Instability of Poiseuille flow in a fluid overlying a porous layer

Journal of Fluid Mechanics

Volumn 564, Issue , 2006, Pages 287-303

  Chang, Min Hsing ^a,b,c   Chen, Falin ^a,b,c   Straughan, Brian ^a,b,c  

^a YUNG TA INSTITUTE OF TECHNOLOGY AND COMMERCE   (Taiwan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^c DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; SHEAR STRESS; STABILITY;

LINEAR INSTABILITY ANALYSIS; POISEUILLE FLOW;

FLOW OF FLUIDS;

EIGENVALUES AND EIGENFUNCTIONS; FLOW OF FLUIDS; MATHEMATICAL MODELS; SHEAR STRESS; STABILITY;

FLUID FLOW; INSTABILITY; POROUS MEDIUM;

EID: 33748854228     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006001583     Document Type: Article

References (47)

1. Allen, M. B. 1984 Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs. Springer.
2. Allen, M. B., Behie, A. & Trangenstein, J. A. 1988 Multiphase Flow in Porous Media: Mechanics, Mathematics, and Numerics. Springer.
3. Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197-207.
4. Blest, D. C., Duffy, B. R., McKee, S. & Zulkifle, A. K. 1999a Curing simulation of thermoset composites. Composites A 30, 1289-1309.
5. Blest, D. C., McKee, S., Zulkifle, A. K. & Marshall, P. 1999b Curing simulation by autoclave resin infusion. Composites Sci. Technol. 59, 2297-2313.
6. Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 1637-1650.
7. Caviglia, G., Morro, A. & Straughan, B. 1992 Reflection and refraction at a variable porosity interface. J. Acoust. Soc. Am. 92, 1113-1119.
8. Chen, B., Cunningham, A., Ewing, R., Peralta, R. & Visser, E. 1994 Two-dimensional modeling of microscale transport and biotransformation in porous media. Numer. Meth. Partial Diff. Equations 10, 65-83.
9. Chen, F. & Chen, C. F. 1988 Onset of finger convection in a horizontal porous layer underlying a fluid layer. J. Heat Transfer 110, 403-409.
10. Chen, K. P. & Crighton, D. G. 1994 Instability of the large Reynolds number flow of a Newtonian fluid over a viscoelastic fluid. Phys. Fluids A 6, 152-163.
11. Ciesjko, M. & Kubik, J. 1999 Compatibility conditions in the fluid-fluid saturated porous solid contact problems. Transport Porous Med. 34, 319-336.
12. Das, D. B., Nassehi, V. & Wakeman, R. J. 2002 A finite volume model for the hydrodynamics of combined free and porous flow in sub-surface regions. Adv. Environ. Res. 7, 35-58.
13. Discacciati, M., Miglio, E. & Quarteroni, A. 2002 Mathematical and numerical models for coupling surface and groundwater flows. Appl. Numer. Maths 43, 57-74.
14. Dongarra, J. J., Straughan, B. & Walker, D. W. 1996 Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. Appl. Numer. Maths 22, 399-435.
15. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
16. Ewing, R. E. 1997 The need for multidisciplinary involvement in groundwater contaminant simulations. Proceedings of Next Generation Environmental Models and Computational Methods (ed. G. Delic & M. Wheeler), pp. 227-245. SIAM, Philadelphia, PA.
17. Ewing, R. E. & Weekes, S. 1998 Numerical methods for contaminant transport in porous media. Computational Maths 202, 75-95.
18. Hooper, A. P. 1989 The stability of two superposed viscous fluids in a channel. Phys. Fluids A 1, 1133-1142.
19. Jäger, W. & Mikelic, A. 1998 On the interface boundary condition by Beavers, Joseph and Saffman. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen der Universtät Heidelberg. Preprint 98-12.
20. Jäger, W., Mikelic, A. & Neuss, N. 1999 Asymptotic analysis of the laminar viscous flow over a porous bed. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen der Universtät Heidelberg. Preprint 99-33.
21. Jones, I. P. 1973 Low Reynolds number flow past a porous spherical shell. Proc. Camb. Phil. Soc. 73, 231-238.
22. Layton, W. J., Schieweck, F. & Yotov, I. 2003 Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40, 2195-2218.
23. McKay, G. 2001 The Beavers and Joseph condition for velocity slip at the surface of a porous medium. In Continuum Mechanics and Applications in Geophysics and the Environment (ed. B. Straughan, R. Greve, H. Ehrentraut & Y. Wang). Springer.
24. Miglio, E., Quarteroni, A. & Saleri, F. 2003 Coupling of free surface and groundwater flows. Computers Fluids 32, 73-83.
25. Murdoch, A. J. & Soliman, A. 1999 On the slip-boundary condition for liquid flow over planar porous boundaries. Proc. R. Soc. Lond. A 455, 1315-1340.
26. Nield, D. A. 1983 The boundary correction for the Rayleigh-Darcy problem; limitations of the Brinkman equation. J. Fluid Mech. 128, 37-46.
27. Nield, D. A. 1991 The limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous mednum and at an interface. Intl J. Heat Fluid Flow 12, 269-272.
28. Nield, D. A. 1998 Modelling the effect of surface tension on the onset of natural convection in a saturated porous medium. Transport Porous Med. 31, 365-368.
29. Nield, D. A. & Bejan, A. 1999 Convection in Porous Media. Springer.
30. Payne, L. E. & Straughan, B. 1998 Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modeling questions. J. Maths Pures Appl. 77, 317-354.
31. Qin, Y. & Kaloni, P. N. 1993 Creeping flow past a porous spherical shell. Z. Angew. Math. Mech. 73, 77-84.
32. Saffman, P. 1971 On the boundary conditions at the surface of a porous medium. Stud. Appl. Maths 50, 93-101.
33. Schaflinger, U., Acrivos, A. & Zhang, K. 1989 Viscous resuspension of a sediment within a laminar and stratified flow. Intl J. Multiphase Flow 16, 567-578.
34. South, M. J. & Hooper, A. P. 1999 Linear growth in two-fluid plane Poiseuille flow. J. Fluid Mech. 381, 121-139.
35. Straughan, B. 1998 Explosive Instabilities in Mechanics. Springer.
36. Straughan, B. 2001 Surface-tension driven convection in a fluid overlying a porous layer. J. Comput. Phys. 170, 320-337.
37. Straughan, B. 2002 Effect of property variation and modeling on convection in a fluid overlying a porous layer. Intl J. Numer. Anal. Meth. Geomech. 26, 75-97.
38. Straughan, B. 2004 The Energy Method, Stability, and Nonlinear Convection, 2nd edn. Springer.
39. Stuart, J. T. 1963 Hydrodynamic stability. In Laminar Boundary Layers (ed. L. Rosenhead), pp. 492-579. Oxford University Press.
40. Suchomel, B. J., Chen, B. M. & Allen, M. B. 1998 Network model of flow, transport and biofilm effects in porous media. Transport Porous Med. 30, 1-23.
41. Taylor, G. I. 1971 A model for the boundary conditions of a porous material. J. Fluid Mech. 49, 319-326.
42. Tilley, B. S., Bankoff, S. G. & Davis, S. H. 1994a Shear and interfacial instabilities in oil-water flow in an inclined channel. Chem. Engng Commun. 141, 41-49.
43. Tilley, B. S., Davis, S. H. & Bankoff, S. G. 1994b Linear stability theory of two-layer flow in an inclined channel. Phys. Fluids 6, 3906-3922.
44. Timoshin, S. N. & Hooper, A. P. 2000 Mode coalescence in a two-fluid boundary-layer stability problem. Phys. Fluids 12, 1969-1978.
45. Waller, J. & Schaflinger, U. 1998 Viscous resuspension of a sediment caused by oscillating stratified flows. Acta Mech. 127, 147-153.
46. Worster, M. G. 1992 Instabilities of the liquid and mushy regions during solidification of alloys. J. Fluid Mech. 237, 649-669.
47. Zhang, K., Acrivos, A. & Schaflinger, U. 1992 On the stability in a 2D Hagen-Poiseuille resuspension flow. Intl J. Multiphase Flow 18, 51-63.