Exact and numerical similarity solutions for compressible perturbations to an incompressible,
two-dimensional, axisymmetric vortex reference flow are presented. The
reference flow consists of a set of two-dimensional, self-similar, incompressible vortices.
Similarity variables, which give explicit expressions for the decay rates of the
velocities and thermodynamic variables in the vortex flows, are used to reduce the
governing partial differential equations to a set of ordinary differential equations. The
ODEs are solved analytically and numerically for a Taylor vortex reference flow, and
numerically for an Oseen vortex reference flow. The solutions are employed to study
the dependences of the temperature, density, entropy, dissipation and radial velocity
on the Prandtl number. Additionally, several integral relations, which allow one to
trace the energy transfer in a slightly compressible vortex, are derived.