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Itamar Procaccia - One of the best experts on this subject based on the ideXlab platform.
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dynamics of the Vortex Line density in superfluid counterflow turbulence
Physical Review B, 2018Co-Authors: D Khomenko, Anna Pomyalov, Victor S Lvov, Itamar ProcacciaAbstract:Describing superfluid turbulence at intermediate scales between the interVortex distance and the macroscale requires an acceptable equation of motion for the density of quantized Vortex Lines $\mathcal{L}$. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides $\mathcal{L}$ and the normal and superfluid velocity fields. In this paper, we offer a minimal closure using one additional anisotropy parameter ${I}_{l0}$. Using the example of counterflow superfluid turbulence, we derive two coupled closure equations for the Vortex Line density and the anisotropy parameter ${I}_{l0}$ 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.
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Kelvin waves and the decay of quantum superfluid turbulence
Physical Review B, 2014Co-Authors: Luiza Kondaurova, Victor S. L'vov, Anna Pomyalov, Itamar ProcacciaAbstract:interVortex distance � . These excitations cascade down to the resolution scale �ξ which in our simulations is of the order �ξ ∼ �/ 100. At this scale, the Kelvin waves are numerically damped by a Line-smoothing procedure, that is supposed to mimic the dissipation of Kelvin waves by phonon and roton emission at the scale of the Vortex core. We show that the Kelvin wave cascade is statistically important: the shortest available Kelvin waves at the end of the cascade determine the mean Vortex-Line curvature S, giving S 30/� , and play a major role
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structure of a quantum Vortex tangle in 4 he counterflow turbulence
Physical Review B, 2014Co-Authors: Luiza Kondaurova, Anna Pomyalov, Victor S Lvov, Itamar ProcacciaAbstract:dynamics in a wide range of temperatures and counterflow velocities. We start with the analysis of the macroscopic characteristics of the quantum Vortex tangle such as Vortex Line density, its mean anisotropic and curvature parameters, the mean friction force between normal and superfluid components, the drift velocity of the Vortex tangle, etc. Next we proceed to the main goal of the paper and move from the traditional macroscopic approach in terms of mean characteristics of the Vortex tangle to the microscopic statistical and kinetic levels of description of quantum turbulence. These include objects that are much less studied or even totally neglected such as the Vortex reconnection rates, the correlations and probability distribution functions (PDFs) of the Vortex loop lengths, of the Line curvature, of the mean curvatures of individual loops, the cross-correlation function between the loop length and its mean curvature, and the autocorrelation function of the Vortex-Line orientations. This detailed statistical information is required for a deeper understanding of quantum turbulence and for the development of its advanced theoretical description. In addition, we identify which of the studied properties are strongly affected by the choice of the reconnection criteria that are traditionally used in the Vortex filament method and which of them are practically insensitive to the reconnection procedure. We conclude that the Vortex filament method is sufficiently robust and well-suited for the description of the steady-state Vortex tangle in the quantum counterflow.
Kazushige Machida - One of the best experts on this subject based on the ideXlab platform.
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Kelvin Waves of Quantized Vortex Lines in Trapped Bose-Einstein Condensates
Physical review letters, 2008Co-Authors: Tapio Simula, Takeshi Mizushima, Kazushige MachidaAbstract:We have theoretically investigated Kelvin waves of quantized Vortex Lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight Vortex Line, driven by a parametric resonance between a quadrupole mode and a pair of Kelvin modes of opposite momenta. Subsequently, Kelvin waves rapidly decay to longer wavelengths emitting sound waves in the process. We present a modified Kelvin wave dispersion relation for trapped superfluids and propose a simple method to excite Kelvin waves of specific wave number.
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beliaev damping and kelvin mode spectroscopy of a bose einstein condensate in the presence of a Vortex Line
Physical Review Letters, 2003Co-Authors: Takeshi Mizushima, Masanori Ichioka, Kazushige MachidaAbstract:It is demonstrated theoretically that the counter-rotating quadrupole mode in a Vortex of Bose-Einstein condensates can decay into a pair of Kelvin modes via the Beliaev process. We calculate the spectral weight of a density-response function within the Bogoliubov framework, taking account of both Beliaev and Landau processes. Good agreement with experiment on 87 Rb by Bretin et al. [Phys. Rev. Lett., 100403 (2003)]] allows us to unambiguously identify the decayed mode as the Kelvin wave propagating along a Vortex Line.
E. A. Kuznetsov - One of the best experts on this subject based on the ideXlab platform.
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development of high vorticity structures and geometrical properties of the Vortex Line representation
Physics of Fluids, 2018Co-Authors: E. A. Kuznetsov, D S Agafontsev, Alexei A MailybaevAbstract:The incompressible three-dimensional Euler equations develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling ωmax ∝ l−2/3 between the vorticity maximum and the pancake thickness, as was observed in the recent numerical experiments [D. S. Agafontsev et al., “Development of high vorticity structures in incompressible 3D Euler equations,” Phys. Fluids 27, 085102 (2015)]. We study the process of pancakes’ development in terms of the Vortex Line representation (VLR), which represents a partial integration of the Euler equations with the explicit conservation of the Cauchy invariants and describes the compressible dynamics of continuously distributed Vortex Lines. We present, for the first time, the numerical simulations of the VLR equations with high accuracy, which we perform in adaptive anisotropic grids of up to 15363 nodes. With these simulations, we show that the vorticity growth is connected with the compressibility of the Vortex Lines and find geometric properties responsible for the observed scaling ωmax ∝ l−2/3.The incompressible three-dimensional Euler equations develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling ωmax ∝ l−2/3 between the vorticity maximum and the pancake thickness, as was observed in the recent numerical experiments [D. S. Agafontsev et al., “Development of high vorticity structures in incompressible 3D Euler equations,” Phys. Fluids 27, 085102 (2015)]. We study the process of pancakes’ development in terms of the Vortex Line representation (VLR), which represents a partial integration of the Euler equations with the explicit conservation of the Cauchy invariants and describes the compressible dynamics of continuously distributed Vortex Lines. We present, for the first time, the numerical simulations of the VLR equations with high accuracy, which we perform in adaptive anisotropic grids of up to 15363 nodes. With these simulations, we show that the vorticity growth is connected with the compressibility of the Vortex Lines and find geometric prop...
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development of high vorticity structures and geometrical properties of the Vortex Line representation
arXiv: Fluid Dynamics, 2017Co-Authors: E. A. Kuznetsov, D S Agafontsev, Alexei A MailybaevAbstract:The incompressible three-dimensional Euler equations develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling $\omega_{max}\sim\ell^{-2/3}$ between the vorticity maximum and the pancake thickness, as was observed in the recent numerical experiments [D.S. Agafontsev et al, Phys. Fluids 27, 085102 (2015)]. We study the process of pancakes' development in terms of the Vortex Line representation (VLR), which represents a partial integration of the Euler equations with respect to conservation of the Cauchy invariants and describes compressible dynamics of continuously distributed Vortex Lines. We present, for the first time, the numerical simulations of the VLR equations with high accuracy, which we perform in adaptive anisotropic grids of up to $1536^3$ nodes. With these simulations, we show that the vorticity growth is connected with the compressibility of the Vortex Lines and find geometric properties responsible for the observed scaling $\omega_{max}\sim\ell^{-2/3}$.
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mixed lagrangian eulerian description of vortical flows for ideal and viscous fluids
Journal of Fluid Mechanics, 2008Co-Authors: E. A. KuznetsovAbstract:It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid is equivalent to the equations of motion of a charged compressible fluid moving due to a self-consistent electromagnetic field. The velocity of new auxiliary fluid coincides with the velocity component normal to the vorticity Line for the primitive equations. Therefore this new hydrodynamics represents hydrodynamics of Vortex Lines. Their compressibility reveals a new mechanism for three-dimensional incompressible vortical flows connected with breaking (or overturning) of Vortex Lines which can be considered as one of the variants of collapses. Transition to the Lagrangian description in the new hydrodynamics corresponds, for the original Euler equations, to a mixed Lagrangian-Eulerian description - the Vortex Line representation (VLR). The Jacobian of this mapping defines the density of Vortex Lines. It is shown also that application of VLR to the Navier-Stokes equations results in an equation of diffusive type for the Cauchy invariant. The diffusion tensor for this equation is defined by the VLR metric.
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Vortex Line representation for flows of ideal and viscous fluids
arXiv: Fluid Dynamics, 2002Co-Authors: E. A. KuznetsovAbstract:It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian description in a new hydrodynamics is equivalent for the original Euler equations to the mixed Lagrangian-Eulerian description - the Vortex Line representation (VLR). Due to compressibility of a "new" fluid the collapse of Vortex Lines can happen as the result of breaking (or overturning) of Vortex Lines. It is found that the Navier-Stokes equation in the Vortex Line representation can be reduced to the equation of the diffusive type for the Cauchy invariant with the diffusion tensor given by the metric of the VLR.
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Vortex Line representation for flows of ideal and viscous fluids
Jetp Letters, 2002Co-Authors: E. A. KuznetsovAbstract:The Euler hydrodynamics describing the Vortex flows of ideal fluids is shown to coincide with the equations of motion obtained for a charged compressible fluid moving under the effect of a self-consistent electromagnetic field. For the Euler equations, the passage to the Lagrange description in the new hydrodynamics is equivalent to a combined Lagrange-Euler description, i.e., to the Vortex Line representation [5]. Owing to the compressibility of the new hydrodynamics, the collapse of a Vortex flow of an ideal fluid can be interpreted as a result of the breaking of Vortex Lines. The Navier-Stokes equation formulated in terms of the Vortex Line representation proves to be reduced to a diffusion-type equation for the Cauchy invariant with the diffusion tensor determined by the metric of this representation.
Boris Svistunov - One of the best experts on this subject based on the ideXlab platform.
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scale separation scheme for simulating superfluid turbulence kelvin wave cascade
Physical Review Letters, 2005Co-Authors: Evgeny Kozik, Boris SvistunovAbstract:A Kolmogorov-type cascade of Kelvin waves-the distortion waves on Vortex Lines-plays a key part in the relaxation of superfluid turbulence at low temperatures. We propose an efficient numeric scheme for simulating the Kelvin-wave cascade on a single Vortex Line. This idea is likely to be generalizable for a full-scale simulation of different regimes of superfluid turbulence. With the new scheme, we are able to unambiguously resolve the cascade spectrum exponent, and thus to settle the controversy between recent simulations of Vinen, Tsubota, and Mitani [Phys. Rev. Lett. 91, 135301 (2003)]] and recently developed analytic theory [Phys. Rev. Lett. 92, 035301 (2004)]].
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superfluid turbulence in the low temperature limit
Physical Review B, 1995Co-Authors: Boris SvistunovAbstract:Dissipationless relaxation kinetics of the superfluid turbulence is analyzed. The possibility and scenario of a specific Kolmogorov-like regime are revealed. Qualitative considerations are corroborated by numerical study of a simplified model of a self-crossing Vortex Line.
N N Rosanov - One of the best experts on this subject based on the ideXlab platform.
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irreversible hysteresis of internal structure of tangle dissipative optical solitons
Physical Review Letters, 2019Co-Authors: S V Fedorov, N A Veretenov, N N RosanovAbstract:For three-dimensional tangle laser solitons that have a number of unclosed and closed Vortex Lines and coexist in a range of the scheme parameters, we predict irreversible hysteretic transformation of their internal structure when a system parameter slowly and regularly varies crossing the boundary of the stability of one or another soliton. During the hysteresis cycle, when restoring the initial parameter value, the soliton topology simplifies (decrease of topological indices), its field energy decreases, and the energy of the medium increases. The transient includes a series of elementary reactions: reconnection of Vortex Lines, separation of closed Vortex loops after strong bending of a parent Vortex Line, and twist of unclosed Vortex Lines changing topological indices. During the transient, new (metastable) types of localized topological structures arise. It is shown that the tangent energy flow along closed Vortex Lines is unidirectional or direction alternating.
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topological Vortex and knotted dissipative optical 3d solitons generated by 2d Vortex solitons
Physical Review Letters, 2017Co-Authors: S V Fedorov, N A Veretenov, N N RosanovAbstract:We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by Vortex Lines where the field vanishes are tangles, i.e., N_{c} knotted or unknotted, linked or unlinked closed Lines and M unclosed Lines that thread all the closed Lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite Vortex Line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all Vortex Lines have unit topological charge: the number of closed Lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed Vortex Lines are unknotted and unlinked, their number M=1, 2, and 3.
