Abstract
Helium II at temperatures below Tλ can be described as a superposition of two interacting fluids. A normal-fluid which has non-zero viscosity, and an inviscid superfluid in which vorticity is confined to quantised vortex filaments. These two fluids are coupled together by the mutual friction force. To model the normal-fluid flow we use the forced Navier-Stokes equation while the superfluid flow is modelled as motion of quantised vortex lines. In this article we describe the numerical methods used for the coupled motion of the two fluids. We also briefly discuss the detailed flow structures observed from the two-dimensional (2-D) and the three-dimensional (3-D) simulations of this problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K. W. Schwarz: Phys. Rev. B 31 5782 (1985).
D. J. Melotte, C. F. Barenghi: Phys. Rev. Lett. 80 4181 (1998).
O. C. Idowu, A. Willis, D. C. Samuels, C. F. Barenghi: Phys. Rev. B 62 3409 (2000).
C. F. Barenghi: J. Phys., Condens. Matter 11 7751 (1999).
H. E. Hall and W. F. Vinen: Proc. Roy. Soc. A 238 215 (1956).
C. O. Idowu, D. Kivotides, C. F. Barenghi, D. C. Samuels: J. Low Temp. Phys. 120 269 (2000)
C. F. Barenghi, R. J. Donnelly, W. F. Vinen: J. Low Temp. Phys. 52 189 (1983).
W. F. Vinen: Proc. Roy. Soc. A 242 493 (1957).
R. J. Donnelly: Quantized Vortices in Helium II, Cambridge University Press (1991).
R. J. Donnelly, C. F. Barenghi: J. Phys. Chem. Ref. Data, Vol.27, No.6, (1998).
R. Peyret, T. D. Taylor: Computational Methods for Fluid Flow, Springer-Verlag (1983).
W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery: Numerical Recipes in Fortran 77 second edition, Cambridge University Press (1992).
R.G.K.M. Aarts, A.T.A.M. deWaele: Phys. Rev. B 50 10069 (1994).
M. W. Harlow, J. E. Welch: Phys. Fluids 8 2182 (1965).
J. Kim, P. Moin: J. Comp. Physics 59 308 (1985).
A. A. Wray: Very Low Storage Time-Advancement Schemes, Internal Report, NASA Ames Research Center, Moffet Field, California (1987).
J. Strikwerda: Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks/Cole (1989).
W. F. Vinen: Phys. Rev. B 61 1410 (2000).
D. C. Samuels, D. Kivotides: Phys. Rev. Lett. 83 5306 (1999).
D. Kivotides, C. F. Barenghi, D. C. Samuels: Science 290 777 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Idowu, O.C., Kivotides, D., Barenghi, C.F., Samuels, D.C. (2001). Numerical Methods for Coupled Normal-Fluid and Superfluid Flows in Helium II. In: Barenghi, C.F., Donnelly, R.J., Vinen, W.F. (eds) Quantized Vortex Dynamics and Superfluid Turbulence. Lecture Notes in Physics, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45542-6_14
Download citation
DOI: https://doi.org/10.1007/3-540-45542-6_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42226-6
Online ISBN: 978-3-540-45542-4
eBook Packages: Springer Book Archive