Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-05T04:55:10.333Z Has data issue: false hasContentIssue false
  • English
  • Français

Cell-pattern sensitivity to box configuration in a saturated porous medium

Published online by Cambridge University Press:  20 April 2006

B. Borkowska-Pawlak  and
W. Kordylewski
B. Borkowska-Pawlak
Affiliation:
Instytut Techniki Cieplnej i Mechaniki Plynow, 50-370 Wroclaw, Poland
W. Kordylewski
Affiliation:
Instytut Techniki Cieplnej i Mechaniki Plynow, 50-370 Wroclaw, Poland
Get access Rights & Permissions [Opens in a new window]

Abstract

Steady small-amplitude thermal convection in a fluid-saturated. infinitely extended porous layer is investigated theoretically in the wavenumber range 1/√2−1. It was shown that the point of multiple bifurcation Ra0 = (3/√2 + 2)π2, α0 = 2−0.25 leads to secondary bifurcation when the wavenumber decreases.

As a result a new branch of a stable, complicated, three-dimensional flow in the square cell was discovered for α close to α0. This branch joins two adjacent branches of three-dimensional flows emanating from the trivial solution and causes their stability transition at the branching points.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 169 - 181
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Borkowska-Pawlak, B. & Kordylewski, W. 1982 Stability of two-dimensional natural convection in a porous layer. Q. J. Mech Appl. Maths 35, 279.Google Scholar
Coullet, P. H. & Spiegel E. A.1982 Woods Hole Geophysical Fluid Dynamics Summer School lectures.
Joseph D. D.1976 Stability of Fluid Motions. Springer.
Keener J. P.1976 Secondary bifurcation in nonlinear diffusion reaction equations. Stud. Appl. Maths 55, 167.Google Scholar
Keener J. P.1979 Secondary bifurcation and multiple eigenvalues. SIAM J. Appl. Maths 37, 330.Google Scholar
Kordylewski, W. & Borkowska-Pawlak B.1981 Stability of nonlinear thermal convection in a porous medium. Proc. 15th Symp. on Advanced Problems and Methods in Fluid Mechanics, Jachranka, Poland
Lapwood E. R.1948 Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 44, 508.Google Scholar
Malkus, W. V. R. & Veronis G.1958 Finite amplitude cellular convection. J. Fluid Mech. 4, 225.Google Scholar
May, R. M. & Leonard W. J.1975 Nonlinear aspects of competition between three species. SIAM J. Appl. Maths 21, 2.Google Scholar
Palm E., Weber, J. E. & Kvernvold O.1972 On steady convection in a porous medium. J. Fluid Mech. 54, 153.Google Scholar
Rudraiah, N. & Srimani P. K.1980 Finite amplitude cellular convection in a fluid-saturated porous layer Proc. R. Soc. Lond. A 373, 199.Google Scholar
Schubert, G. & Straus J. M.1979 Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh number. J. Fluid Mech. 94, 25.Google Scholar
Straus, J. M. & Schubert G.1979 Three-dimensional convection in a cubic box of fluid-saturated porous material. J. Fluid Mech. 91, 155.Google Scholar
Segel L. A.1962 The non-linear interaction of two disturbances in the thermal convection problem. J. Fluid Mech. 14, 97.Google Scholar
Zebib, H. & Kassoy P. R.1978 Three-dimensional natural convection motion in a confined porous medium. Phys. Fluids 21, 1.Google Scholar