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Original Articles

Scale selection in low-order spectral models of two-dimensional thermal convection

Pages 458-479 | Received 25 Aug 1982, Accepted 02 May 1983, Published online: 15 Dec 2016

References

  • Chandrasekhar, S. 1961. Hydrodynamic and hydro-magnetic stability. Oxford University press. 643 pp.
  • Charney, J. G. and Devore, J. G. 1979. Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci. 36, 1205–1216.
  • Clever, R. M. and Busse, F. H., 1974. Transition to Tellus 36A (1984), 5 time-dependent convection. J. Fluid. Mech. 65, 625–645.
  • Fjertoft, R. 1953. On the changes in the spectral distribution of kinetic energy for two-dimensional non-divergent flow. Tellus 5, 225–230.
  • Haken, H. 1978. Synergetics-an introduction. Non-equilibrium phase transitions and self-organisation in physics, chemistry and biology, 2nd edition. Springer Verlag. 355 pp.
  • Hart. J. E. 1981. Wave number selection in non-linear baroclinic instability. J. Atmos. Sci. 38, 400–408.
  • Kfilkn, E. and Wiin-Nielsen, A. C. 1980. Non-linear, low-order interactions. Tellus 32, 393–409.
  • Koschmeider, E. L. 1974. Bénard convection. Adv. Chem. Phys. 26, 177–212.
  • Kuo, H. L. and Platzman, W. 1961. A normal mode non-linear solution of the Rayleigh convection problem. Contr. Atmos. Phys. 33, 137–168.
  • Krishnamurti, R. 1975. On cellular cloud patterns. Part 3: applicability of mathematical and laboratory models. J. Atmos. &I. 32, 1373–1383.
  • Lorenz, E. N. 1960. Maximum simplification of the dynamic equations. Tellus 12, 243–254.
  • Lorenz, E. N. 1963. Deterministic non-periodic flow. J. Atmos. sci. 20, 130–141.
  • Lorenz, E. N. 1982. Low-order models of atmospheric circulations. J. Meteorot Soc. Japan 60, 255–267.
  • Malkus, W. V. R. 1954. Discreet transitions in turbulent convection. Proc. R. Soc. 4225, 185–195.
  • Malkus, W. V. R. 1981. The amplitude of convection. In: Evolution of physical oceanography, ed. by B. A. Warren and L. Wunsch. MIT Press, 384–393.
  • Malkus, W. V. R. and Veronis, G. 1958. Finite amplitude cellular convection. J. Fluid Mech. 4, 225–260.
  • Merrilees, P. E. and Warn, H. 1975. On energy and enstrophy exchanges in two-dimensional non-diver-gent flow. J. Fluid Mech. 69, 625–630.
  • Rayleigh, L. 1916. On convection currents in a hori-zontal layer of fluid, when the higher temperature is on the under side. Phil. Mag. 32, 529–546.
  • Saltzman, B. 1962. Finite amplitude-free convection as aninitial value problem (I). J. Atmos. Sci. 19, 329–341.
  • Segel, L. A. 1962. The non-linear interaction of two disturbances in the thermal convection problem. J. Fluid Mech. 14, 97–114.
  • Sheu, P., Agee, E. M. and Tribbia, J. J. 1980. A numerical study of the physical processes affecting convective cellular geometry. J. Meteorot Soc. Japan 58.489–499.
  • Shirer, H. and Dutton, J. 1979. The branching hierarchy of multiple solutions in a model of moist convection. J. Atmos. Sci. 36, 1705–1721.
  • Sparrow, C. 1982. The Lorenz equations: bifurcation, chaos and strange attractors. Applied mathematical sciences 41, Springer Verlag. 269 pp.
  • Spiegel, E. A. and Veronis, G. 1960. On the Boussinesq approximation for a compressible fluid. Astrophy. J. 131, 442–447.
  • Veronis, G. 1966. Large-amplitude Bénard convection. J. Fluid Mech. 26, 49–68.
  • Walter, B. A. 1980. Winter-time observations of roll clouds over the Bering sea. Mon. Wea. Rev. 108, 2024–2031.
  • Wilkinson, J. H. & Reinsch, C. (eds.) 1971. Linear algebra. Springer Verlag. 327–338.
  • Willis, G. E., Deardorf, J. W. & Somerville, R. C. J. 1972. Roll-diameter dependence in Rayleigh con-vection and its dependence upon heat flux. J. Fluid Mech. 54, 351–367.
  • Young, J. A. 1968. Comparative properties of some time differencing schemes for linear and nonlinear oscillations. Mon. Wea. Rev. 96, 357–364.