The Roles of an Expanding Wind Field and Inertial Stability in Tropical Cyclone Secondary Eyewall Formation

The Weather and Research and Forecasting Model (WRF) is used to simulate secondary eyewall formation (SEF) in a tropical cyclone (TC) on the β plane. The simulated SEF process is accompanied by an outward expansion of kinetic energy and the TC warm core. An absolute angular momentum budget demonstrates that this outward expansion is predominantly a symmetric response to the azimuthal-mean and wavenumber-1 components of the transverse circulation. As the kinetic energy expands outward, the kinetic energy efficiency in which latent heating can be retained as local kinetic energy increases near the developing outer eyewall. The kinetic energy efficiency associated with SEF is examined further using a symmetric linearized, nonhydrostatic vortex model that is configured as a balanced vortex model. Given the symmetric tangential wind and temperature structure from WRF, which is close to a state of thermal wind balance above the boundary layer, the idealized model provides the transverse circulation associated with the symmetric latent heating and friction prescribed from WRF. In a number of ways, this vortex response matches the azimuthal-mean secondary circulation in WRF. These calculations suggest that sustained azimuthal-mean latent heating outside of the primary eyewall will eventually lead to SEF. Sensitivity experiments with the balanced vortex model show that, for a fixed amount of heating, SEF is facilitated by a broadening TC wind field.