  The instability of non-homoentropic axisymmetric flow of perfect fluid with
respect to non-axisymmetric infinitesimal perturbations was investigated by
numerical integration of hydrodynamical differential equations in
two-dimensional approximation. The non-trivial influence of entropy gradient on
unstable sound and surface gravity waves was revealed. In particular, both
decrease and growth of entropy against the direction of effective gravitational
acceleration $g_{eff}$ give rise to growing surface gravity modes which are
stable with the same parameters in the case of homoentropic flow. At the same
time increment of sound modes either grows monotonically while the rate of
entropy decrease against $g_{eff}$ gets higher or vanishes at some values of
positive and negative entropy gradient in the basic flow. The calculations have
showed also that growing internal gravity modes appear only in the flow
unstable to axisymmetric perturbations. At last, the analysis of boundary
problem with free boundaries uncovered that's incorrect to set the entropy
distribution according to polytropic law with polytropic index different from
adiabatic value, since in this case perturbations don't satisfy the free
boundary conditions.
