Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Journal of Engineering Thermophysics
Published in: Journal of Engineering Thermophysics 1/2020

01-02-2020

Statistical Signature of Vortex Filaments in Classical Turbulence: Dog or Tail?

Author: S. K. Nemirovskii

Published in: Journal of Engineering Thermophysics | Issue 1/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

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 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.
previous article Crisis of Nucleate Boiling in a Finite-Height Horizontal Layer of Liquid
next article Combustion of Sludge-Lignin in Water-Oxygen Mixture

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Frisch, U., Turbulence, Cambridge: Cambridge Univ. Press, 1995.
2.
Chorin, A., Vorticity and Turbulence, Applied Mathematical Sciences, Springer-Verlag, 1994.
3.
Migdal, A.A., Fokker–Planck Vortex Equation, Vopr. Kib., 1986, p. 122.
4.
Tsubota, M. and Kobayashi, M., Energy Spectra of Quantum Turbulence, in Progress in Low Temperature Physics: Quantum Turbulence, vol. 16, Elsevier, 2009, pp. 1–43.
5.
Vincent, A. and Meneguzzi, M., The Spatial Structure and Statistical Properties of Homogeneous Turbulence, J. Fluid Mech., 1991, vol. 225, pp. 1–20.
6.
Schwarz, K.W., Three-Dimensional Vortex Dynamics in Superfuid \(^{4}\)He: Homogeneous Superfluid Turbulence, Phys. Rev. B, 1988, vol. 38, no. 4, pp. 2398–2417.
7.
Chorin, A.J., Vortex Methods and Vortex Motion, Philadelphia, PA: SIAM, 1991, p. 195.
8.
Leonard, A., Vortex Methods for Flow Simulation, J. Comput. Phys., 1980, vol. 37, iss. 3, pp. 289–335.
9.
Siggia, E.D., Collapse and Amplification of a Vortex Filament,Phys. Fluids, 1985, vol. 28, pp. 794–805.
10.
Klein, R. and Majda, A.J., Self-Stretching of a Perturbed Vortex Filament I. The Asymptotic Equation for Deviations from a Straight Line, Phys. D: Nonlin. Phen., 1991, vol. 49, no. 3, pp. 323–353.
11.
Hansen, A. and Nelkin, M., Absence of Small-Scale Structure in Homogeneous Superfluid Turbulence, Phys. Rev. B, 1986, vol. 34, no. 7, pp. 4894–4896.
12.
Nemirovskii, S.K. and Fiszdon, W., Chaotic Quantized Vortices and Hydrodynamic Processes in Superfluid Helium, Rev. Mod. Phys., 1995, vol. 67, no. 1. pp. 37–84.
13.
Eyink, G.L. and Sreenivasan, K.R., Onsager and the Theory of Hydrodynamic Turbulence, Rev. Mod. Phys., 2006, vol. 78, pp. 87–135.
14.
Moffatt, H.K., Kida, S., and Ohkitani, K., Stretched Vortices—The Sinews of Turbulence; Large-Reynolds-Number Asymptotics,J. Fluid Mech., 1994, vol. 259, pp. 241–264.
15.
Vinen, W.F., Classical Character of Turbulence in a Quantum Liquid, Phys. Rev. B, 2000, vol. 61, no. 2, pp. 1410–1420.
16.
Kobayashi, M. and Tsubota, M., Kolmogorov Spectrum of Superfluid Turbulence: Numerical Analysis of the Gross–Pitaevskii Equation with a Small-Scale Dissipation, Phys. Rev. Lett., 2005, vol. 94, no. 6, p. 065302.
17.
Vinen, W., Quantum Turbulence: Achievements and Challenges,J. Low Temp. Phys., 2010, vol. 161, pp. 419–444.
18.
Skrbek, L. and Sreenivasan, K.R., Developed Quantum Turbulence and Its Decay, Phys. Fluids., 2012, vol. 24, no. 1, p. 011301.
19.
Tsubota, M., Kobayashi, M., and Takeuchi, H., Quantum Hydrodynamics, Phys. Rep., 2013, vol. 522, no. 3, pp. 191–238.
20.
Barenghi, C.F., Skrbek, L., and Sreenivasan, K.R., Introduction to Quantum Turbulence, Procs. Nat. Acad. Sci., 2014, vol. 111, no. 1, pp. 4647–4652.
21.
Walmsley, P.M., Golov, A.I., Hall, H.E., Levchenko, A.A., and Vinen, W.F., Dissipation of Quantum Turbulence in the Zero Temperature Limit, Phys. Rev. Lett., 2007, vol. 99, p. 265302.
22.
Kleinert, H., Gauge Fields in Condenced Matter Physics, Singapore: World Scientific, 1990.
23.
Nemirovskii, S.K., Gaussian Model of Vortex Tangle in He II,Phys. Rev. B, 1998, vol. 57, no. 10, pp. 5972–5986.
24.
Nemirovskii, S.K., Evolution of a Network of Vortex Loops in He-II: Exact Solution of the Rate Equation, 2006, Phys. Rev. Lett., vol. 96, no. 1, p. 015301.
25.
Nemirovskii, S.K., Kinetics of a Network of Vortex Loops in He II and a Theory of Superfluid Turbulence, Phys. Rev. B, 2008, vol. 77, no. 21, p. 214509.
26.
Nemirovskii, S.K., Quantum Turbulence: Theoretical and Numerical Problems, Phys. Rep., 2013, vol. 524, no. 3, pp. 85–202.
27.
Zakharov, V.E., L’vov, V.S., and Falkovich, G.,Kolmogorov Spectra of Turbulence I, Berlin: Springer-Verlag, 1992.
28.
Feynman, R.P., Progress in Low Temperature Physics, vol. 1, Gorter, C.J., Ed., Amsterdam: North-Holland, 1955, p. 17.
29.
Schwarz, K.W., Turbulence in Superfluid Helium: Steady Homogeneous Counterflow, Phys. Rev. B, 1978, vol. 18, no. 1, pp. 245–262.
30.
Nemirovskii, S. and Baltsevich, A., Stochastic Dynamics of a Vortex Loop. Large-Scale Stirring Force, Lect. Notes Phys., 2001, vol. 571, pp. 219–225.
31.
Nemirovskii, S.K., Pakleza, J., and Poppe, W., Notes et Documents LIMSI (Laboratoire d’Informatique pour la Mecanique et les Sciences de l’Ingenieur), No. 91-14, 1991.
32.
Wyld, H.W., Formulation of the Theory of Turbulence in an Incompressible Fluid, Ann. Phys., 1961, vol. 14, pp. 143–165.
33.
Araki, T., Tsubota, M., and Nemirovskii, S.K., Energy Spectrum of Superfluid Turbulence with no Normal-Fluid Component, Phys. Rev. Lett., 2002, vol. 89, no. 14, p. 145301.
34.
Kivotides, D., Vassilicos, C.J., Samuels, D.C., and Barenghi, C.F., Velocity Spectra of Superfluid Turbulence, EPL (Europhysics Letters), 2002, vol. 57, no. 6, p. 845.
35.
Kivotides, D., Barenghi, C.F., and Samuels, D.C., Superfluid Vortex Reconnections at Finite Temperature, Europhys. Lett., 2001, vol. 54, p. 774.
36.
Procaccia, I. and Sreenivasan, K., The State of the Art in Hydrodynamic Turbulence: Past Successes and Future Challenges,Phys. D: Nonlin. Phenom., 2008, vol. 237, nos. 14–17, pp. 2167–2183.
37.
Nore, C., Abid, M., and Brachet, M.E., Kolmogorov Turbulence in Low-Temperature Superflows, Phys. Rev. Lett., 1997, vol. 78, no. 20, pp. 3896–3899.
38.
Nore, C., Abid, M., and Brachet, M.E., Decaying Kolmogorov Turbulence in a Model of Superflow, Phys. Fluids, 1997, vol. 9, p. 2644.
39.
Sasa, N., Kano, T., Machida, M., L’vov, V.S., Rudenko, O., and Tsubota, M., Energy Spectra of Quantum Turbulence: Large-Scale Simulation and Modeling, Phys. Rev. B, 2011, vol. 84, p. 054525.
40.
Nemirovskii, S.K., Reconnection of Quantized Vortex Filaments and the Kolmogorov Spectrum, Phys. Rev. B, 2014, vol. 90, no. 10, p. 104506.
41.
Nemirovskii, S.K., Tsubota, M., and Araki, T., Energy Spectrum of the Random Velocity Field Induced by a Gaussian Vortex Tangle in He II, J. Low Temp. Phys., 2002, vol. 126, pp. 1535–1540.
42.
Kondaurova, L. and Nemirovskii, S.K., Full Biot–Savart Numerical Simulation of Vortices in He II, J. Low Temp. Phys., 2005, vol. 138, pp. 555–560.
43.
Nemirovskii, S., Energy Spectrum of the 3D Velocity Field, Induced by Vortex Tangle, J. Low Temp. Phys., 2013, vol. 171, nos. 5, 6, pp. 504–510.
44.
de Waele, A.T. and Aarts, R.G., Route to Vortex Reconnection,Phys. Rev. Lett., 1994, vol. 72, no. 4, pp. 482–485.
45.
Kuznetsov, E. and Ruban, V., Collapse of Vortex Lines in Hydrodynamics, J. Exp. Theor. Phys., 2000, vol. 91, no. 4, pp. 775–785.
46.
Kerr, R.M., Swirling, Turbulent Vortex Rings Formed from a Chain Reaction of Reconnection Events, Phys. Fluids, 2013, vol. 25, no. 6, p. 065101.
47.
Boué, L., Khomenko, D., L’vov, V.S., and Procaccia, I., Analytic Solution of the Approach of Quantum Vortices towards Reconnection, Phys. Rev. Lett., 2013, vol. 111, p. 145302.
48.
Andryushchenko, V.A., Kondaurova, L.P., and Nemirovskii, S.K., Dynamics of Nonplanar Quantized Vortex Rings before Reconnection at Finite Temperatures, J. Low Temp. Phys., 2017, vol. 187, no. 5, pp. 523–530.
49.
Fedoryuk, M.V., Metod perevala (The Saddle-Point Method), Moscow: Nauka, 1977.
50.
Bustamante, M.D. and Kerr, R.M., 3D Euler about a 2D Symmetry Plane, Phys. D: Nonlin. Phen., 2008, vol. 237, nos. 14–17, pp. 1912–1920.
51.
Kivotides, D., Vassilicos, J.C., Samuels, D.C., and Barenghi, C.F., Kelvin Waves Cascade in Superfluid Turbulence, Phys. Rev. Lett., 2001, vol. 86, no. 14, pp. 3080–3083.
52.
L’vov, V., Nazarenko, S., and Rudenko, O., Gradual Eddy-Wave Crossover in Superfluid Turbulence, J. Low Temp. Phys., 2008, vol. 153, p. 140.
53.
L’vov, V.S., Nazarenko, S.V., and Rudenko, O., Bottleneck Crossover between Classical and Quantum Superfluid Turbulence,Phys. Rev. B, 2007, vol. 76, p. 024520.
54.
Boué, L., Dasgupta, R., Laurie, J., L’vov, V., Nazarenko, S., and Procaccia, I., Phys. Rev. B, 2011, vol. 84, p. 064516.
55.
Svistunov, B.V., Superfluid Turbulence in the Low-Temperature Limit, Phys. Rev. B, 1995, vol. 52, no. 5, pp. 3647–3653.
56.
Kozik, E. and Svistunov, B., Kelvin-Wave Cascade and Decay of Superfluid Turbulence, Phys. Rev. Lett., 2004, vol. 92, no. 3, p. 035301.
57.
Kozik, E. and Svistunov, B., Scale-Separation Scheme for Simulating Superfluid Turbulence: Kelvin-Wave Cascade, Phys. Rev. Lett., 2005, vol. 94, no. 2, p. 025301.
58.
Kozik, E. and Svistunov, B., Theory of Decay of Superfluid Turbulence in the Low-Temperature Limit, J. Low Temp. Phys., 2009, vol. 156, pp. 215–267.
59.
Kozik, E. and Svistunov, B., Geometric Symmetries in Superfluid Vortex Dynamics, Phys. Rev. B, 2010, vol. 82, no. 14, p. 140510.
60.
Laurie, J., L’vov, V.S., Nazarenko, S., and Rudenko, O.,Phys. Rev. B, 2010, vol. 81, no. 10, p. 104526.
61.
Lebedev, V. and L’vov, V., Symmetries and Interaction Coefficients of Kelvin Waves, J. Low Temp. Phys., 2010, vol. 161, pp. 548–554.
62.
Nazarenko, S., Private communication, 2013.
63.
Bradley, D.I., Clubb, D.O., Fisher, S.N., Guénault, A.M., Haley, R.P., Matthews, C.J., Pickett, G.R., Tsepelin, V., and Zaki, K., Phys. Rev. Lett., 2006, vol. 96, no. 3, p. 035301.
64.
Kondaurova, L. and Nemirovskii, S.K., Numerical Study of Decay of Vortex Tangles in Superfluid Helium at Zero Temperature,Phys. Rev. B, 2012, vol. 86, p. 134506.
65.
Nemirovskii, S.K., Diffusion of Inhomogeneous Vortex Tangle and Decay of Superfluid Turbulence, Phys. Rev. B, 2010, vol. 81, no. 6, p. 064512.
66.
Kondaurova, L., Andryuschenko, V., and Nemirovskii, S., Numerical Simulations of Superfluid Turbulence under Periodic Conditions, J. Low Temp. Phys., 2008, vol. 150, pp. 415–419.
Metadata
Title
Statistical Signature of Vortex Filaments in Classical Turbulence: Dog or Tail?
Author
S. K. Nemirovskii
Publication date
01-02-2020
Publisher
Pleiades Publishing
Published in
Journal of Engineering Thermophysics / Issue 1/2020
Print ISSN: 1810-2328
Electronic ISSN: 1990-5432
DOI
https://doi.org/10.1134/S1810232820010026

Other articles of this Issue 1/2020

Journal of Engineering Thermophysics 1/2020 Go to the issue

OriginalPaper

Thermal Diffusivity Measurement of Cerium in the Temperature Range of 300-1800 K

OriginalPaper

Title High-Power Heat Release in Supercritical Water: Insight into the Heat Transfer Deterioration Problem

OriginalPaper

Geometrical Evaluation of a Channel with Alternated Mounted Blocks under Mixed Convection Laminar Flows Using Constructal Design

OriginalPaper

Crisis of Nucleate Boiling in a Finite-Height Horizontal Layer of Liquid

OriginalPaper

Mechanism of Disappearance of Vortex Breakdown in a Confined Flow

OriginalPaper

Fluid Flow and Heat Transfer Studies on a Discretely and Differently Heated Electronic Board

Premium Partners

    Image Credits