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Abstract: The question is addressed whether stellar differentially rotating radiativezones like the solar tachocline excite nonaxisymmetric r-modes which can beobserved. To this end the hydrodynamical stability of latitudinal differentialrotation is studied. The amount of rotational shear required for theinstability is estimated in dependence of the character of radialstratification and the flow patterns excited by the instability are found. Theeigenvalue equations for the nonaxisymmetric disturbances are formulated in 3Dand then solved numerically. Radial displacements and entropy disturbances areincluded. The equations contain the 2D approximation of strictly horizontaldisplacements as a special limit. The critical magnitude of the latitudinaldifferential rotation for onset of the instability is considerably reduced inthe 3D theory compared to the 2D approximation. The instability requires asubadiabatic stratification. It does not exist in the bulk of convection zonewith almost adiabatic stratification but may switch on near its base in theregion of penetrative convection. Growth rates and symmetry types of the modesare computed in dependence on the rotation law parameters. The S1 mode with itstransequatorial toroidal vortices is predicted as the dominating instabilitymode. The vortices show longitudinal drift rates retrograde to the basicrotation which are close to that of the observed weak r-mode signatures at thesolar surface.

Autor: L.L. Kitchatinov, G. Rüdiger


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