Abstract
We generalize the analysis of second sound nonlinear waves to include the case in which a turbulent tangle of superfluid vortices is present in the flow. In the limit of weakly nonlinear perturbations the analysis reduces to examining the effect of friction arising from a given vortex tangle on a propagating wave, so that the considered model describes temperature waves propagating in a background of constant quantized vorticity. The obtained analytical solution yields a simple criterion showing that a localized disturbance develops into the temperature discontinuity provided the gradient of the initial disturbance exceeds a critical value; the latter is found as a function of temperature and superfluid vortex line density.
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REFERENCES
L. D. Landau and E. M. Lifschitz, Fluid Mechanics, Course of Theoretical Physics, 2nd ed., Pergamon, Oxford (1987).
S. J. Putterman, Superfluid Hydrodynamics, North Holland/Elsevier, New York (1974).
D. V. Osborne, Proc. Phys. Soc. London A 64, 114 (1951).
I. M. Khalatnikov, An Introduction To the Theory of Superfluidity, W. A. Benjamin, New York (1965).
V. B. Efimov, G. V. Kolmakov, A. S. Kuliev, and L. P. Mezhov-Deglin, J. Low Temp. Phys. 24, 81 (1998).
M. Mohazzab and N. Mulders, Phys. Rev. B 61, 609 (2000).
R. J. Donnelly, Quantized Vortices in Helium II, CUP, Cambridge (1991).
M. R. Smith, R. J. Donnelly, N. Goldenfeld, and W. F. Vinen, Phys. Rev. Lett. 71, 2583 (1993); S. R. Stalp, L. Skrbek, and R. J. Donnelly, Phys. Rev. Lett. 82, 4381 (1999).
J. Maurer and P. Tabeling, Europhys. Lett. 43, 29 (1998).
M. R. Smith, D. K. Hilton, and S. V. VanSciver, Phys. Fluids 11, 751 (1999); M. Niemetz, W. Schoepe, J. T. Simola, and J. T. Tuoriniemi, Physica B 280, 559 (2000).
L. P. Kondaurova, S. K. Nemirovskii, and M. V. Nedoboiko, J. Low Temp. Phys. 25, 475 (1999).
H. E. Hall and W. F. Vinen, Proc. R. Soc. London A 238, 204 (1956).
R. J. Donnelly and C. E. Swanson, J. Fluid Mech. 173, 387 (1986).
D. J. Melotte and C. F. Barenghi, Phys. Rev. Lett. 80, 4181 (1998).
C. F. Barenghi, R. J. Donnelly, and W. F. Vinen, J. Low Temp. Phys. 52, 189 (1983).
S. K. Nemirovskii and V. V. Lebedev, Sov. Phys. JETP 57, 1009 (1983).
W. F. Fiszdon, M. von Schwerdtner, G. Stamm, and W. Popper, J. Fluid Mech. 212, 663 (1990).
A. H. Nayfeh, Perturbation Methods, John Wiley, New York (1973).
W. F. Vinen, Proc. R. Soc. London A 240, 128 (1957).
S. Braun, A. Kluwick, and M. S. Cramer, Phys. Fluids 8, 2513 (1996).
A. Kluwick, ZAMM 63, 161 (1983).
G. B. Witham, Linear and Nonlinear Waves, John Wiley, New York (1974).
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Sergeev, Y.A., Barenghi, C.F. Interaction of Weakly Nonlinear Second Sound Waves with a Vortex Tangle in Helium II. Journal of Low Temperature Physics 127, 203–214 (2002). https://doi.org/10.1023/A:1015226202501
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DOI: https://doi.org/10.1023/A:1015226202501