33 research outputs found
Comment on "Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence"
In the paper by Khomenko et al. [Phys. Rev. B \textbf{91}, 180504 (2015)] the
authors, analyzing numerically the steady counterflowing helium in
inhomogeneous channel flow, concluded that the production term in
the Vinen equation is proportional to (where is vortex line density and
is the counterflow velocity). In present comment we
demonstrated that the procedure, implemented by the authors includes a number
of questionable steps, such as a decomposition of velocity of line and
interpretation of the flux term. Additionally, the overall strategy -
extracting information on the temporal behavior from the stationary solution
also remains questionable. Because of that the method of determination of the
explicit shape of Vinen equation is very sensitive to the listed elements, the
final conclusion of the authors cannot be considered as unambiguous.Comment: 3 page
Coarse-grained Hydrodynamics of turbulent superfluids: HVBK approach and the bundle structure of the vortex tangle
In the comment I develop a critical analysis of the use of the HVBK method
for the study of three-dimensional turbulent flows of superfluids. The
conception of the vortex bundles forming the structure of quantum turbulence is
controversial and does not justify the use of the HVBK method. In addition,
this conception is counterproductive, because it gives incorrect ideas about
the structure of the vortex tangle as a set of bundles containing parallel
lines. The only type of dynamics of vortex filaments inside these bundles is
possible, namely, Kelvin waves running along the filaments. At the same time,
as shown in numerous numerical simulations, a vortex tangle consists of a set
of entangled vortex loops of different sizes and having a random walk
structure. These loops are subject to large deformations (due to highly
nonlinear dynamics), they reconnect with each other and with the wall, split
and merge, creating a lot of daughter loops. They also bear Kelvin waves on
them, but the latter have little impact.
I also propose and discuss an alternative variant of study of
three-dimensional turbulent flows, in which the vortex line density is not associated with , but it
is an independent variable described by a separate equation.Comment: 6 pages, 40 ref. There are some changes after discussion with the
referee
Reconnection of vortex filaments and Kolmogorov spectrum
The energy spectrum of the 3D velocity field, induced by collapsing vortex
filaments is studied. One of the aims of this work is to clarify the appearance
of the Kolmogorov type energy spectrum , observed in
many numerical works on discrete vortex tubes (quantized vortex filaments in
quantum fluids). Usually, explaining classical turbulent properties of quantum
turbulence, the model of vortex bundles, is used. This model is necessary to
mimic the vortex stretching, which is responsible for the energy transfer in
classical turbulence. In our consideration we do not appeal to the possible
"bundle arrangement" but explore alternative idea that the turbulent spectra
appear from singular solution, which describe the collapsing line at moments of
reconnection. One more aim is related to an important and intensively discussed
topic - a role of hydrodynamic collapse in the formation of turbulent spectra.
We demonstrated that the specific vortex filament configuration generated the
spectrum close to the Kolmogorov dependence and discussed the reason for
this as well as the reason for deviation. We also discuss the obtained results
from point of view of the both classical and quantum turbulence.Comment: 4 pages,4 figure
Langevin dynamics of vortex lines in the counterflowing He II. Talk given at the Low Temperature Conference, Kazan, 2015
The problem of the statistics of a set of chaotic vortex lines in a
counterflowing superfluid helium is studied. We introduced a Langevin-type
force into the equation of motion of the vortex line in presence of relative
velocity . This random force is supposed to be Gaussian
satisfying the fluctuation-dissipation theorem. The corresponding Fokker-Planck
equation for probability functional in the vortex loop configuration space is
shown to have a solution in the form of Gibbs distribution with the
substitution E\{\mathbf{s\}\rightarrow }E(\{\mathbf{% s\}-P(v_{n}-v_{s})},
where is the energy of the vortex configuration
, and is the Lamb impulse. Some physical
consequences of this fact are discussed.\\ \newline PACS numbers: 47.32.C-
(Vortex dynamics) 47.32.cf (Vortex reconnection and rings), 47.37.+q
(Hydrodynamic aspects of superfluidity)Comment: 4 pages, talk given at the Low Temperature Conference, Kazan, 201
On the Nonuniform Quantum Turbulence in Superfluids
The problem of quantum turbulence in a channel with an inhomogeneous
counterflow of superfluid turbulent helium is studied. \ The counterflow
velocity along the channel is supposed to have a parabolic
profile in the transverse direction . Such statement corresponds to the
recent numerical simulation by Khomenko et al. [Phys. Rev. B \textbf{91},
180504 (2015)]. The authors reported about a sophisticated behavior of the
vortex line density (VLD) , different from , which follows from the naive,
straightforward application of the conventional Vinen theory. It is clear, that
Vinen theory should be refined by taking into account transverse effects and
the way it ought to be done is the subject of active discussion in the
literature. In the work we discuss several possible mechanisms of the
transverse flux of VLD which should be incorporated
in the standard Vinen equation to describe adequately the inhomogeneous quantum
turbulence (QT). It is shown that the most effective among these mechanisms is
the one that is related to the phase slippage phenomenon. The use of this flux
in the modernized Vinen equation corrects the situation with an unusual
distribution of the vortex line density, and satisfactory describes the
behavior both in stationary and nonstationary
situations. The general problem of the phenomenological Vinen theory in the
case of nonuniform and nonstationary quantum turbulence is thoroughly
discussed.Comment: 7 pages, 3 figure
Chaotic Quantum Vortexes In A Weakly Non Ideal Bose Gas. Thermodynamic Equilibrium And Turbulence
We study the stochastic behavior of a set of chaotic vortex loops appeared in
imperfect Bose gas. Dynamics of Bose-gas is supposed to obey Gross-Pitaevskii
equation with additional noise satisfying fluctuation-dissipation relation. The
corresponding Fokker-Planck equation for probability functional has solution
where
is the Ginzburg-Landau free energy. Considering vortex
filaments as topological defects of field we derive a
Langevin-type equation of motion of the line with the correspondingly
transformed stirring force. The respective Fokker-Planck equation for
probability functional in vortex loop
configuration space is shown to have a solution in the form of where is the
normalizing factor and is energy of vortex line configurations.
Analyzing this result we discuss possible reasons for destruction of the
thermodynamic equilibrium and follow the mechanisms of transition to the
turbulent stateComment: 10 pages, RevTeX, submitted to JLT
Applications of Gaussian model of the vortex tangle in the superfluid turbulent HeII
In spite of an appearance of some impressive recent results in understanding
of the superfluid turbulence in HeII they fail to evaluate many characteristics
of vortex tangle needed for both applications and fundamental study. Early we
reported the Gaussian model of the vortex tangle in superfluid turbulent HeII.
That model is just trial distribution functional in space of vortex loop
configurations constructed on the basis of well established properties of
vortex tangle. It is designed to calculate various averages taken over
stochastic vortex loop configurations. In this paper we use this model to
calculate some important characteristics of the vortex tangle. In particular we
evaluate the average superfluid mass current J induced by vortices and the
average energy E associated with the chaotic vortex filament.Comment: latex, 7 pages, 1 Postscript figure, uses subeqnar.sty, sprmindx.sty,
cropmark.sty, physprbb.sty, svmult.cls, to be published in "Quantized vortex
dynamics and superfluid turbulence", Ed. C. Barenghi (Springer Verlag,
Berlin, 2001
Diffusive Decay of the Vortex Tangle and Kolmogorov turbulence in quantum fluids
The idea that chaotic set of quantum vortices can mimic classical turbulence,
or at least reproduce many main features, is currently actively being
developed. Appreciating significance of the challenging problem of the
classical turbulence it can be expressed that the idea to study it in terms of
quantized line is indeed very important and may be regarded as a breakthrough.
For this reason, this theory should be carefully scrutinized. One of the basic
arguments supporting this point of view is the fact that vortex tangle decays
at zero temperature, when the apparent mechanism of dissipation (mutual
friction) is absent. Since the all possible mechanisms of dissipation of the
vortex energy, discussed in the literature, are related to the small scales, it
is natural to suggest that the Kolmogorov cascade takes the place with the flow
of the energy, just as in the classical turbulence. In a series of recent
experiment attenuation of vortex line density was observed and authors
attribute this decay to the properties of the Kolmogorov turbulence. In the
present work we discuss alternative possibility of decay of the vortex tangle,
which is not related to dissipation at small scales. This mechanism is just the
diffusive like spreading of the vortex tangle. We discuss a number of the key
experiments, considering them both from the point of view of alternative
explanation and of the theory of Kolmogorov turbulence in quantum fluids.Comment: The work was presented at SUR 2010, submitted in JLT
Statistical signature of vortex filaments in classic turbulence: dog or tail?
The title of this paper echoes the title of a paragraph in the famous book by
Frisch on classical turbulence. In the relevant chapter, the author discusses
the role of the statistical dynamics of vortex filaments in the fascinating
problem of turbulence and the possibility of a breakthrough in constructing an
advanced theory. This aspect arose due to the large amount of evidence, both
experimental and numerical, that the vorticity field in turbulent flows has a
pronounced filamentary structure. In fact, there is unquestionably a strong
relationship between the dynamics of chaotic vortex filaments and turbulent
phenomena. However, the question arises as to whether the basic properties of
turbulence (cascade, scaling laws. etc.) are a consequence of the dynamics of
the vortex filaments (the `dog' concept), or whether the latter have only a
marginal significance (the `tail' concept). Based on well-established results
regarding the dynamics of quantized vortex filaments in superfluids, we
illustrate how these dynamics can lead to the main elements of the theory of
turbulence. We cover key topics such as the exchange of energy between
different scales, the possible origin of Kolmogorov-type spectra and the free
decay behavior.Comment: 19 pages, 4 figure
Energy spectrum of the 3D velocity field, induced by vortex tangle
A review of various exactly solvable models on the determination of the
energy spectra of 3D-velocity field, induced by chaotic vortex lines
is proposed. This problem is closely related to the sacramental question
whether a chaotic set of vortex filaments can mimic the real hydrodynamic
turbulence. The quantity can be exactly calculated,
provided that we know the probability distribution functional of vortex loops configurations. The
knowledge of is identical to the full
solution of the problem of quantum turbulence and, in general, is
unknown. In the paper we discuss several models allowing to evaluate spectra in
the explicit form. This cases include standard vortex configurations such as a
straight line, vortex array and ring. Independent chaotic loops of various
fractal dimension as well as interacting loops in the thermodynamic equilibrium
also permit an analytical solution. We also describe the method of an obtaining
the 3D velocity spectrum induced by the straight line perturbed with chaotic 1D
Kelvin waves on it.Comment: 7 pages, 1 figure. Paper is submitted to JLTP, Proceedings of QFS
2012 (Lancaster 2012