On the basis of Arnold's construction of a generalized rigid body [2,3] and its extensins to the case of motionin external forcing fields [4,5],te equations of motion of a heavy top in the field of Coriolis forces are interpreted as a model for a baroclinic flow of a rotating fluid in the gravity field.I the absence of gravity,the equations of motion are interpreed as a model for a barotropic flow of a rotating fluid.The two models possess the fundamental properties f symmetry of hydrodynamic equations and describe the motions of weakly stratified and homogeneous fluids within a rotating ellipsoid,respectively,on the class of spatially linear velocity(and temperature in the presence of stratification)fields.If the Rossby number is small,the barotropic model describes slow precessions of the top in the direction opposite to the general rotation,which can be regarded as mecanical prototypes of planetary waves,and the projection of kinetic moment along the direction of general rotation remains invariant accurate to the square of the Rossby number,much as the vertical vorticity of global barotropic geophysical flows with compressibility disregarded is a Lagrange invariant with the same accuracy.The quasi-geostrophic approximation constructed for the baroclinic model strictly by the procedure used in geophysical fluid dynamics coincides with the Euler equations of gyroscope fre motion in which the vertical vorticity and the thermal-wind components are dependent variables,and the vertical-stratification parameter appears in these equations as a specified quantity.A comparison between numerical solutions of the quasi-geostrophic and starting model equations gives the impression that a slow quasi-geostrophic manifold of the equations of motion of a heavy top consists of closed"two-sided mirror" surfaces fromwhich thephase trajectories of the unreduced model are reflected,and this manifold remains so even whenthe motionis no longer quasigeostrophic.It is shown that there is a the shold initial negative value of the stratification parameter beginning at which ageostrophic motion becomes stochastic.
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