Eyewall replacement cycle (ERC) is frequently observed during the evolution of intensifying Tropical Cyclones (TCs). Although intensely studied in recent years, the underlying mechanisms of ERC are still poorly understood, and the forecast of ERC remains a great challenge. To advance our understanding of ERC and provide insights in improvement of numerical forecast of ERC, a series of numerical simulations is performed to investigate ERCs in TC-like vortices on a f-plane. The simulated ERCs possess key features similar to those observed in real TCs including the formation of a secondary tangential wind maximum associated with the outer eyewall. The Sawyer-Eliassen equation and tangential momentum budget analyses are performed to diagnose the mechanisms underlying the secondary eyewall formation (SEF) and ERC. Our diagnoses reveal crucial roles of outer rainband heating in governing the formation and development of the secondary tangential wind maximum and demonstrate that the outer rainband convection must reach a critical strength relative to the eyewall before SEF and the subsequent ERC can occur. A positive feedback among low-level convection, acceleration of tangential winds in the boundary layer, and surface evaporation that leads to the development of ERC and a mechanism for the demise of inner eyewall that involves interaction between the transverse circulations induced by eyewall and outer rainband convection are proposed. The tangential momentum budget indicates that the net tendency of tangential wind is a small residual resultant from a large cancellation between tendencies induced by the resolved and sub-grid scale (SGS) processes. The large SGS contribution to the tangential wind budget explains different characteristics of ERC shown in previous numerical studies and poses a great challenge for a timely correct forecast of ERC. The sensitivity experiments show that ERCs are strongly subjected to model physics, vortex radial structure and background wind. The impact of model physics on ERC can be well understood with the interaction among eyewall/outer rainband heating, radilal inflow in the boundary layer, surface layer turbulent processes, and shallow convection in the moat. However, further investigations are needed to fully understand the exhibited sensitivities of ERC to vortex radial structure and background wind.
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