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The hydrodynamic stability of accretion disks is considered. The particularquestion is whether the combined action of a (stable) vertical densitystratification and a (stable) radial differential rotation gives rise to a newinstability for nonaxisymmetric modes of disturbances. The existence of such aninstability is not suggested by the well-known Solberg-Hoiland criterion. It isalso not suggested by a local analysis for disturbances in generalstratifications of entropy and angular momentum which is presented in ourSection 2 confirming the results of the Solberg-Hoiland criterion also fornonaxisymmetric modes within the frame of ideal hydrodynamics but only in theframe of a short-wave approximation for small m. As a necessary condition forstability we find that only conservative external forces are allowed toinfluence the stable disk. As magnetic forces are never conservative, lineardisk instabilities should only exist in the magnetohydrodynamical regime whichindeed contains the magnetorotational instability as a much-promisingcandidate. To overcome some of the used approximations in a numericalapproach,the equations of the compressible adiabatic hydrodynamics areintegrated imposing initial nonaxisymmetric velocity perturbations with m=1 tom=200.  Only solutions with decaying kinetic energy are found. The system alwayssettles in a vertical equilibrium stratification according to pressure balancewith the gravitational potential of the central object. keywords: accretiondisks -- hydrodynamic instabilities -- turbulenceComment: 6 pages, 4 figures, 1 table, Astronomy and Astrophysics (subm.

Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification