1,105 research outputs found
Spatiotemporal perspective on the decay of turbulence in wall-bounded flows
Using a reduced model focusing on the in-plane dependence of plane Couette
flow, it is shown that the turbulent-to-laminar relaxation process can be
understood as a nucleation problem similar to that occurring at a thermodynamic
first-order phase transition. The approach, apt to deal with the large
extension of the system considered, challenges the current interpretation in
terms of chaotic transients typical of temporal chaos. The study of the
distribution of the sizes of laminar domains embedded in turbulent flow proves
that an abrupt transition from sustained spatiotemporal chaos to laminar flow
can take place at some given value of the Reynolds number R_{low}, whether or
not the local chaos lifetime, as envisioned within low-dimensional dynamical
systems theory, diverges at finite R beyond R_{low}.Comment: 9 pages, 3 figures, published in 2009 as a Rapid Communication in
Phys. Rev. E, vol. 79, article 025301, corrected to include erratum Phys.
Rev. E 79, 039904. References to now published material have been updated. A
note has been added pointing to recent related work by D. Barkley
(arXiv:1101.4125v1
Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model
On its way to turbulence, plane Couette flow - the flow between
counter-translating parallel plates - displays a puzzling steady oblique
laminar-turbulent pattern. We approach this problem via Galerkin modelling of
the Navier-Stokes equations. The wall-normal dependence of the hydrodynamic
field is treated by means of expansions on functional bases fitting the
boundary conditions exactly. This yields a set of partial differential
equations for the spatiotemporal dynamics in the plane of the flow. Truncating
this set beyond lowest nontrivial order is numerically shown to produce the
expected pattern, therefore improving over what was obtained at cruder
effective wall-normal resolution. Perspectives opened by the approach are
discussed.Comment: to appear in Fluid Dynamics Research; 14 pages, 5 figure
Critical properties of phase transitions in lattices of coupled logistic maps
We numerically demonstrate that collective bifurcations in two-dimensional
lattices of locally coupled logistic maps share most of the defining features
of equilibrium second-order phase transitions. Our simulations suggest that
these transitions between distinct collective dynamical regimes belong to the
universality class of Miller and Huse model with synchronous update
Large scale flow around turbulent spots
Numerical simulations of a model of plane Couette flow focusing on its
in-plane spatio-temporal properties are used to study the dynamics of turbulent
spots.Comment: 16 pages, 6 figure
Grain boundary dynamics in stripe phases of non potential systems
We describe numerical solutions of two non potential models of pattern
formation in nonequilibrium systems to address the motion and decay of grain
boundaries separating domains of stripe configurations of different
orientations. We first address wavenumber selection because of the boundary,
and possible decay modes when the periodicity of the stripe phases is different
from the selected wavenumber for a stationary boundary. We discuss several
decay modes including long wavelength undulations of the moving boundary as
well as the formation of localized defects and their subsequent motion. We find
three different regimes as a function of the distance to the stripe phase
threshold and initial wavenumber, and then correlate these findings with domain
morphology during domain coarsening in a large aspect ratio configuration.Comment: 8 pages, 8 figure
Lyapunov analysis captures the collective dynamics of large chaotic systems
We show, using generic globally-coupled systems, that the collective dynamics
of large chaotic systems is encoded in their Lyapunov spectra: most modes are
typically localized on a few degrees of freedom, but some are delocalized,
acting collectively on the trajectory. For globally-coupled maps, we show
moreover a quantitative correspondence between the collective modes and some of
the so-called Perron-Frobenius dynamics. Our results imply that the
conventional definition of extensivity must be changed as soon as collective
dynamics sets in.Comment: 4 pages, 4 figures; small changes, mostly stylistic, made in v
Tilt grain boundary instabilities in three dimensional lamellar patterns
We identify a finite wavenumber instability of a 90 tilt grain
boundary in three dimensional lamellar phases which is absent in two
dimensional configurations. Both a stability analysis of the slowly varying
amplitude or envelope equation for the boundary, and a direct numerical
solution of an order parameter model equation are presented. The instability
mode involves two dimensional perturbations of the planar base boundary, and is
suppressed for purely one dimensional perturbations. We find that both the most
unstable wavenumbers and their growth rate increase with , the
dimensionless distance away from threshold of the lamellar phase.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
On the decay of turbulence in plane Couette flow
The decay of turbulent and laminar oblique bands in the lower transitional
range of plane Couette flow is studied by means of direct numerical simulations
of the Navier--Stokes equations. We consider systems that are extended enough
for several bands to exist, thanks to mild wall-normal under-resolution
considered as a consistent and well-validated modelling strategy. We point out
a two-stage process involving the rupture of a band followed by a slow
regression of the fragments left. Previous approaches to turbulence decay in
wall-bounded flows making use of the chaotic transient paradigm are
reinterpreted within a spatiotemporal perspective in terms of large deviations
of an underlying stochastic process.Comment: ETC13 Conference Proceedings, 6 pages, 5 figure
Modeling transitional plane Couette flow
The Galerkin method is used to derive a realistic model of plane Couette flow
in terms of partial differential equations governing the space-time dependence
of the amplitude of a few cross-stream modes. Numerical simulations show that
it reproduces the globally sub-critical behavior typical of this flow. In
particular, the statistics of turbulent transients at decay from turbulent to
laminar flow displays striking similarities with experimental findings.Comment: 33 pages, 10 figure
Soliton turbulences in the complex Ginzburg-Landau equation
We study spatio-temporal chaos in the complex Ginzburg-Landau equation in
parameter regions of weak amplification and viscosity. Turbulent states
involving many soliton-like pulses appear in the parameter range, because the
complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger
equation. We find that the distributions of amplitude and wavenumber of pulses
depend only on the ratio of the two parameters of the amplification and the
viscosity. This implies that a one-parameter family of soliton turbulence
states characterized by different distributions of the soliton parameters
exists continuously around the completely integrable system.Comment: 5 figure
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