arXiv subjects

Sergey K. Nemirovskii

Publications and source records attributed to Sergey K. Nemirovskii.

At least 19 recordsLinked to original sources

arXiv2024

Thermodynamics of random walking vortex loops in counterflowing superfluids

Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluids in the presence of a counterflow, the influence of a vortex tangle on various thermodynamic phenomena in quantum liquids is studied. Using the early calculated partition function we study some of the properties of He II related to counterflow, such as the distribution of vortex loops in their length, the suppression of the superfluid density $\rho _{s}$ and the shift $T_{\lambda}$. Good agreement with the early obtained results is a fairly strong argument in favor of the point of view that the gas of string-like topological excitations can indeed be considered as a additional kind of quasi-particles having the inner structure at high temperatures, especially near the phase transition. The application of the developed formalism to the theory of quantum turbulence is briefly discussed.

cond-mat.soft↗

arXiv2022

Comment on "On the relations between large-scale models of superfluid helium-4" [Phys. Fluids 33, 127124 (2021]"

We comment on the paper by M. S\'ykora, M. Pavelka, M. La Mantia, D. Jou, and M. Grmela "On the relations between large-scale models of superfluid helium-4," Physics of Fluids, 33(12):127124(2021), where the authors have developed a formalism for describing a coarse-grained flow of superfluid helium. This formalism is greatly based on the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) model. We strongly disagree with the use of the HVBK equation approach for the case of the three-dimensional quantum turbulence and expose our objections in this comment. We discuss the HVBK method and also criticize the so-called vortex bundles model, which serves as a basis for using the HVBK method in a three-dimensional quantum turbulence.

cond-mat.quant-gas↗

arXiv2020

On the cavity evolution and the Rayleigh--Plesset equation in superfluid helium

On the basis of the two-fluid hydrodynamics, an analogue of the famous Rayleigh-Plesse equation for the dynamics of a spherical bubble in superfluid helium is obtained. The mass flow velocity $v$ and the velocity of the normal component $v_{n}$ were chosen as independent variables. Due to the two-fluid nature of HeII, the cross terms in the evolution equation for the boundary position $\ R(t)$ appeared, which were absent in classical Rayleigh-Plesset equation in ordinary fluids. One of them renormilizes the coefficient in front of $(dR/dt)^{2}$. Another additional term formally coinciding with the viscous term, describes the attenuation of the boundary oscillations. This "extra-damping" term, greatly exceeding the usual viscous term, leads to a significant difference in the dynamics of cavity compared to HeI. In particular, this results in the interesting effect of abnormal suppression of oscillations of the vapor--liquid boundary observed in many works. There is also an additional term proportional to the squared velocity of the normal component, which is independent of the derivative $dR/dt$, and can be included in the pressure drop. Its physical meaning is that it describes a "Bernoulli" -like pressure created by the flow of a normal component. The obtained result declares that some results on the dynamics of the cavity in superfluid helium should be reviewed

cond-mat.soft↗

arXiv2019

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 $ \mathcal{L}(r,t)$ is not associated with $\nabla \times \mathbf{v}_{s}$, but it is an independent variable described by a separate equation.

cond-mat.other↗

arXiv2019

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.

physics.flu-dyn↗

arXiv2017

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 $V_{ns}^{x}(y)$ along the channel is supposed to have a parabolic profile in the transverse direction $y$. 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) $\mathcal{L}(\mathbf{r},t)$, different from $% \mathcal{L}\propto V_{ns}^{x}(y)^{2}$, 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 $\mathcal{L}(\mathbf{r},t)$ 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 $\mathcal{L}(\mathbf{r},t)$ 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.

cond-mat.other↗

arXiv2016

Statistical signature of vortex filaments: dog or tail? Talk given at QFS 2016

The title of the paper coincides with the title of a paragraph in the famous book by U. Frisch (1995)on classical turbulence. In this paragraph the author discussed the role of statistical dynamics of vortex filaments in the theory of turbulence and put the above question. In other words, whether the main properties of turbulence (cascade, scaling laws) are the sequence of the vortex line dynamics or the latter have only marginal signature. Quantum fluids, where the vortex filaments are the real objects, give an excellent opportunity to explore the role of discrete vortices in turbulent phenomena. The aim of this paper is to discuss which elements of vortex dynamics would lead to the main ingredients of the theory of turbulence. We discuss how the nonlinear dynamics of vortex filaments can result in an exchange of energy between different scales, the formation of the Kolmogorov-type energy spectra and the decay of turbulence.

cond-mat.soft↗

arXiv2016

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 $\mathcal{P}$ in the Vinen equation is proportional to $\left\vert \mathbf{V}_{ns}\right\vert ^{3}\mathcal{L}^{1/2}$ (where $\mathcal{L}$ is vortex line density and $\mathbf{V}_{ns}$ 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.

cond-mat.other↗

arXiv2015

Vortex bundle collapse and Kolmogorov spectrum. Talk given at the Low Temperature Conference, Kazan, 2015

The statement of problem is motivated by the idea of modeling the classical turbulence with a set of chaotic quantized vortex filaments in superfluids. Among various arguments supporting the idea of quasi-classic behavior of quantum turbulence, the strongest, probably, is the $k$ dependence of the spectra of energy, $E(k)\propto k^{-5/3}$ obtained in numerical simulations and experiments. At the same time the mechanism of classical vs quantum turbulence (QT) is not clarified and the source of the $k^{-5/3}$ dependence is unclear. In this work we concentrated on the nonuniform vortex vortex bundles. This choice is related to actively discussed question concerning a role of collapses in the vortex dynamics in formation of turbulent spectra. We demonstrate that the nonuniform vortex vortex bundles, which appear in result of nonlinear vortex dynamics generates the energy spectrum, which close to the Kolmogorov dependence $\propto k^{-5/3}$.

cond-mat.other↗

arXiv2015

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 $\mathbf{v_{ns}}$. 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 $E\{\mathbf{s\}}$ is the energy of the vortex configuration $\{\mathbf{s\}}$, and $\mathbf{P}$ 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)

cond-mat.other↗

arXiv2014

Probing of quantum turbulence with radiating vortex loops

The statistics of vortex loops emitted from the domain with quantum turbulence is studied. The investigation is performed on the supposition that the vortex loops have the Brownian or random walking structure with the generalized Wiener distribution. The main goal is to relate the properties of the emitted vortex loops with the parameters of quantum turbulence. The motivation of this work connected with recent studies, both numerical and experimental, on study of emitted vortex loops. This technique opens up new opportunities to probe superfluid turbulence. We demonstrated how the statistics of emitted loops is expressed in terms of the vortex tangle parameters and performed the comparison with numerical simulations.\newline PACS number(s): 67.25.dk, 47.37.+q

cond-mat.other↗

arXiv2014

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 $E(k)\varpropto k^{-5/3}$, 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 $E(k)$ 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.

cond-mat.soft↗

arXiv2012

Fluctuations of the vortex line density in turbulent flows of quantum fluids

We present an analytical study of fluctuations of the Vortex Line Density (VLD) $<δ\mathcal{L}(ω) δ\mathcal{L}(-ω)>$ in turbulent flows of quantum fluids. Two cases are considered. The first one is the counterflowing (Vinen) turbulence, where the vortex lines are disordered, and the evolution of quantity $\mathcal{L}(t)$ obeys the Vinen equation. The second case is the quasi-classic turbulence, where vortex lines are believed to form the so called vortex bundles, and their dynamics is described by the HVBK equations. The latter case, is of a special interest, since a number of recent experiments demonstrate the $ω^{-5/3}$ dependence for spectrum VLD, instead of $ω^{1/3}$ law, typical for spectrum of vorticity. In nonstationary situation, in particular, in the fluctuating turbulent flow there is a retardation between the instantaneous value of the normal velocity and the quantity $\mathcal{L}$. This retardation tends to decrease in the accordance with the inner dynamics, which has a relaxation character. In both cases the relaxation dynamics of VLD is related to fluctuations of the relative velocity, however if for the Vinen case the rate of temporal change for $\mathcal{L}(t)$ is directly depends on $δ\mathbf{v}_{ns}$, for the HVBK dynamics it depends on $\nabla \times δ\mathbf{v}_{ns}$. As a result, for the disordered case the spectrum $<δ\mathcal{L}(ω) δ\mathcal{L}(-ω)>$ coincides with the spectrum $ω^{-5/3} $. In the case of the bundle arrangement, the spectrum of the VLD varies (at different temperatures) from $ω^{1/3}$ to $ω^{-5/3}$ dependencies. This conclusion may serve as a basis for the experimental determination of what kind of the turbulence is implemented in different types of generation.

cond-mat.other↗

arXiv2012

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 $E (k) $ 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 $<\mathbf{v(k)v(-k)}>$ can be exactly calculated, provided that we know the probability distribution functional $% \mathcal{P}(\{\mathbf{s}(ξ,t)\})$ of vortex loops configurations. The knowledge of $\mathcal{P}(\{\mathbf{s}(ξ,t)\})$ is identical to the full solution of the problem of quantum turbulence and, in general, $\mathcal{P}$ 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.

cond-mat.stat-mech↗

arXiv2010

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.

cond-mat.other↗

arXiv2009

Vortex Fluid Relaxation Model for Torsional Oscillation Responses of Solid 4He

A phenomenological model is developed to explain a new set of detailed torsional oscillator data for hcp 4He. The model is based on Anderson's idea of the vortex fluid (vortex tangle) in solid 4He. Utilizing a well-studied treatment of dynamics of quantized vortices we describe how the "local superfluid component" is involved in rotation (torsional oscillation) via a polaried vortices tangle. The polarization in the tangle appears both due to aligning the remnant or thermal vortices and due to penetration of additional vortices into volume. Both are supposed to occur in a relaxation manner, and the inverse full relaxation time tau^-1 is the sum of them. One of them is found to change linearly with respect to the rim velocity Vac. The developed approach explains the behavior of both NLRS and Delta Q^-1 seen in the experiment. We reproduce not only the unique Vac dependence, but also obtain new information about the vortices tangle, for example, a divergence in tau at extrapolated T ~ 30 mK.

cond-mat.other↗

arXiv2009

Diffusion of Inhomogeneous Vortex Tangle and Decay of Superfluid Turbulence

The theory describing the evolution of inhomogeneous vortex tangle at zero temperature is developed on the bases of kinetics of merging and splitting vortex loops. Vortex loops composing the vortex tangle can move as a whole with some drift velocity depending on their structure and their length. The flux of length, energy, momentum etc. executed by the moving vortex loops takes a place. Situation here is exactly the same as in usual classical kinetic theory with the difference that the "carriers" of various physical quantities are not the point particles, but extended objects (vortex loops), which possess an infinite number of degrees of freedom with very involved dynamics. We offer to fulfill investigation basing on supposition that vortex loops have a Brownian structure with the only degree of freedom, namely, lengths of loops $l$. This conception allows us to study dynamics of the vortex tangle on the basis of the kinetic equation for the distribution function $n(l,t)$ of the density of a loop in the space of their lengths. Imposing the coordinate dependence on the distribution function $n(l,\mathbf{% r},t)$ and modifying the "kinetic" equation with regard to inhomogeneous situation, we are able to investigate various problem on the transport processes in superfluid turbulence. In this paper we derive relation for the flux of the vortex line density $\mathcal{L}(x,t)$. The correspoding evolution of quantity $\mathcal{L}(x,t)$ obeys the diffusion type equation as it can be expected from dimensional analysis. The according diffusion coefficient is evaluated from calculation of the (size dependent) free path of the vortex loops. We use this equation to describe the decay of the vortex tangle at very low temperature. We compare that solution with recent experiments on decay of the superfluid turbulence.

cond-mat.other↗

arXiv2008

Numerical simulation of stochastic motion of vortex loops under action of random force. Evidence of the thermodynamic equilibrium

Numerical simulation of stochastic dynamics of vortex filaments under action of random (Langevin) force is fulfilled. Calculations are performed on base of the full Biot--Savart law for different intensities of the Langevin force. A new algorithm, which is based on consideration of crossing lines, is used for vortex reconnection procedure. After some transient period the vortex tangle develops into the stationary state characterizing by the developed fluctuations of various physical quantities, such as total length, energy etc. We tested this state to learn whether or not it the thermodynamic equilibrium is reached. With the use of a special treatment, so called method of weighted histograms, we process the distribution energy of the vortex system. The results obtained demonstrate that the thermodynamical equilibrium state with the temperature obtained from the fluctuation dissipation theorem is really reached. PACS-numbers: 67.40.Vs 98.80.Cq 7.37.+q

cond-mat.stat-mech↗