Environmental Modeling & Assessment

, Volume 1, Issue 4, pp 243–261 | Cite as

Forced oscillations with damping proportional to velocity on a beta plane: the Southern Oscillation connection

  • A. H. Gordon


An analogy is made between mechanical and electrical oscillating systems and an oscillating atmospheric system. The problem is to study the behaviour of an oscillator driven by zonal forcing of the annual cycle with damping on an earth beta plane. When the Coriolis parameter is constant the system oscillates in a simple linear manner with the forcing frequency. When the Coriolis parameter is allowed to vary as a function of its latitudinal position, the equations for horizontal motion become non-linear and their numerical solutions exhibit non-linear and sometimes chaotic properties. If the oscillator is initially forced with a west to east (positive) pressure gradient the motion is convergent and stable in character. If it is initially forced with an east to west (negative) pressure gradient the motion is divergent and can be sensitive dependent on the exact starting latitude. Regular periodicities develop for the former case but in the latter case peaks and troughs of apparent cycles are aperiodic, chaotic or blow up. A connection is drawn between the behaviour of such an oscillating dynamical system and the ENSO phenomenon. A paradigm for the latter's observed behaviour is suggested.


Mathematical Modeling Dynamical System Pressure Gradient Industrial Mathematic Annual Cycle 
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  1. [1]
    W.E. Boyce and R.C. Di Prima,Elementary Differential Equations, 3rd ed., Wiley, New York, 1977.Google Scholar
  2. [2]
    J.A.T. Bye, R.A.D. Byron-Scott and A.H. Gordon, Climate the elements, J. Clim. (July 1996).Google Scholar
  3. [3]
    T.H. Chen, Bifurcation in cross-equatorial flow: a non-linear characteristic of Lagrangian modelling. J. Atmos. Sci. 52 (1995) 1383–1400.Google Scholar
  4. [4]
    Commonwealth Bureau of Meteorology, Monthly climate analysis, 1995.Google Scholar
  5. [5]
    A.H. Gordon, Interhemispheric contrasts of mean global temperature anomalies, Int. J. Clim. 12 (1993) 11–9.Google Scholar
  6. [6]
    A.H. Gordon and R.C. Taylor, Computations of surface layer air parcel trajectories and weather in the oceanic tropics. International Indian Ocean Expedition Monographs 7, East-West Press, Honolulu, Hawaii, 1975, 112 pp.Google Scholar
  7. [7]
    C.G. Lambe,Applied Mathematics for Engineers and Scientists, English Universities Press, London, 1958.Google Scholar
  8. [8]
    R.S. Lindzen and J.R. Holten, A theory of the quasi-biennial oscillation, J. Atmos. Sci. 25 (1968) 1095–1107.Google Scholar
  9. [9]
    E.N. Lorenz, Can chaos and intransitivity lead to interannual variability, Tellus 42A (1990) 378–389.Google Scholar

Copyright information

© Baltzer Science Publishers 1996

Authors and Affiliations

  • A. H. Gordon
    • 1
  1. 1.Flinders Institute for Atmospheric and Marine ScienceThe Flinders University of South AustraliaBedford ParkAustralia

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