The motion of Lagrangian particles launched on a geopotential surface of a rotating sphere (e.g. weather balloons in the Atmosphere) where the latter is zonally perturbed by some traveling pressure wave (e.g. tidal waves) is studied. The motion of these particles is described by a near integrable, two-degrees-of-freedom Hamiltonian system. The standard instability mechanisms which are known to exist in such systems, such as homoclinic chaos, cannot explain some of the findings of field experiments; There, it is observed that the averaged poleward velocity of high altitude weather balloons may, on rare occasions, be much higher than the observed averaged poleward winds, while their eastward velocity is much slower than the observed averaged eastward winds. Analyzing the structure of the energy surfaces of the integrable system reveals that it possesses a degenerate form of a parabolic-resonance instability whose dynamics is in accordance with the field experiments observations.
The study of this particular model lead to general results regarding the appearance of parabolic resonant tori and other degeneracies in degrees of freedom near-integrable systems. The basic ideas of this theory will be presented in the 2 d.o.f. context.
Collaborators: N. Paldor, Y. Dvorkin, A. Litvak-Hinnenzon.