Intensification of Supertyphoon Hagibis (2019) with Concentric Eyewall Formation as Explored by the Extended Sawyer–Eliassen Equation

Abstract This study utilizes the extended Sawyer–Eliassen (SE) equation, which relaxes the thermal wind balance, to investigate the capability of the unbalanced SE solution in depicting the intensification of Supertyphoon Hagibis (2019) as simulated by a high-resolution Weather Research and Forecasting (WRF) Model. The nonlinear simulation successfully reproduces the rapid intensification (RI) and then weakening associated with the secondary eyewall formation (SEF). The analysis results show that the unbalanced SE solution captures most features of the transverse circulation of the nonlinear simulation at both stages, thus producing the vortex intensification similar to the actual nonlinear simulation. The induced RI of the lower-tropospheric vortex is attributed to significantly stronger spinup by the mean radial advection (MRA) in the boundary layer and moderate spinup by both mean vertical advection (MVA) and eddy vertical advection (EVA) above. The progressive SEF from the RI stage to the weakening stage may speed up by the virtue of a vertical connection of the spinup by MRA in the boundary layer and the spinup by MVA above the boundary layer, as illustrated by the unbalanced SE solution and nonlinear simulation. However, asymmetric eddy advection only gives secondary contributions to the SEF, as compared to the mean advection mainly induced by diabatic heating. The SEF well coincides with the developing supergradient force in the lower troposphere above the upper boundary layer. The impact of the residual in the tangential velocity tendency equation on the unbalanced SE solution is also investigated. Both solutions with and without this residual produce similar features of the transverse circulation; however, the former can improve the detailed variations of the vortex intensification.