AbstractA mechanistic axisymmetric Eliassen balanced vortex model is presented for the investigation of the role of diabatic heating in the dynamic evolution of a cut‐off cyclone and the related stratosphere‐troposphere exchange. As an initial state, a balanced upper‐level vortex is chosen representing an idealized cut‐off cyclone. After specifying a diabatic heating field, which is supposed to simulate latent heat release in deep convection, one can diagnose the induced cross‐vortex circulation and calculate the ensuing vortex evolution. Tropospheric heating with a maximum of some 10 K d−1underneath the lowered tropopause leads to the decay of the upper‐level vortex within a few days. During the decay there is a sizeable, diabatically induced mass flux across the PV‐defined tropopause: air in the vortex centre which initially was part of the lower stratosphere gradually turns into tropospheric air. This stratosphere‐troposphere exchange depends sensitively on the heating profile around the tropopause level and, hence, on the maximum height reached by the convection. The inclusion of diabatic cooling to account for the effect of radiation at cloud tops leaves the vortex evolution almost unchanged but increases the rate of stratosphere‐troposphere exchange dramatically. Cross‐isentropic mixing alone may result in strengthening rather than in weakening the vortex thus re‐emphasizing the role of diabat