Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., DuCroz, J. Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. & Sorenson, D. 1999 LAPACK Users' Guide, 3rd edn. SIAM.
Armfield, S. W. & Street, R. 1999 The fractional-step method for the Navier–Stokes equations on staggered grids: The accuracy of three variations. J. Comput. Phys. 153, 660–665.
Armfield, S. W. & Street, R. 2002 An analysis and comparison of the time accuracy of fractional-step methods for the Navier–Stokes equations on staggered grids. Intl J. Numer. Meth. Fluids. 38, 255–282.
Armfield, S. & Street, R. 2003 The pressure accuracy of fractional-step methods for the Navier–Stokes equations on staggered grids. ANZIAM J. 44, C20–C39.
Bark, F. H., Alavyoon, F. & Dahlkild, A. A. 1992 On unsteady free convection in vertical slots due to prescribed fluxes of heat and mass at the vertical walls. J. Fluid Mech. 235, 665–689.
Bergholz, R. F. 1978 Instabilities of steady natural convection in a vertical fluid layer. J. Fluid Mech. 84, 743–768.
Birikh, R. V. 1966 On small perturbations of a plane parallel flow with cubic velocity profile. J. Appl. Math. Mech. 30, 432–438.
Birikh, R. V., Gershuni, G. Z., Zhukhovitskii, E. M. & Rudakov, R. N. 1972 On oscillatory instability of plane–parallel convective motion in a vertical channel. J. Appl. Math. Mech. 36, 707–710.
Boyd, J. P. 2001 Chebyshev and Fourier Spectral Methods, 2nd edn. Dover.
Bratsun, D. A., Zyuzgin, A. V. & Putin, G. F. 2003 Non-linear dynamics and pattern formation in a vertical fluid layer heated from the side. Intl J. Heat Fluid Flow. 24, 835–852.
Chen, Y.-M. & Perlstein, A. J. 1989 Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots. J. Fluid Mech. 198, 513–541.
Christov, C. I. & Homsy, G. M. 2001 Nonlinear dynamics of two-dimensional convection in a vertically stratified slot with and without gravity modulation. J. Fluid Mech. 430, 335–360.
Davis, P. J. & Rabinowitz, P. 1984 Methods of Numerical Integration, 2nd edn. Academic.
Desrayaud, G. 1990 Stability of flow near a heat-flux plate and comparison with numerical simulations in a square cavity. Report 1990/LT/01. CNAM.
Desrayaud, G. & Nguyen, T. H. 1989 Instabilités thermonconvectives dans une cavité à flux imposés. In Comptes Rendus. Douzième Congrès Canadien de Mécanique Appliquée (ed. Erki, M. A. & Kirkhope, J.), vol. 2, pp. 716–717. Carleton University.
Desrayaud, G., Nguyen, T. H. & LePeutrec, Y. Peutrec, Y. 1989 Stability of a buoyancy-layer. In itNatural Convection in Enclosures, Eurotherm Seminar No. 11, Extended Abstracts (ed. Quarini, G. L. & Lauriat, G.), pp. 67–69. Eurotherm.
Eaton, J. W. 2002 GNU. Octave Manual. Network Theory.
Eklund, A., Alavyoon, F., Simonsson, D., Karlsson, R. I. & Bark, F. H. 1991 Theoretical and experimental studies of free convection and stratification of electrolyte in a copper refining cell. Electrochim. Acta. 36, 1345–1354.
Fornberg, B. 1996 A Practical Guide to Pseudospectral Methods. Cambridge University Press.
Frazer, R. A., Duncan, W. J. & Collar, A. R. 1938 Elementary Matrices and Some Applications to Dynamics and Differential Equations. Cambridge University Press.
Fröberg, C.-E. 1965 Introduction to Numerical Analysis. Addison-Wesley.
Gautschi, W. 1994 Algorithm 726: ORTHPOL – a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software. 20, 21–62.
Gershuni, G. Z. & Zhukhovitskii, E. M. 1976 Convective Stability of Incompressible Fluids. Israel Program for Scientific Translations.
Gill, A. E. & Davey, A. 1969 Instabilities of a buoyancy driven system. J. Fluid Mech. 35, 775–798.
Greig, D. M. 1980 Optimisation. Longman.
Hochstrasser, U. W. 1965 Orthogonal polynomials. In Handbook of Mathematical Functions (ed. Abramowitz, M. & Stegun, I.), chap. 22, pp. 771–802. Dover.
Iyer, P. A. 1973 Instabilities in buoyancy driven buoyancy flows in a stably stratified medium. Boundary Layer Met. 5, 53–66.
Iyer, P. A. & Kelly, R. E. 1978 Supercritical solutions for the buoyancy boundary layer. J. Heat Transfer. 100, 648–652.
Joseph, D. D. 1976 Stability of Fluid Motions II. Springer.
Kimura, S. & Bejan, A. 1984 The boundary layer natural convection regime in a rectangular cavity with uniform heat flux from the side. J. Heat Transfer. 106, 98–103.
Kolobkov, N. 1960 Our Atmospheric Ocean. Foreign Languages.
Kurtz, E. F. & Crandall, S. H. 1962 Computer-aided analysis of hydrodynamic stability. J. Mathes Phys. 41, 264–279.
Laurie, D. P. 2001 Computation of Gauss-type quadrature formulas. J. Comput. Appl. Math. 127, 201–217.
Levine, H. A. & Weinberger, H. F. 1986 Inequalities between Dirichlet and Neumann eigenvalues. Arch. Rat. Mech. Anal. 94 (3), 193–208.
Manins, P. C. & Sawford, B. L. 1979 A model of katabatic winds. J. Atmos. Sci. 36, 619–630.
McBain, G. D. 2004 Skirting subsets of the plane, with application to marginal stability curves. ANZIAM J. 45 (E), C78–C91.
McBain, G. D. & Armfield, S. W. 2004 Natural convection in a vertical slot: Accurate solution of the linear stability equations. ANZIAM J. 45 (E), C92–C105.
Morley, A. 1954 Strength of Materials, 11th edn. Longmans, Green and Co.
Nachtsheim, P. R. 1963 Stability of free-convection boundary-layer flows. Tech. Note D-2089. NASA.
Peacock, T., Stocker, R. & Aristoff, J. M. 2004 An experimental investigation of the angular dependence of diffusion-driven flow. Phys. Fluids. 16, 3503–3505.
Phillips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep-Sea Res. 17, 435–440.
Plapp, J. E. 1957 The analytic study of laminar boundary-layer stability in free convection. J. Aeronaut. Sci. 24, 318–319.
Polymeropoulos, C. E. & Gebhart, B. 1966 Stability of free convection flow over a vertical uniform flux plate. AIAA J. 4, 2066–2068.
Prandtl, L. 1952 Essentials of Fluid Dynamics. Blackie.
Shapiro, A. & Fedorovich, E. 2004 a Prandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid. Intl J. Heat Mass Transfer. 47, 4911–4927.
Shapiro, A. & Fedorovich, E. 2004 b Unsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid. J. Fluid Mech. 498, 333–352.
Skyllingstad, E. D. 2003 Large-eddy simulation of katabatic flows. Boundary Layer Met. 106, 217–243.
Stuart, J. T. 1958 On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 1–21.
Szewcyzk, A. A. 1962 Stability and transition of the free-convection layer along a vertical flat plate. Intl J. Heat Mass Transfer. 5, 903–914.
Tao, J. 2006 Nonlinear global instability in buoyancy-driven boundary-layer flows. J. Fluid Mech. 566, 377–388.
Tao, J., LeQuéré, P. Quéré, P. & Xin, S. 2004 a Absolute and convective instabilities of natural convection flow in boundary-layer regime. Phys. Rev. E 70, 066311.
Tao, J., LeQuéré, P. Quéré, P. & Xin, S. 2004 b Spatio-temporal instability of the natural-convection boundary layer in thermally stratified medium. J. Fluid Mech. 518, 363–379.
Villadsen, J. V. & Stewart, W. E. 1967 Solution of boundary-value problems by orthogonal collocation. Chem. Engng Sci. 22, 1483–1501.
Weideman, J. A. C. & Reddy, S. C. 2000 A MATLAB differentiation matrix suite. ACM Trans. Math. Software. 26, 465–519.
Wunsch, C. 1970 On oceanic boundary mixing. Deep-Sea Res. 17, 293–301.