Modeling Tropical Cyclone Rapid Intensification via the AMDCF Memory-Driven Flux Law

This paper presents a novel climatological application of the Adaptive Memory-Driven Coupling Framework (AMDCF). We adapt the AMDCF Turbulence Flux Law to model the radial dynamics of tropical cyclones. By introducing a non-Markovian memory kernel to represent ocean heat content and an adaptive diffusion term to simulate the formation of the hurricane eyewall, we successfully reproduce the "Rapid Intensification" (RI) phase. The simulation quantitatively captures the sudden surge in peak vortex intensity when thermal forcing is applied, while the dynamic safety valve ensures numerical stability during extreme wind bursts. The spatiotemporal flux maps reveal the characteristic anatomy of a hurricane: the calm eye, the highly energetic eyewall, and the dissipating outer bands. This framework provides a new mathematical foundation for early-warning systems and climate modeling.