Antisymmetric polar modes of thermal convection in rotating spherical fluid shells at high taylor numbers.

The onset of thermal convection in a rotating spherical shell of intermediate radius ratio eta=0.4 is studied numerically for Taylor numbers Ta > or = 10(11) and the Prandtl number of the liquid sodium (sigma=0.01). For the first time, it is shown that at very high Taylor numbers the first unstable mode can be antisymmetric with respect to the equator and confined inside a cylinder tangent to the inner sphere at the equator (polar mode). The exponent of the power law determined from the asymptotic dependence of the critical Rayleigh number for very high Ta is 0.57, lower than 2/3, given theoretically for the spiraling columnar modes, and than 0.63, found numerically for the outer equatorially attached modes.