematically equivalent to photon spheres around black holes in cosmology.
The fluidic photon spheres satisfy explicit differential equations whose
outermost limit cycles are optimal Lagrangian vortex boundaries. As an
application, we uncover super-coherent material eddies in the South Atlantic,
which yield specific Lagrangian transport estimates for Agulhas rings.Comment: To appear in JFM Rapid
Anharmonic Self-Energy of Phonons: Ab Initio Calculations and Neutron Spin Echo Measurements
We have calculated (ab initio) and measured (by spin-echo techniques) the
anharmonic self-energy of phonons at the X-point of the Brillouin zone for
isotopically pure germanium. The real part agrees with former, less accurate,
high temperature data obtained by inelastic neutron scattering on natural
germanium. For the imaginary part our results provide evidence that transverse
acoustic phonons at the X-point are very long lived at low temperatures, i.e.
their probability of decay approaches zero, as a consequence of an unusual
decay mechanism allowed by energy conservation.Comment: 8 pages, 2 figures, pdf fil
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
Recent developments in dynamical systems theory have revealed long-lived and
coherent Lagrangian (i.e., material) eddies in incompressible,
satellite-derived surface ocean velocity fields. Paradoxically, observed
drifting buoys and floating matter tend to create dissipative-looking patterns
near oceanic eddies, which appear to be inconsistent with the conservative
fluid particle patterns created by coherent Lagrangian eddies. Here we show
that inclusion of inertial effects (i.e., those produced by the buoyancy and
size finiteness of an object) in a rotating two-dimensional incompressible flow
context resolves this paradox. Specifically, we obtain that anticyclonic
coherent Lagrangian eddies attract (repel) negatively (positively) buoyant
finite-size particles, while cyclonic coherent Lagrangian eddies attract
(repel) positively (negatively) buoyant finite-size particles. We show how
these results explain dissipative-looking satellite-tracked surface drifter and
subsurface float trajectories, as well as satellite-derived \emph{Sargassum}
distributions.Comment: Submitted to \emph{Chaos} Focus Issue on Objective detection of
Lagrangian Coherent Structures. Revised 23-Feb-1
Precision Measurements of Stretching and Compression in Fluid Mixing
The mixing of an impurity into a flowing fluid is an important process in
many areas of science, including geophysical processes, chemical reactors, and
microfluidic devices. In some cases, for example periodic flows, the concepts
of nonlinear dynamics provide a deep theoretical basis for understanding
mixing. Unfortunately, the building blocks of this theory, i.e. the fixed
points and invariant manifolds of the associated Poincare map, have remained
inaccessible to direct experimental study, thus limiting the insight that could
be obtained. Using precision measurements of tracer particle trajectories in a
two-dimensional fluid flow producing chaotic mixing, we directly measure the
time-dependent stretching and compression fields. These quantities, previously
available only numerically, attain local maxima along lines coinciding with the
stable and unstable manifolds, thus revealing the dynamical structures that
control mixing. Contours or level sets of a passive impurity field are found to
be aligned parallel to the lines of large compression (unstable manifolds) at
each instant. This connection appears to persist as the onset of turbulence is
approached.Comment: 5 pages, 5 figure
Coherent Lagrangian vortices: the black holes of turbulence
We introduce a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. Solutions to this problem turn out to be mathematically equivalent to photon spheres around black holes in cosmology. The fluidic photon spheres satisfy explicit differential equations whose outermost limit cycles are optimal Lagrangian vortex boundaries. As an application, we uncover super-coherent material eddies in the South Atlantic, which yield specific Lagrangian transport estimates for Agulhas ring
Persistent Transport Barrier on the West Florida Shelf
Analysis of drifter trajectories in the Gulf of Mexico has revealed the
existence of a region on the southern portion of the West Florida Shelf (WFS)
that is not visited by drifters that are released outside of the region. This
so-called ``forbidden zone'' (FZ) suggests the existence of a persistent
cross-shelf transport barrier on the southern portion of the WFS. In this
letter a year-long record of surface currents produced by a Hybrid-Coordinate
Ocean Model simulation of the WFS is used to identify Lagrangian coherent
structures (LCSs), which reveal the presence of a robust and persistent
cross-shelf transport barrier in approximately the same location as the
boundary of the FZ. The location of the cross-shelf transport barrier undergoes
a seasonal oscillation, being closer to the coast in the summer than in the
winter. A month-long record of surface currents inferred from high-frequency
(HF) radar measurements in a roughly 60 km 80 km region on the WFS off
Tampa Bay is also used to identify LCSs, which reveal the presence of robust
transient transport barriers. While the HF-radar-derived transport barriers
cannot be unambiguously linked to the boundary of the FZ, this analysis does
demonstrate the feasibility of monitoring transport barriers on the WFS using a
HF-radar-based measurement system. The implications of a persistent cross-shelf
transport barrier on the WFS for the development of harmful algal blooms on the
shoreward side of the barrier are considered.Comment: Submitted to Geophysical Research Letter
Nonholonomic systems with symmetry allowing a conformally symplectic reduction
Non-holonomic mechanical systems can be described by a degenerate
almost-Poisson structure (dropping the Jacobi identity) in the constrained
space. If enough symmetries transversal to the constraints are present, the
system reduces to a nondegenerate almost-Poisson structure on a ``compressed''
space. Here we show, in the simplest non-holonomic systems, that in favorable
circumnstances the compressed system is conformally symplectic, although the
``non-compressed'' constrained system never admits a Jacobi structure (in the
sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of
HAMSYS 200
Parabolic resonances and instabilities in near-integrable two degrees of freedom Hamiltonian flows
When an integrable two-degrees-of-freedom Hamiltonian system possessing a
circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It
is proved that its occurrence is generic for one parameter families
(co-dimension one phenomenon) of near-integrable, t.d.o. systems. Numerical
experiments indicate that the motion near a parabolic resonance exhibits new
type of chaotic behavior which includes instabilities in some directions and
long trapping times in others. Moreover, in a degenerate case, near a {\it flat
parabolic resonance}, large scale instabilities appear. A model arising from an
atmospherical study is shown to exhibit flat parabolic resonance. This supplies
a simple mechanism for the transport of particles with {\it small} (i.e.
atmospherically relevant) initial velocities from the vicinity of the equator
to high latitudes. A modification of the model which allows the development of
atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities
are clearly observed
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