We revisit the balanced, axisymmetric dynamics of concentric eyewalls using an analytical solution of the transverse circulation equation that is derived for an idealized five-region model containing an eye, inner eyewall, moat, outer eyewall, and far-field. Incorporating data from Hurricane Frances (2004), the model solution provides a partial dynamical explanation of how an eyewall replacement cycle can act as a temporary brake on rapid intensification of a tropical cyclone. Our idealized results do not support the hypothesis that the inner eyewall collapses as a direct result of subsidence from the outer eyewall. However, these solutions illustrate how the diabatic heating in the inner eyewall, imbedded in a region of high inertial stability, induces larger temperature tendencies than the diabatic heating in the outer eyewall, which borders the far-field region of low inertial stability. Thus, as the inner eyewall dies, the storm temporarily loses its ability to produce an intense, localized warm region. This ability is restored during the contraction and intensification of the outer eyewall. Finally, this simple model suggests both subsidence and warming temperatures in the moat are strongly controlled by the enhanced inertial stability associated with a strengthening outer eyewall. Consequently, the moat is expected to quickly acquire eye-like characteristics as a secondary eyewall begins to form. These results are compared with more realistic axisymmetric and 3D cloud-resolving, nonhydrostatic simulations of tropical cyclones with concentric eyewalls.