The statistical equilibrium solution of a primitive-equation model

Article English OPEN
Errico, Ronald M. (2011)

The statistical equilibrium solution of an f-plane, primitive-equation model with a single quadratic energy invariant is determined by numerical integration. The initial condition resembles the atmosphere in terms of the shape and magnitude of its energy spectrum. The equilibrium solution is one in which energy is equipartitioned among all the linearly independent modes of the system. This state is attained after two simulated years. The approach to equilibrium is explored in detail. It is characterized by (at least) two stages. The first is dominated by quasi-geostrophic dynamics and nonlinear balances. The approximate conservation of quasi-geostrophic potential enstrophy is important during this stage, so that the solution initially tends to the equilibrium solution of a quasi-geostrophic form of the model. The second stage is characterized by a very slow transfer of energy from geostrophic modes to inertial-gravity waves. The rate of transfer of energy during this stage is shown to be very sensitive to initial conditions.DOI: 10.1111/j.1600-0870.1984.tb00221.x
  • References (15)
    15 references, page 1 of 2

    Errico, R. M. 1982a. Normal mode initializationand the generation of gravity waves by quasi-geostrophic forcing. J. Atmos. Sci. 39,573-586.

    Errico. R. M. 1982b. The strong e k t s of non-quasigeostrophicdynamic processes on atmospheric energy spectra. J. Atmos. Sci. 39.96 1-986.

    Fox, D. 0.and Orszag, S. A. 1973. Invisciddynamicsof two-dimensional turbulence. Phys. Fluidr 16, 169- 171.

    Frederiksen, J. S. 1981. Scale selection and energy spectra of disturbancesin Southern Hemisphereflows. J. Aimos. Sci. 38,2573-2584.

    Frederiksen. J. S. and Sawford, B. L. 1980. Statistical dynamics of two-dimensional invisc4d flow on a sphere. J. Atmos. Sci. 37,7 17-732.

    Haltiner. G. J. 1971. Numerical weatherprediction. New York: John Wiley & Sons, 3I7 pp.

    Hoskins, B. J. and Bretherton, F. P. 1972. Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci. 29, 11-37.

    Kasahara, A. and Puri, K. 1981. Spectralrepresentation of three-dimensional global data by expansion in normal mode functions. Mon. Weu. Reu. 109.37-5 1.

    Kraichnan, R. H. 1967. Inertial ranges in twodimensionalturbulence. Phys. Fluids 10.14 17- 1423.

    Leith, C. E. 1980. Nonlinear normal mode initialization and quasi-geostrophic theory. J. Armos. Scf. 37, 958-968.

  • Metrics
    No metrics available
Share - Bookmark