187 research outputs found
Additive Equivalence in Turbulent Drag Reduction by Flexible and Rodlike Polymers
We address the "Additive Equivalence" discovered by Virk and coworkers: drag
reduction affected by flexible and rigid rodlike polymers added to turbulent
wall-bounded flows is limited from above by a very similar Maximum Drag
Reduction (MDR) asymptote. Considering the equations of motion of rodlike
polymers in wall-bounded turbulent ensembles, we show that although the
microscopic mechanism of attaining the MDR is very different, the macroscopic
theory is isomorphic, rationalizing the interesting experimental observations.Comment: 8 pages, PRE, submitte
Statistical Description of Acoustic Turbulence
We develop expressions for the nonlinear wave damping and frequency
correction of a field of random, spatially homogeneous, acoustic waves. The
implications for the nature of the equilibrium spectral energy distribution are
discussedComment: PRE, Submitted. REVTeX, 16 pages, 3 figures (not included) PS Source
of the paper with figures avalable at
http://lvov.weizmann.ac.il/onlinelist.htm
Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+\epsilon dimensions
The statistics of 2-dimensional turbulence exhibit a riddle: the scaling
exponents in the regime of inverse energy cascade agree with the K41 theory of
turbulence far from equilibrium, but the probability distribution functions are
close to Gaussian like in equilibrium. The skewness \C S \equiv
S_3(R)/S^{3/2}_2(R) was measured as \C S_{\text{exp}}\approx 0.03. This
contradiction is lifted by understanding that 2-dimensional turbulence is not
far from a situation with equi-partition of enstrophy, which exist as true
thermodynamic equilibrium with K41 exponents in space dimension of . We
evaluate theoretically the skewness \C S(d) in dimensions ,
show that \C S(d)=0 at , and that it remains as small as \C
S_{\text{exp}} in 2-dimensions.Comment: PRL, submitted, REVTeX 4, 4 page
Identification of Kelvin waves: numerical challenges
Kelvin waves are expected to play an essential role in the energy dissipation
for quantized vortices. However, the identification of these helical
distortions is not straightforward, especially in case of vortex tangle. Here
we review several numerical methods that have been used to identify Kelvin
waves within the vortex filament model. We test their validity using several
examples and estimate whether these methods are accurate enough to verify the
correct Kelvin spectrum. We also illustrate how the correlation dimension is
related to different Kelvin spectra and remind that the 3D energy spectrum E(k)
takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at
http://www.springerlink.co
The Polymer Stress Tensor in Turbulent Shear Flows
The interaction of polymers with turbulent shear flows is examined. We focus
on the structure of the elastic stress tensor, which is proportional to the
polymer conformation tensor. We examine this object in turbulent flows of
increasing complexity. First is isotropic turbulence, then anisotropic (but
homogenous) shear turbulence and finally wall bounded turbulence. The main
result of this paper is that for all these flows the polymer stress tensor
attains a universal structure in the limit of large Deborah number \De\gg 1.
We present analytic results for the suppression of the coil-stretch transition
at large Deborah numbers. Above the transition the turbulent velocity
fluctuations are strongly correlated with the polymer's elongation: there
appear high-quality "hydro-elastic" waves in which turbulent kinetic energy
turns into polymer potential energy and vice versa. These waves determine the
trace of the elastic stress tensor but practically do not modify its universal
structure. We demonstrate that the influence of the polymers on the balance of
energy and momentum can be accurately described by an effective polymer
viscosity that is proportional to to the cross-stream component of the elastic
stress tensor. This component is smaller than the stream-wise component by a
factor proportional to \De ^2 . Finally we tie our results to wall bounded
turbulence and clarify some puzzling facts observed in the problem of drag
reduction by polymers.Comment: 11 p., 1 Fig., included, Phys. Rev. E., submitte
Superfluid vortex front at T -> 0: Decoupling from the reference frame
Steady-state turbulent motion is created in superfluid 3He-B at low
temperatures in the form of a turbulent vortex front, which moves axially along
a rotating cylindrical container of 3He-B and replaces vortex-free flow with
vortex lines at constant density. We present the first measurements on the
thermal signal from dissipation as a function of time, recorded at 0.2 Tc
during the front motion, which is monitored using NMR techniques. Both the
measurements and the numerical calculations of the vortex dynamics show that at
low temperatures the density of the propagating vortices falls well below the
equilibrium value, i.e. the superfluid rotates at a smaller angular velocity
than the container. This is the first evidence for the decoupling of the
superfluid from the container reference frame in the zero-temperature limit.Comment: 4 pages, 4 figure
Instability and Chaos in Non-Linear Wave Interaction: a simple model
We analyze stability of a system which contains an harmonic oscillator
non-linearly coupled to its second harmonic, in the presence of a driving
force. It is found that there always exists a critical amplitude of the driving
force above which a loss of stability appears. The dependence of the critical
input power on the physical parameters is analyzed. For a driving force with
higher amplitude chaotic behavior is observed. Generalization to interactions
which include higher modes is discussed.
Keywords: Non-Linear Waves, Stability, Chaos.Comment: 16 pages, 4 figure
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
We propose a mathematical derivation of Brinkman's force for a cloud of
particles immersed in an incompressible fluid. Our starting point is the Stokes
or steady Navier-Stokes equations set in a bounded domain with the disjoint
union of N balls of radius 1/N removed, and with a no-slip boundary condition
for the fluid at the surface of each ball. The large N limit of the fluid
velocity field is governed by the same (Navier-)Stokes equations in the whole
domain, with an additional term (Brinkman's force) that is (minus) the total
drag force exerted by the fluid on the particle system. This can be seen as a
generalization of Allaire's result in [Arch. Rational Mech. Analysis 113
(1991), 209-259] who treated the case of motionless, periodically distributed
balls. Our proof is based on slightly simpler, though similar homogenization
techniques, except that we avoid the periodicity assumption and use instead the
phase-space empirical measure for the particle system. Similar equations are
used for describing the fluid phase in various models for sprays
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
Stable topological textures in a classical 2D Heisenberg model
We show that stable localized topological soliton textures (skyrmions) with
topological charge exist in a classical 2D Heisenberg
model of a ferromagnet with uniaxial anisotropy. For this model the soliton
exist only if the number of bound magnons exceeds some threshold value depending on and the effective anisotropy constant .
We define soliton phase diagram as the dependence of threshold energies and
bound magnons number on anisotropy constant. The phase boundary lines are
monotonous for both and , while the solitons with
reveal peculiar nonmonotonous behavior, determining the transition regime from
low to high topological charges. In particular, the soliton energy per
topological charge (topological energy density) achieves a minimum neither for
nor high charges, but rather for intermediate values or
.Comment: 8 pages, 4 figure
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