232 research outputs found
Disentangling Scaling Properties in Anisotropic and Inhomogeneous Turbulence
We address scaling in inhomogeneous and anisotropic turbulent flows by
decomposing structure functions into their irreducible representation of the
SO(3) symmetry group which are designated by indices. Employing
simulations of channel flows with Re we demonstrate that
different components characterized by different display different scaling
exponents, but for a given these remain the same at different distances
from the wall. The exponent agrees extremely well with high Re
measurements of the scaling exponents, demonstrating the vitality of the SO(3)
decomposition.Comment: 4 page
Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity
Understanding the mechanical properties of glasses remains elusive since the
glass transition itself is not fully understood, even in well studied examples
of glass formers in two dimensions. In this context we demonstrate here: (i) a
direct evidence for a diverging length scale at the glass transition (ii) an
identification of the glass transition with the disappearance of fluid-like
regions and (iii) the appearance in the glass state of fluid-like regions when
mechanical strain is applied.
These fluid-like regions are associated with the onset of plasticity in the
amorphous solid. The relaxation times which diverge upon the approach to the
glass transition are related quantitatively.Comment: 5 pages, 5 figs.; 2 figs. omitted, new fig., quasi-crystal discussion
omitted, new material on relaxation time
Dynamics of the vortex line density in superfluid counterflow turbulence
Describing superfluid turbulence at intermediate scales between the
inter-vortex distance and the macroscale requires an acceptable equation of
motion for the density of quantized vortex lines . The closure of such
an equation for superfluid inhomogeneous flows requires additional inputs
besides and the normal and superfluid velocity fields. In this paper
we offer a minimal closure using one additional anisotropy parameter .
Using the example of counterflow superfluid turbulence we derive two coupled
closure equations for the vortex line density and the anisotropy parameter
with an input of the normal and superfluid velocity fields. The
various closure assumptions and the predictions of the resulting theory are
tested against numerical simulations.Comment: 7 pages, 5 figure
Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multi-scaling
This manuscript is a draft of work in progress, meant for network
distribution only. It will be updated to a formal preprint when the numerical
calculations will be accomplished. In this draft we develop a consistent
closure procedure for the calculation of the scaling exponents of the
th order correlation functions in fully developed hydrodynamic turbulence,
starting from first principles. The closure procedure is constructed to respect
the fundamental rescaling symmetry of the Euler equation. The starting point of
the procedure is an infinite hierarchy of coupled equations that are obeyed
identically with respect to scaling for any set of scaling exponents .
This hierarchy was discussed in detail in a recent publication [V.S. L'vov and
I. Procaccia, Phys. Rev. E, submitted, chao-dyn/9707015]. The scaling exponents
in this set of equations cannot be found from power counting. In this draft we
discuss in detail low order non-trivial closures of this infinite set of
equations, and prove that these closures lead to the determination of the
scaling exponents from solvability conditions. The equations under
consideration after this closure are nonlinear integro-differential equations,
reflecting the nonlinearity of the original Navier-Stokes equations.
Nevertheless they have a very special structure such that the determination of
the scaling exponents requires a procedure that is very similar to the solution
of linear homogeneous equations, in which amplitudes are determined by fitting
to the boundary conditions in the space of scales. The re-normalization scale
that i necessary for any anomalous scaling appears at this point. The Holder
inequalities on the scaling exponents select the renormalizaiton scale as the
outer scale of turbulence .Comment: 10 pages, 5 figs. to be submitted PR
Shell Model of Two-dimensional Turbulence in Polymer Solutions
We address the effect of polymer additives on two dimensional turbulence, an
issue that was studied recently in experiments and direct numerical
simulations. We show that the same simple shell model that reproduced drag
reduction in three-dimensional turbulence reproduces all the reported effects
in the two-dimensional case. The simplicity of the model offers a
straightforward understanding of the all the major effects under consideration
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