7,758 research outputs found
Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence
We perform a direct numerical simulation (DNS) of the forced, incompressible
two-dimensional Navier-Stokes equation coupled with the FENE-P equations for
the polymer-conformation tensor. The forcing is such that, without polymers and
at low Reynolds numbers \mbox{Re}, the film attains a steady state that is a
square lattice of vortices and anti-vortices. We find that, as we increase the
Weissenberg number \mbox{Wi}, a sequence of nonequilibrium phase transitions
transforms this lattice, first to spatially distorted, but temporally steady,
crystals and then to a sequence of crystals that oscillate in time,
periodically, at low \mbox{Wi}, and quasiperiodically, for slightly larger
\mbox{Wi}. Finally, the system becomes disordered and displays spatiotemporal
chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram
for this system, in the \mbox{Wi} - \Omega plane, where \Omega \propto
{\mbox{Re}}, and show that (a) the boundary between the crystalline and
turbulent phases has a complicated, fractal-type character and (b) the
Okubo-Weiss parameter provides us with a natural measure for
characterizing the phases and transitions in this diagram.Comment: 16 pages, 17 figure
Collective frequency variation in network synchronization and reverse PageRank
A wide range of natural and engineered phenomena rely on large networks of
interacting units to reach a dynamical consensus state where the system
collectively operates. Here we study the dynamics of self-organizing systems
and show that for generic directed networks the collective frequency of the
ensemble is {\it not} the same as the mean of the individuals' natural
frequencies. Specifically, we show that the collective frequency equals a
weighted average of the natural frequencies, where the weights are given by an
out-flow centrality measure that is equivalent to a reverse PageRank
centrality. Our findings uncover an intricate dependence of the collective
frequency on both the structural directedness and dynamical heterogeneity of
the network, and also reveal an unexplored connection between synchronization
and PageRank, which opens the possibility of applying PageRank optimization to
synchronization. Finally, we demonstrate the presence of collective frequency
variation in real-world networks by considering the UK and Scandinavian power
grids
Spatiotemporal properties of multiscale two-dimensional ows
The extraordinary complexity of turbulence has motivated the study of some of its key
features in
flows with similar structure but simpler or even trivial dynamics. Recently,
a novel class of such
flows has been developed in the laboratory by applying multiscale
electromagnetic forcing to a thin layer of conducting
fluid. In spite of being stationary,
planar, and laminar these
flows have been shown to resemble turbulent ones in terms of
energy spectra and particle dispersion. In this thesis, some extensions of these
flows are
investigated through simulations of a layer-averaged model carried out using a bespoke
semi-Lagrangian spline code. The selected forcings generalise the experimental ones by
allowing for various kinds of self-similarity and planetary motion of the multiple scales.
The spatiotemporal structure of the forcings is largely reflected on the
flows, since they
mainly arise from a linear balance between forcing and bottom friction. The exponents
of the approximate power laws found in the wavenumber spectra can thus be related to
the scaling and geometrical forcing parameters. The Eulerian frequency spectra of the
unsteady
flows exhibit similar power laws originating from the sweeping of the multiple
flow scales by the forcing motions. The disparity between
fluid and sweeping velocities
makes it possible to justify likewise the observed Lagrangian power laws, but precludes
a proper analogy with turbulence. In the steady case, the absolute dispersion of tracer
particles presents ballistic and diffusive stages, while relative dispersion shows a superquadratic
intermediate stage dominated by separation bursts due to the various scales.
In the unsteady case, the absence of trapping by fixed streamlines leads to appreciable
enhancement of relative dispersion at low and moderate rotation frequency. However,
the periodic reversals of the large scale give rise to subdiffusive absolute dispersion and
severely impede relative dispersion at high frequency
Numerical simulation and comparison of symmetrical/supercritical airfoils for the near tip region of a helicopter in forward flight
Aerodynamic loads on a multi-bladed helicopter rotor in forward flight at transonic tip conditions are calculated. The unsteady, three-dimensional, time-accurate compressible Reynolds-averaged thin layer Navier-Stokes equations are solved in a rotating coordinate system on a body-conformed, curvilinear grid of C-H topology. Detailed boundary layer and global numerical comparisons of NACA-0012 symmetrical and CAST7-158 supercritical airfoils are made under identical forward flight conditions. The rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blade. This correction is obtained by computing the local induced downwash velocity with a free wake analysis program. The calculations are performed on the Numerical Aerodynamic Simulation Cray 2 and the VPS32 (a derivative of a Cyber 205 at the Langley Research Center) for a model helicopter rotor in forward flight
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