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Finger-interaction mechanisms in stratified Hele-Shaw flow

Published online by Cambridge University Press:  20 April 2006

Grétar Tryggvason  and
Hassan Aref
Grétar Tryggvason
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island 02912 Present address: Courant Institute of Mathematical Sciences, New York, NY 10012.
Hassan Aref
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island 02912
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Abstract

Interactions between a few fingers in sharply stratified Hele-Shaw flow are investigated by numerical integration of the initial-value problem. It is shown that fingers evolving from an initial perturbation of an unstable interface consisting of a single wave are rather insensitive to variations of the control parameters governing the flow. Initial perturbations with at least two waves, on the other hand, lead to important finger-interaction and selection mechanisms at finite amplitude. On the basis of the results reported here many features of an earlier numerical study of the ‘statistical-fingering’ regime can be rationalized.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 154 , May 1985 , pp. 287 - 301
Copyright
© 1985 Cambridge University Press

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References

Aref, H. & Siggia, E. D. 1980 Vortex dynamics of the two-dimensional turbulent shear layer. J. Fluid Mech. 100, 705–737.Google Scholar
Aref, H. & Tryggvason, G. 1984a Vortex dynamics of passive and active interfaces. Physica 12D, 59–70.Google Scholar
Aref, H. & Tryggvason, G. 1984b Interface dynamics by the vortex-in-cell method. Presented at 16th Intl Congr. Theoretical and Applied Mechanics, Lyngby. Denmark, (unpublished).
De Josselin De Jong 1960 Singularity distributions for the analysis of multiple-fluid flow through porous media. J. Geophys. Res. 65, 3739–3758.Google Scholar
Mclean, J. W. & Saffman, P. G. 1981 The effect of surface-tension on the shape of fingers in a Hele-Shaw cell. J. Fluid Mech. 102, 455–469.Google Scholar
Park, C.-W., Gorell, S. & Homsy, G. M. 1984 Two-phase displacement in Hele-Shaw cells: experiments on viscously driven instabilities. J. Fluid Mech. 141, 257–287, Corrigendum: J. Fluid Mech. 144, 468–469.Google Scholar
Park, C.-W. & Homsy, G. M. 1984 Two-phase displacement in Hele-Shaw cells: theory, J. Fluid Mech. 139, 291–308.Google Scholar
Pitts, E. 1980 Penetration of fluid into a Hele-Shaw cell: the Saffman-Taylor experiment. J. Fluid Mech. 97, 53–64.Google Scholar
Saffman, P. G. 1959 Exact solutions for the growth of fingers from a flat interface between two fluids in a porous medium or Hele-Shaw cell. Q. J. Mech. Appl. Maths 12, 146–150.Google Scholar
Saffman, P. G. & Taylor, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312–329.Google Scholar
Taylor, G. I. & Saffman, P. G. 1958 Cavity flow of viscous liquids in narrow spaces. In Proc. 2nd Symp. on Naval Hydrodynamics.
Taylor, G. I. & Saffman, P. G. 1959 A note on the motion of bubbles in a Hele-Shaw cell and porous medium. Q. J. Mech. Appl. Maths 12, 265–279.Google Scholar
Tryggvason, G. & Aref, H. 1983 Numerical experiments on Hele-Shaw flow with a sharp interface. J. Fluid Mech. 136, 1–30.Google Scholar
Vanden-Broeck, J.-M. 1983 Fingers in a Hele-Shaw cell with surface tension. Phys. Fluids 26, 2033–34.Google Scholar
Wooding, R. A. 1969 Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell. J. Fluid Mech. 39, 477–495.Google Scholar
Wooding, R. A. & Morel-Seytoux, H. J. 1976 Multiphase fluid flow through porous media. Ann. Rev. Fluid Mech. 8, 233–274.Google Scholar