Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels
By: Lidia Saluto and Maria Stella Mongioví
References
- 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,, vol. 1434, pp. 231–238, 2011. DOI:10.1063/1.4706925.
- 2. J. Maurer and P. Tabeling, Local investigation of superfluid turbulence,, vol. 43, no. 1, p. 29, 1998.
- 3. P.-E. Roche, P. Diribarne, T. Didelot, O. Français, L. Rousseau, and H. Willaime, Vortex density spectrum of quantum turbulence,, vol. 77, no. 6, p. 66002, 2007.
- 4. A. W. Baggaley, L. K. Sherwin, C. F. Barenghi, and Y. A. Sergeev, Thermally and mechanically driven quantum turbulence in helium II,, vol. 86, p. 104501, 2012.
- 5. R. J. Donnelly,. Cambridge: Cambridge University Press, 1991.
- 6. C. F. Barenghi, R. J. Donnelly, and W. F. Vinen,. Berlin: Springer, 2001.
- 7. M. Tsubota, M. Kobayashi, and H. Takeuchi, Quantum hydrodynamics,, vol. 522, pp. 191–238, 2012. DOI:10.1016/j.physrep.2012.09.007.
- 8. S. van Sciver,. Berlin: Springer, second ed., 2012.
- 9. S. K. Nemirovskii, Quantum turbulence: Theorethical and numerical problems,, vol. 524, pp. 85–202, 2013. DOI:10.1016/j.physrep.2012.10.005.
- 10. W. F. Vinen, Mutual friction in a heat current in liquid helium II-III. theory of the mutual friction,, vol. A240, pp. 493–515, 1957. DOI:10.1098/rspa.1957.0191.
- 11. J. Castiglione, P. J. Murphy, J. T. Tough, F. Mayot, and Y. Pomeau, Propagating and stationary superfluid turbulent fronts,, vol. 100, pp. 575–595, 1995. DOI:10.1007/BF00751526.
- 12. J. F. Kafkalidis, G. Klinich III, and J. T. Tough, Superfluid turbulence in a nonuniform rectangular channel,, vol. 50, p. 15909 (20 pages), 1994. DOI:10.1103/PhysRevB.50.15909.
- 13. G. Klinich III, J. F. Kafkalidis, and J. T. Tough, Superfluid Turbulence in Converging and Diverging Rectangular Channels,, vol. 107, pp. 327–346, 1997. DOI:10.1007/BF02397461.
- 14. J. P. Murphy, J. Castiglione, and J. T. Tough, Superfluid turbulence in a nonuniform circular channel,, vol. 92, pp. 307–334, 1993. DOI:10.1007/BF00682294.
- 15. J. F. Kafkalidis, G. Klinich III, and J. T. Tough, The vortex line density in nonuniform superfluid turbulence,, vol. 194–196, pp. 717–718, 1994. DOI:10.1016/0921-4526(94)90688-2.
- 16. S. K. Nemirovskii, Diffusion of inhomogeneous vortex tangle and decay of superfluid turbulence,, vol. 81, p. 64512 (10 pages), 2010. DOI:10.1103/PhysRevB.81.064512.
- 17. S. K. Nemirovskii, Propagation of a Turbulent Fronts in Quantum Fluids,, vol. 162, pp. 347–353, 2011. DOI:10.1007/s10909-010-0252-x.
- 18. L. Kondaurova and S. K. Nemirovskii, Numerical study of decay of vortex tangles in superfluid helium at zero temperature,, vol. 86, p. 134506 (13 pages), 2012. DOI:10.1103/PhysRevB.86.134506.
- 19. J. A. Geurst, Hydrodynamics of quantum turbulence in He II: Vinen’s equation derived from energy and impulse of vortex tangle,, vol. 154, pp. 327–343, 1989. DOI:10.1016/0921-4526(89)90167-1.
- 20. J. A. Geurst, Hydrodynamic theory of superfluid turbulence in He II and Schwarz’s vortex modelling,, vol. 183, pp. 279–303, 1992..
- 21. J. A. Geurst and H. van Beelen, Hydrodynamics of superfluid turbulence in He II: three-dimensional theory,, vol. 206, pp. 58–92, 1994..
- 22. M. S. Mongiovì and D. Jou, Thermodynamical derivation of a hydrodynamical model of inhomogeneous superfluid turbulence,, vol. 75, p. 24507 (14 pages), 2007. DOI:10.1103/PhysRevB.75.024507.
- 23. L. Saluto, M. S. Mongiovì, and D. Jou, Vortex diffusion and vortex-line hysteresis in radial quantum turbulence,, vol. 440C, pp. 99–103, 2014. DOI:10.1016/j.physb.2014.01.041.
- 24. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He 4: Homogeneous superfluid turbulence,, vol. 38, pp. 2398–2417, 1988. DOI:10.1103/PhysRevB.38.2398.
- 25. L. Saluto, D. Jou, and M. S. Mongiovì, Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence,, vol. 406, pp. 272–280, 2014. DOI:10.1016/j.physa.2014.03.062.
- 26. L. J. Campbell, Driven, dissipative superfluids: Radial counter-flow of rotatingHe,, vol. 36, pp. 6773–6781, 1987. DOI:10.1103/PhysRevB.36.6773.
- 27. M. S. Mongiovì and D. Jou, Generalization of Vinen’s equation including transition to superfluid turbulence,, vol. 17, pp. 4423–4440, 2005..
- 28. L. Saluto, M. S. Mongiovì, and D. Jou, Longitudinal counterflow in turbulent liquid helium: velocity profile of the normal component,, vol. 65, pp. 531–548, 2014. DOI:10.1007/s00033-013-0372-7.
- 29. L. Saluto, Stationary heat flux profile in turbulent helium II in a semi-infinite cylindrical channel, in, vol. V, pp. 133–144, Aracne, 2012.
- 30. M. Sciacca, M. S. Mongiovì, and D. Jou, Alternative Vinen equation and its extension to rotating counterflow superfluid turbulence,, vol. 4038, pp. 2215–2224, 2008. DOI:10.1016/j.physb.2007.12.001.
- 31. K. P. Martin and J. T. Tough, Evolution of superfluid turbulence in thermal counterflow,, vol. 27(5), pp. 2788–2799, 1983. DOI:10.1103/PhysRevB.27.2788.
DOI: https://doi.org/10.1515/caim-2016-0010 | Journal eISSN: 2038-0909
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
Keywords:
Related subjects:
© 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.