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Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels Cover

Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

Open Access
|May 2016

References

  1. 1. P. Granieri, B. Baudouy, A. Four, F. Lentijo, A. Mapelli, P. Petagna, and D. Tommasini, Steady-state heat transfer through micro-channels in pressurized He II, AIP Conf. Proc., vol. 1434, pp. 231–238, 2011. DOI:10.1063/1.4706925.10.1063/1.4706925
  2. 2. J. Maurer and P. Tabeling, Local investigation of superfluid turbulence, EPL (Europhysics Letters), vol. 43, no. 1, p. 29, 1998.10.1209/epl/i1998-00314-9
  3. 3. P.-E. Roche, P. Diribarne, T. Didelot, O. Français, L. Rousseau, and H. Willaime, Vortex density spectrum of quantum turbulence, EPL (Europhysics Letters), vol. 77, no. 6, p. 66002, 2007.
  4. 4. A. W. Baggaley, L. K. Sherwin, C. F. Barenghi, and Y. A. Sergeev, Thermally and mechanically driven quantum turbulence in helium II, Phys. Rev. B, vol. 86, p. 104501, 2012.
  5. 5. R. J. Donnelly, Quantized vortices in helium II. Cambridge: Cambridge University Press, 1991.
  6. 6. C. F. Barenghi, R. J. Donnelly, and W. F. Vinen, Quantized Vortex Dynamics and Superfluid Turbulence. Berlin: Springer, 2001.10.1007/3-540-45542-6
  7. 7. M. Tsubota, M. Kobayashi, and H. Takeuchi, Quantum hydrodynamics, Phys. Rep., vol. 522, pp. 191–238, 2012. DOI:10.1016/j.physrep.2012.09.007.10.1016/j.physrep.2012.09.007
  8. 8. S. van Sciver, Helium cryogenics. Berlin: Springer, second ed., 2012.10.1007/978-1-4419-9979-5
  9. 9. S. K. Nemirovskii, Quantum turbulence: Theorethical and numerical problems, Phys. Rep., vol. 524, pp. 85–202, 2013. DOI:10.1016/j.physrep.2012.10.005.10.1016/j.physrep.2012.10.005
  10. 10. W. F. Vinen, Mutual friction in a heat current in liquid helium II-III. theory of the mutual friction, Proc. Roy. Soc. London, vol. A240, pp. 493–515, 1957. DOI:10.1098/rspa.1957.0191.10.1098/rspa.1957.0191
  11. 11. J. Castiglione, P. J. Murphy, J. T. Tough, F. Mayot, and Y. Pomeau, Propagating and stationary superfluid turbulent fronts, Phys. B, vol. 100, pp. 575–595, 1995. DOI:10.1007/BF00751526.10.1007/BF00751526
  12. 12. J. F. Kafkalidis, G. Klinich III, and J. T. Tough, Superfluid turbulence in a nonuniform rectangular channel, Rep. Prog. Phys., vol. 50, p. 15909 (20 pages), 1994. DOI:10.1103/PhysRevB.50.15909.10.1103/PhysRevB.50.159099975960
  13. 13. G. Klinich III, J. F. Kafkalidis, and J. T. Tough, Superfluid Turbulence in Converging and Diverging Rectangular Channels, J. Low Temp. Phys., vol. 107, pp. 327–346, 1997. DOI:10.1007/BF02397461.10.1007/BF02397461
  14. 14. J. P. Murphy, J. Castiglione, and J. T. Tough, Superfluid turbulence in a nonuniform circular channel, J. Low Temp. Phys., vol. 92, pp. 307–334, 1993. DOI:10.1007/BF00682294.10.1007/BF00682294
  15. 15. J. F. Kafkalidis, G. Klinich III, and J. T. Tough, The vortex line density in nonuniform superfluid turbulence, Physica B, vol. 194–196, pp. 717–718, 1994. DOI:10.1016/0921-4526(94)90688-2.10.1016/0921-4526(94)90688-2
  16. 16. S. K. Nemirovskii, Diffusion of inhomogeneous vortex tangle and decay of superfluid turbulence, Phys. Rev. B, vol. 81, p. 64512 (10 pages), 2010. DOI:10.1103/PhysRevB.81.064512.10.1103/PhysRevB.81.064512
  17. 17. S. K. Nemirovskii, Propagation of a Turbulent Fronts in Quantum Fluids, J. Low Temp. Phys., vol. 162, pp. 347–353, 2011. DOI:10.1007/s10909-010-0252-x.10.1007/s10909-010-0252-x
  18. 18. L. Kondaurova and S. K. Nemirovskii, Numerical study of decay of vortex tangles in superfluid helium at zero temperature, Phys. Rev. B, vol. 86, p. 134506 (13 pages), 2012. DOI:10.1103/PhysRevB.86.134506.10.1103/PhysRevB.86.134506
  19. 19. J. A. Geurst, Hydrodynamics of quantum turbulence in He II: Vinen’s equation derived from energy and impulse of vortex tangle, Physica B, vol. 154, pp. 327–343, 1989. DOI:10.1016/0921-4526(89)90167-1.10.1016/0921-4526(89)90167-1
  20. 20. J. A. Geurst, Hydrodynamic theory of superfluid turbulence in He II and Schwarz’s vortex modelling, Physica A, vol. 183, pp. 279–303, 1992. http://EconPapers.repec.org/RePEc:eee:phsmap:v:183:y:1992:i:3:p:279-303.10.1016/0378-4371(92)90148-J
  21. 21. J. A. Geurst and H. van Beelen, Hydrodynamics of superfluid turbulence in He II: three-dimensional theory, Physica A, vol. 206, pp. 58–92, 1994. http://EconPapers.repec.org/RePEc:eee:phsmap:v:206:y:1994:i:1:p:58-92.10.1016/0378-4371(94)90118-X
  22. 22. M. S. Mongiovì and D. Jou, Thermodynamical derivation of a hydrodynamical model of inhomogeneous superfluid turbulence, Phys. Rev. B, vol. 75, p. 24507 (14 pages), 2007. DOI:10.1103/PhysRevB.75.024507.10.1103/PhysRevB.75.024507
  23. 23. L. Saluto, M. S. Mongiovì, and D. Jou, Vortex diffusion and vortex-line hysteresis in radial quantum turbulence, Physica B, vol. 440C, pp. 99–103, 2014. DOI:10.1016/j.physb.2014.01.041.10.1016/j.physb.2014.01.041
  24. 24. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He 4: Homogeneous superfluid turbulence, Phys. Rev. B, vol. 38, pp. 2398–2417, 1988. DOI:10.1103/PhysRevB.38.2398.10.1103/PhysRevB.38.23989946544
  25. 25. L. Saluto, D. Jou, and M. S. Mongiovì, Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence, Physica A, vol. 406, pp. 272–280, 2014. DOI:10.1016/j.physa.2014.03.062.10.1016/j.physa.2014.03.062
  26. 26. L. J. Campbell, Driven, dissipative superfluids: Radial counter-flow of rotating 4He, Phys. Rev. B, vol. 36, pp. 6773–6781, 1987. DOI:10.1103/PhysRevB.36.6773.10.1103/PhysRevB.36.67739942400
  27. 27. M. S. Mongiovì and D. Jou, Generalization of Vinen’s equation including transition to superfluid turbulence, J. Phys., vol. 17, pp. 4423–4440, 2005. http://stacks.iop.org/0953-8984/17/i=28/a=003.
  28. 28. L. Saluto, M. S. Mongiovì, and D. Jou, Longitudinal counterflow in turbulent liquid helium: velocity profile of the normal component, Z. Angew. Math. Phys., vol. 65, pp. 531–548, 2014. DOI:10.1007/s00033-013-0372-7.10.1007/s00033-013-0372-7
  29. 29. L. Saluto, Stationary heat flux profile in turbulent helium II in a semi-infinite cylindrical channel, in Bollettino di Matematica Pura e Applicata, vol. V, pp. 133–144, Aracne, 2012.
  30. 30. M. Sciacca, M. S. Mongiovì, and D. Jou, Alternative Vinen equation and its extension to rotating counterflow superfluid turbulence, Physica B, vol. 4038, pp. 2215–2224, 2008. DOI:10.1016/j.physb.2007.12.001.10.1016/j.physb.2007.12.001
  31. 31. K. P. Martin and J. T. Tough, Evolution of superfluid turbulence in thermal counterflow, Phys. Rev. B, vol. 27(5), pp. 2788–2799, 1983. DOI:10.1103/PhysRevB.27.2788.10.1103/PhysRevB.27.2788
Language: English
Page range: 130 - 149
Submitted on: Dec 31, 2014
Accepted on: Jun 17, 2015
Published on: May 20, 2016
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2016 Lidia Saluto, Maria Stella Mongioví, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.