To analyze the flowfield inside the vortex formed at the leading edge of a highly swept wing at an angle of attack, conical similarity solutions of the compressible Euler equations have been obtained and compared to incompressible conical similarity flow solutions. It is shown that, in contrast to the incompressible flow case, the velocity components inside the vortex core remain finite in the interior of the vortex. The compressible and inviscid flow solution exhibits vacuum conditions at the axis of the vortex core. Two different families of solutionshave been numerically obtained, one representing jetlike swirling flows olutions and the other wakelike swirling flow solutions. Considering the flow solutions in more detail reveals that, at the edge of the vortex core, the normal component of the velocity is negative (inflow) for jetlike swirling flows and positive (outflow) for wakelike swirling flows. The velocity and the vorticity vector are parallel for jetlike swirling flows and antiparallel for wakelike swirling flows. Furthermore, the azimuthal component of the vorticity has a different direction for both flow solutions. Varying the boundary conditions, for instance, the swirl number or the Mach number, at the edge of the vortex core does not change the character of the flow solutions significantly.