Motion of Barotropic and Baroclinic Tops as Mechanical Prototypes for the General Circulation of Barotropic and Baroclinic Inviscid Atmospheres

  • Felix V. Dolzhansky
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 103)


Given the dual interpretation of the equations of motion of a rigid body with a fixed point, these precessions of a barotropic top can be regarded as a mechanical prototype of the process of propagation of planetary waves that carry away the angular momentum of the atmosphere in the direction opposite to the Earth’s rotation. In turn, the approximate invariance of the projection of its angular momentum to the direction of m 0 can be thought of as a mechanical prototype of the approximate Lagrangian invariance of the vertical vorticity of global atmospheric movements, expressed by the Obukhov–Charney equation.


Angular Momentum Phase Portrait Rossby Wave Planetary Wave Slow Manifold 
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  1. F.V. Dolzhansky and V.M. Ponomarev, The simplest slow manifolds of barotropic and baroclinic motions of a rotating fluid, Izv. RAN, Ser. FAO, Vol. 38, 2002. Google Scholar
  2. F.V. Dolzhansky, On the mechanical prototypes of the fundamental hydrodynamic invariants and slow manifolds, UFN, Vol. 175, No. 12, 2005. Google Scholar
  3. E.B. Gledzer, F.V. Dolzhansky, and A.M. Obukhov, Systems of Hydrodynamical Type and Their Applications, Nauka, Moscow, 1981 Google Scholar
  4. A.E. Gledzer, On slow motions in the reduced equations of a stratified fluid in a Coriolis force field, Izv. RAN Ser. FAO, Vol. 39, No. 6, 2003. Google Scholar
  5. A.E. Gledzer et al., The Hadley and Rossby regimes in the simplest convection model of a rotating fluid, Izv. RAN, Ser. FAO, Vol. 42, No. 3, 2006. Google Scholar
  6. A.B. Glukhovsky and F.V. Dolzhansky, Three-mode geostrophical convection models of a rotating fluid, Izv. Academy of Sciences USSR, Ser. FAO, Vol. 16, No. 5, 1980. Google Scholar
  7. E.N. Lorenz, Attractor sets and quasi-geostrophic equilibrium, J. Atm. Sci. Vol. 37, pp. 1685, 1980. MathSciNetCrossRefGoogle Scholar
  8. E.N. Lorenz, On the existence of a slow manifold, J. Atm Sci. Vol. 43, pp. 1547, 1986. MathSciNetCrossRefGoogle Scholar
  9. E.N. Lorenz and V.J. Krishnamurthy, On the nonexistence of a slow manifold, J. Atm. Sci., Vol. 44, No. 20, 1987. Google Scholar
  10. A.M. Obukhov, On the geostrophic wind, Izv. Acad. Sci. USSR, Vol. 13, No. 4, 1949. (Reprinted in the book. Obukhov, A.M. Turbulence and the atmosphere dynamics, Gidrometeoizdat, Leningrad, 1988). Google Scholar
  11. J. Pedlosky, Geophysical Fluid Dynamics, Part II, Springer, Berlin, 1987 CrossRefGoogle Scholar
  12. S.L. Ziglin, Proc. Mosk. Math. Society, Vol. 41, 1980. Google Scholar

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Authors and Affiliations

  • Felix V. Dolzhansky
    • 1
  1. 1.

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