Flame propagation into a swirling flow allows the creation of burnt gas vorticity which may enhance the forward motion of the flame. This baroclinic push on the dame differs from the axial pressure model suggested by Chomiak (1976). In particular, the baroclinic enhancement will depend upon the location of the burnt gas with respect to the flame, as shown by two Vortex configurations: straight and curved. Additionally, the baroclinic effect, depending upon the flame density gradient and the swirling dow radial pressure gradient, will provide an enhancement that is proportional to the ambient pressure.