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Unsteady Adjustment Problems

Part of the Lecture Notes in Physics Monographs book series (LNPMGR, volume 5)

Abstract

The basic approximations are formulated with a view to filtering acoustic waves out of the solutions of equations for atmospheric motions, because such waves are of no importance concerning weather prediction. On the other hand, when considering the approximate, simplified set of equations (primitive equations, Boussinesq equations or quasi-geostrophic model equation), one is allowed to specify a set of initial conditions less in number than for the “exact” equations. This is due to the fact that the limiting process which leads to the approximate model, filters out some time derivatives. Due to this one encounters the problem of deciding what initial conditions one may prescribe and in what way these are related to the initial conditions associated with the exact, full, equations? The latter are not in general consistent with the estimates of basic orders of magnitude implied by the asymptotic model. A physical process of time evolution is necessary to bring the initial set to a consistent level as far as the orders of magnitude is concerned. Such a process is called one of ADJUSTMENT of the initial set of data to the asymptotic structure of the model under consideration. The process of adjustment, which occurs in many fields of Fluid Mechanics besides Meteorology, is short on the time scale of the asymptotic model considered, and at the end of it, in an asymptotic sence, we obtain values far the set of initial conditions suitable to the model.

Keywords

Boussinesq Equation Primitive Equation Full Equation Asymptotic Model Geostrophic Balance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Background Reading

  1. Some examples of application of asymptotic techniques to the derivation of models for atmosopheric flows. Mecanique Theorique, Université de Paris 6. (Unpublished manuscript; C.I.S.M, Udine, Italy).Google Scholar

References to Works Cited in the Text

  1. J.Meteorol. 2, 113–119.MathSciNetGoogle Scholar
  2. Theory and Application of the Boltzmann equation. Scottish Academic Press.Google Scholar
  3. Reviews of Geophysics and Space Physics, 10, 485–528.CrossRefADSGoogle Scholar
  4. Geofys. Publikasjoner Norske Videnskaps-Akad. Oslo, 20, 1.Google Scholar
  5. Phys. of Fluids, vol. 12, suppl. II, pp. II, 3–II, 12.ADSGoogle Scholar
  6. The Theory of ratating fluids. Cambridge Univ. PressGoogle Scholar
  7. Tellus, 34, 50–54.ADSCrossRefGoogle Scholar
  8. Geophys. Astrophys. fluid Dynamics 15, 283.zbMATHCrossRefADSGoogle Scholar
  9. DAN SSSR, 104, 60–63 (in Russian).zbMATHMathSciNetGoogle Scholar
  10. An Introduction to the hydrodynamical Method of short period Weather Forecasting, Moscow (in Russian).Google Scholar
  11. C.R.Acad. Sci. Paris, t. 276 A, 759–762 and t. 277 A, 363–366.MathSciNetGoogle Scholar
  12. Izv.Akad.Nauk SSSR, ser. Geofiz. 497.Google Scholar
  13. Prognos pogody kak zadacha fiziki. Izd.Nauka, Moscow (in Russian).Google Scholar
  14. Perturbation methods. John Wiley and Sons.Google Scholar
  15. Izv.Akad.Nauk SSSR, ser. Geogr. i Geofiz., 13, 281.Google Scholar
  16. Correction de Fromm pour les schémas Open image in new windowet applications au phénoméne d’adaptation au quasi-statisme en Météorologie. These de 3e cycle. Université de Paris 6, Mécanique Théorique.Google Scholar
  17. Rev.Geophys., 1,2, 123–176.CrossRefADSGoogle Scholar
  18. Weather Prediction by Numerical Process. Cambridge-reprinted by Dover Publications in 1966.Google Scholar
  19. J.Marine Res. 1, 239–263.Google Scholar
  20. Introduction to the Theory of Fourier integrals. Oxford, Clarendon Press.Google Scholar
  21. VAN DYKE, M. (1962) _ Perturbation methods in Fluid Mechanics. Academic Press, N-Y.Google Scholar
  22. Deep-Sea Res., 3, no3, 157.CrossRefGoogle Scholar
  23. C.R.Acad.Sci., Paris, t.299, I, no20, 1033–36.zbMATHMathSciNetGoogle Scholar
  24. Asymptotic modeling of Atmospheric Flows. Springer-Verlag, Heidelberg.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

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