Centrifugal instability of compressible flows and the hydrodynamic stability of accretion disks

Abstract: A recent analysis of the centrifugal instability in the case of pressure-supported compressible relativistic rotation, with application to astrophysical jets, yielded a generalisation of the famous Rayleigh criterion for Newtonian flows. According to this criterion, the centrifugal instability is strongly affected by the flow Mach number, and not only in the relativistic fluid dynamics but also in its Newtonian limit. To validate the Newtonian version of this criterion, we performed axisymmetric numerical simulations of non-relativistic transonic rotating flows which are stable according to the original Rayleigh criterion but can be either stable or unstable according to the new one. The results of computer simulations are found to be in perfect agreement with the theory. The hydrodynamic stability of accretion disks is often explained by referring to the original Rayleigh criterion, even if their rotation is highly supersonic. To clarify the matter, we analysed the hydrodynamic stability of flows rotating about central compact object and derived an instability criterion that retains the explicit dependence on the flow Mach number. This criterion turns out to be equivalent to the standard Solberg-Høiland criterion, which does not involve the Mach number. The same applies to the case of pressure-supported rotation, where the role of gravity is played by the centrifugal force.