Two-fluid hydrodynamics of superfluid 4He: GENERIC formulation

Journal of Non-Newtonian Fluid Mechanics

Volumn 152, Issue 1-3, 2008, Pages 27-35

  Grmela, Miroslav ^a  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

GENERIC; Nonequilibrium thermodynamics; Superfluids

Indexed keywords

FLUID DYNAMICS; HEAT FLUX; THERMODYNAMICS;

EXTENDED IRREVERSIBLE THERMODYNAMICS; HOLM-KUPERSHMIDT FORMULATION; NONEQUILIBRIUM THERMODYNAMICS; TWO-FLUID HYDRODYNAMICS;

SUPERFLUID HELIUM;

FLUID DYNAMICS; HEAT FLUX; SUPERFLUID HELIUM; THERMODYNAMICS;

EID: 43649086619     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2007.07.004     Document Type: Article

References (41)

1. Grmela M. Particle and bracket formulations of kinetic equations. Contemp. Math. 28 (1984) 125-132
2. Grmela M. Hamiltonian dynamics of incompressible elastic fluids. Phys. Lett. A 130 (1988) 81-86
3. Grmela M. Bracket formulation of diffusion-convection equation. Physica D 21 (1986) 179-212
4. Grmela M. Mesoscopic dynamics and thermodynamics: applications to polymeric fluids. In: Casas-Vazquez J., and Jou D. (Eds). Rheological Modelling: Thermodynamic and Statistical Approaches, Lecture Notes in Physics, vol. 381 (1991), Springer, Berlin 99-125
5. Beris A.N., and Edwards B.J. The Thermodynamics of Flowing Systems (1994), Oxford University Press
6. Grmela M., and Oettinger H.C. Dynamics and thermodynamics of complex fluids. Part I. Illustration of a general formalism. Phys. Rev. E 56 (1997) 6620-6632
7. Oettinger H.C., and Grmela M. Dynamics and thermodynamics of complex fluids. Part II. Development of a general formalism. Phys. Rev. E 56 (1997) 6632-6655
8. Oettinger H.C. Beyond Equilibrium Thermodynamics (2005), Wiley-Interscience
9. A. Clebsch, Ueber die Integration der hydrodynamischen Gleichungen, J. Reine Angew. Math. 56 (1895) 1-10.
10. Arnold V.I. Sur la geometrie differentielle des groupes de Lie de dimension infini et ses applications l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16 (1966) 319-361
11. J.E. Marsden, T.S. Ratiu, Introduction to mechanics and symmetry, in: Texts in Applied Mathematics, vol. 17, 2nd ed., Springer-Verlag, 1999.
12. Tisza L. Nature 141 (1938) 913
13. Landau L.D. J. Phys. 5 (1941) 71
14. Holm D.D., and Kupershmidt B.A. Superfluid plasmas: multivelocity nonlinear hydrodynamics of superfluid solutions with charged condensates coupled electromagnetically. Phys. Rev. A 36 (1987) 3947-3956
15. Jou D., Casas-Vazquez J., and Lebon G. Extended Irreversible Thermodynamics. 2nd ed. (1996), Springer, Berlin
16. Seliger R.L., and Whitham G.B. Proc. Roy. Soc. Lond., Ser. A (1968) 305
17. Salmon R. Hamiltonian fluid mechanics. Ann. Rev. Fluid Mech. 20 (1988) 225-256
18. Sieniutycz S. Conservation Laws in Variational Thermodynamics (1994), Kluwer Acad. Publ.
19. Zilsel P.R. Liquid helium II: the hydrodynamics of the Tw-fluid model. Phys. Rev. 79 (1979) 309
20. 4He, Phys. Rev B 22 (1980) 3207-3220.
21. Grmela M. Geometry of mesoscopic dynamics and thermodynamics. J. Non-Newtonian Fluid Mech. 120 (2004) 137-147
22. Grmela M., Jou D., Casas-Vazquez J., Bousmina M., and Lebon G. Ensemble averaging in turbulence modelling. Phys. Lett. A 330 (2004) 54-64
23. Khalatnikov M. An Introduction to the Theory of Superfluidity (1965), Benjamin, New York, Amsterdam
24. Mongiovi M.S. Extended Irreversible Thermodynamics of Liquid Helium II. Phys. Rev. B 48 (1993) 6276-6283
25. Mongiovi M.S. Extended irreversible thermodynamics of liquid helium II: boundary conditions and propagation of fourth sound. Physica A 292 (2001) 55-74
26. Lhuillier D., Francois M., and Karatchentzeff M. Conjugate variables and a variational principle in superfluid helium. Phys. Rev. B 12 (1975) 2656
27. Callen H.B. Thermodynamics an Introduction to Thermostatics. 2nd ed. (1985), Wiley, New York
28. Liu I.S. Method of Lagrange multipliers for exploiting the entropy principle. Arch. Rat. Mech. Anal. 46 (1972) 131-148
29. C.F. Barenghi, R.J. Donnelly, W.F. Vinen (Eds.), Quantized Vortex Dynamics and Superfluid Turbulence, Springer, Berlin, 2001.
30. Vinen W.F., and Niemela J.J. Quantum turbulence. J. Low Temp. Phys. 128 (2002) 167-231
31. Hall H.E., and Vinen W.F. Proc Roy. Soc. Lond. A 238 (1956) 215
32. Vinen W.F. Proc. Roy. Soc. A 240 (1957) 114
33. Vinen W.F. Proc. Roy. Soc. A 240 (1957) 128
34. Vinen W.F. Proc. Roy. Soc. A 242 (1957) 493
35. Vinen W.F. Proc. Roy. Soc. A 243 (1957) 400
36. Yamada K., Kashiwamura S., and Miyake K. Stochastic theory of vortex tangle in superfluid turbulence. Physica B 154 (1989) 318-326
37. Jou D., and Mongiovi M.S. Description and evolution of anisotropy in superfluid vortex tangles with counterflow and rotation. Phys. Rev. B 74 (2006) 054509-1-054509-11
38. Grmela M. Thermodynamical lift of the nonlinear Onsager-Casimir vector field. In: Harnad J., and Masden J.E. (Eds). Hamiltonian Systems, Transformation Groups and Spectral Transform Methods (1990), CRM, Universite de Montral
39. Hermann R. Geometry, Physics and Systems (1973), Dekker, New York
40. Mrugala R., Nulton J.D., Schoen J.C., and Salamon P. Phys. Rev. A 41 (1990) 3156
41. Arnold V.I. Mathematical Methods of Classical Mechanics (1989), Springer, New York