Secondary Eyewall Formation in an Idealized Tropical Cyclone Simulation – Further Examination of the Balanced and Unbalanced Dynamics

The secondary eyewall formation (SEF) in an idealized simulation of a tropical cyclone (TC) is examined from the perspective of both the balanced and unbalanced dynamics, and through the tangential wind (Vt) budget analysis. It is found that the expansion of the azimuthal mean Vt above the boundary layer occurs prior to the development of radial moisture convergence in the boundary layer. The Vt expansion results primarily from the inward angular momentum transport by the mid-lower tropospheric inflow induced by stratiform heating in the spiral rainbands. In response to the Vt broadening is the development of radial inflow convergence and the supergradient flow within the boundary layer. Results from the Vt budget analysis show that the combined effect of the mean advection and the surface friction is to spin down Vt in the boundary layer, while the eddy processes (eddy radial and vertical advection) contribute positively to the spin-up of Vt in the SEF region in the boundary layer. Therefore, eddies should play an important role in the spin-up of Vt in the boundary layer during SEF. The balanced Saywer-Eliassen solution can well capture the secondary circulation in the full physics model simulation. The radial inflow diagnosed from the Sawyer-Eliassen equation is shown to spin up Vt and maintain the vortex above the boundary layer. However, the axisymmetric balanced dynamics could not explain the spin-up of Vt in the boundary layer, which results mainly from the eddy processes.