Anisotropie porous penetrative convection

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1944, 1996, Pages 97-115

  Straughan, B ^a   Walker, D W ^b  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746750027     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0006     Document Type: Article

References (23)

1. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic stability. Cambridge University Press.
2. Gardner, D. R., Trogdon, S. A. & Douglas, R. W. 1989 A modified tau spectral method that eliminates spurious eigenvalues. J. Comput. Phys. 80, 137-167.
3. George, J. H., Gunn, R. D. Straughan, B. 1989 Patterned ground formation and penetrative convection in porous media. Geophys. Astrophys. Fluid Dyn. 46, 135-158.
4. Matthews, P. C. 1988 A model for the onset of penetrative convection. J. Fluid Mech. 188, 571-583.
5. Moler, C. B. &z Stewart, G. W. 1973 An algorithm for generalized matrix eigenproblems. SIAM. Jl Numer. Analys. 10, 241-250.
6. Nield, D. A. & Bejan, A. 1992 Convection in porous media. Berlin: Springer.
7. Or, A. C. 1989 The effects of temperature-dependent viscosity and the instabilities in the convection rolls of a layer of fluid-saturated porous medium. J. Fluid Mech. 206, 497-515.
8. Payne, L. E., Song, J. C. & Straughan, B. 1988 Double diffusive porous penetrative convection; thawing subsea permafrost. Int. J. Engng Sci. 26, 797-809.
9. Payne, L. E. fc Straughan, B. 1987 Unconditional nonlinear stability in penetrative convection. Geophys. Astrophys. Fluid Dyn. 39, 57-63
10. (see also, Corrected and extended numerical results. Geophys. Astrophys. Fluid Dyn. 43, 307-309).
11. Qin, Y. & Kaloni, P. N. 1992 Steady convection in a porous medium based upon the Brinkman model. IMA Jl Appl. Math. 35, 85-95.
12. Qin, Y. fc Kaloni, P. N. 1993 A nonlinear stability problem of convection in a porous vertical slab. Physics Fluids A 5, 2067-2069.
13. Qin, Y. fc Kaloni, P. N. 1994 Convective instability in an anisotropic porous medium. Stud. Appl. Math. 91, 189-204.
14. Qin, Y., Guo, J. fc Kaloni, P. N. 1995 Double diffusive penetrative convection in porous media. Int. J. Engng Sci., 33, 303-312.
15. Richardson, L. L. fe Straughan, B. 1993 Convection with temperature dependent viscosity in a porous medium: nonlinear stability and the Brinkman effect. Atti Accad. Naz. Lined, (series IX) 4, 223-230.
16. Roberts, P. H. 1967 Convection in horizontal layers with internal heat generation. Theory. J. Fluid Mcch. 30, 33-49.
17. Straughan, B. 1985 Finite amplitude instability thresholds in penetrative convection. Geophys. Astrophys. Fluid Dyn. 34, 227-242.
18. Straughan, B. 1992 The energy method, stability, and nonlinear convection. Berlin: Springer.
19. Straughan, B. 1993 Mathejnatical aspects of penetrative convection. Harknv: Longman.
20. Straughan, B. 1996 Stability thresholds for convection when the viscosity has a general form of temperature dependence. In Energy methods in continuum mechanics (ed. S. N. Antontsev, J. I. Diaz & S. I. Shmarev). Dordrecht: Kluwer (in the press).
21. Straughan, B. fc Walker, D. W. 1996 Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems (to appear).
22. Tyvand, P. A. & Storesletten, L. 1991 Onset of convection in an anisotropic porous medium with oblique principal axes. J. Fluid Mech. 220, 371-382.
23. Veronis, G. 1903 Penetrative convection. Astrophys. J. 137, C41-C63.