115 research outputs found
Shell Model for Drag Reduction with Polymer Additive in Homogeneous Turbulence
Recent direct numerical simulations of the FENE-P model of non-Newtonian
hydrodynamics revealed that the phenomenon of drag reduction by polymer
additives exists (albeit in reduced form) also in homogeneous turbulence. We
introduce here a simple shell model for homogeneous viscoelastic flows that
recaptures the essential observations of the full simulations. The simplicity
of the shell model allows us to offer a transparent explanation of the main
observations. It is shown that the mechanism for drag reduction operates mainly
on the large scales. Understanding the mechanism allows us to predict how the
amount of drag reduction depends of the various parameters in the model. The
main conclusion is that drag reduction is not a universal phenomenon, it peaks
in a window of parameters like Reynolds number and the relaxation rate of the
polymer
Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem
We consider transport of dynamically passive quantities in the Batchelor
regime of smooth in space velocity field. For the case of arbitrary temporal
correlations of the velocity we formulate the statistics of relevant
characteristics of Lagrangian motion. This allows to generalize many results
obtained previously for the delta-correlated in time strain, thus answering the
question of universality of these results.Comment: 11 pages, revtex; added references, typos correcte
Scaling Exponents in Anisotropic Hydrodynamic Turbulence
In anisotropic turbulence the correlation functions are decomposed in the
irreducible representations of the SO(3) symmetry group (with different
"angular momenta" ). For different values of the second order
correlation function is characterized by different scaling exponents
. In this paper we compute these scaling exponents in a Direct
Interaction Approximation (DIA). By linearizing the DIA equations in small
anisotropy we set up a linear operator and find its zero-modes in the inertial
interval of scales. Thus the scaling exponents in each -sector follow
from solvability condition, and are not determined by dimensional analysis. The
main result of our calculation is that the scaling exponents
form a strictly increasing spectrum at least until , guaranteeing that
the effects of anisotropy decay as power laws when the scale of observation
diminishes. The results of our calculations are compared to available
experiments and simulations.Comment: 10 pages, 4 figures, PRE submitted. Fixed problems with figure
Anomalous and dimensional scaling in anisotropic turbulence
We present a numerical study of anisotropic statistical fluctuations in
homogeneous turbulent flows. We give an argument to predict the dimensional
scaling exponents, (p+j)/3, for the projections of p-th order structure
function in the j-th sector of the rotational group. We show that measured
exponents are anomalous, showing a clear deviation from the dimensional
prediction. Dimensional scaling is subleading and it is recovered only after a
random reshuffling of all velocity phases, in the stationary ensemble. This
supports the idea that anomalous scaling is the result of a genuine inertial
evolution, independent of large-scale behavior.Comment: 4 pages, 3 figure
Stabilization of Hydrodynamic Flows by Small Viscosity Variations
Motivated by the large effect of turbulent drag reduction by minute
concentrations of polymers we study the effects of a weakly space-dependent
viscosity on the stability of hydrodynamic flows. In a recent Letter [Phys.
Rev. Lett. {\bf 87}, 174501, (2001)] we exposed the crucial role played by a
localized region where the energy of fluctuations is produced by interactions
with the mean flow (the "critical layer"). We showed that a layer of weakly
space-dependent viscosity placed near the critical layer can have a very large
stabilizing effect on hydrodynamic fluctuations, retarding significantly the
onset of turbulence. In this paper we extend these observation in two
directions: first we show that the strong stabilization of the primary
instability is also obtained when the viscosity profile is realistic (inferred
from simulations of turbulent flows with a small concentration of polymers).
Second, we analyze the secondary instability (around the time-dependent primary
instability) and find similar strong stabilization. Since the secondary
instability develops around a time-dependent solution and is three-dimensional,
this brings us closer to the turbulent case. We reiterate that the large effect
is {\em not} due to a modified dissipation (as is assumed in some theories of
drag reduction), but due to reduced energy intake from the mean flow to the
fluctuations. We propose that similar physics act in turbulent drag reduction.Comment: 10 pages, 17 figs., REVTeX4, PRE, submitte
Drag Reduction by Polymers in Turbulent Channel Flows: Energy Redistribution Between Invariant Empirical Modes
We address the phenomenon of drag reduction by dilute polymeric additive to
turbulent flows, using Direct Numerical Simulations (DNS) of the FENE-P model
of viscoelastic flows. It had been amply demonstrated that these model
equations reproduce the phenomenon, but the results of DNS were not analyzed so
far with the goal of interpreting the phenomenon. In order to construct a
useful framework for the understanding of drag reduction we initiate in this
paper an investigation of the most important modes that are sustained in the
viscoelastic and Newtonian turbulent flows respectively. The modes are obtained
empirically using the Karhunen-Loeve decomposition, allowing us to compare the
most energetic modes in the viscoelastic and Newtonian flows. The main finding
of the present study is that the spatial profile of the most energetic modes is
hardly changed between the two flows. What changes is the energy associated
with these modes, and their relative ordering in the decreasing order from the
most energetic to the least. Modes that are highly excited in one flow can be
strongly suppressed in the other, and vice versa. This dramatic energy
redistribution is an important clue to the mechanism of drag reduction as is
proposed in this paper. In particular there is an enhancement of the energy
containing modes in the viscoelastic flow compared to the Newtonian one; drag
reduction is seen in the energy containing modes rather than the dissipative
modes as proposed in some previous theories.Comment: 11 pages, 13 figures, included, PRE, submitted, REVTeX
A simple model for drag reduction
Direct Numerical Simulations established that the FENE-P model of
viscoelastic flows exhibits the phenomenon of turbulent drag reduction which is
caused in experiments by dilute polymeric additives. To gain analytic
understanding of the phenomenon we introduce in this Letter a simple
1-dimensional model of the FENE-P equations. We demonstrate drag reduction in
the simple model, and explain analytically the main observations which include
(i) reduction of velocity gradients for fixed throughput and (ii) increase of
throughput for fixed dissipation.Comment: submitted to PR
Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear
An effect of a mean velocity shear on a turbulence and on the effective force
which is determined by the gradient of Reynolds stresses is studied. Generation
of a mean vorticity in a homogeneous incompressible turbulent flow with an
imposed mean velocity shear due to an excitation of a large-scale instability
is found. The instability is caused by a combined effect of the large-scale
shear motions (''skew-induced" deflection of equilibrium mean vorticity) and
''Reynolds stress-induced" generation of perturbations of mean vorticity.
Spatial characteristics, such as the minimum size of the growing perturbations
and the size of perturbations with the maximum growth rate, are determined.
This instability and the dynamics of the mean vorticity are associated with the
Prandtl's turbulent secondary flows. This instability is similar to the
mean-field magnetic dynamo instability. Astrophysical applications of the
obtained results are discussed.Comment: 8 pages, 3 figures, REVTEX4, submitted to Phys. Rev.
Comparison of some Reduced Representation Approximations
In the field of numerical approximation, specialists considering highly
complex problems have recently proposed various ways to simplify their
underlying problems. In this field, depending on the problem they were tackling
and the community that are at work, different approaches have been developed
with some success and have even gained some maturity, the applications can now
be applied to information analysis or for numerical simulation of PDE's. At
this point, a crossed analysis and effort for understanding the similarities
and the differences between these approaches that found their starting points
in different backgrounds is of interest. It is the purpose of this paper to
contribute to this effort by comparing some constructive reduced
representations of complex functions. We present here in full details the
Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM)
together with other approaches that enter in the same category
Distortion in a 7xxx aluminum alloy during liquid phase sintering
The distortion in a sintered 7xxx aluminum alloy, Al-7Zn-2.5Mg-1Cu (wt. pct), has been investigated by sintering three rectangular bars in each batch at 893 K (620 °C) for 0 to 40 minutes in nitrogen, followed by air or furnace cooling. They were placed parallel to each other, equally spaced apart at 2 mm, with their long axes being perpendicular to the incoming nitrogen flow. Pore evolution in each sample during isothermal sintering was examined metallographically. The compositional changes across sample mid-cross section and surface layers were analyzed using energy dispersive X-ray spectroscopy and X-ray photoelectron spectroscopy depth profiling, respectively. The two outer samples bent toward the middle one, while the middle sample was essentially distortion free after sintering. The distortion in the outer samples was a result of differential shrinkage between their outer and inner surfaces during isothermal sintering. The porous outer surface showed an enrichment of oxygen around the large pores as well as lower magnesium and zinc contents than the interior and inner surface of the same sample, while the inner surface was distinguished by the presence of AlN. The differential shrinkage was caused by different oxygen contents in local sintering atmosphere and unbalanced loss of magnesium and zinc between the outer and inner surfaces
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