A storm-relative annular potential-vorticity-gradient gate for early typhoon rapid intensification

Rapid intensification (RI) remains difficult to predict because favorable large-scale and oceanic conditions do not identify where the storm inner core becomes dynamically receptive to rapid strengthening. Here we test a narrower hypothesis: that a storm-relative annulus near the radius of maximum wind acts as a gate for early RI. Starting from an unequal-depth two-layer quasi-geostrophic model, we derive coupled barotropic--baroclinic nonlinear Schr\"odinger equations in which the effective radial potential-vorticity gradient $P_e$ controls both dispersion and focusing: dispersion scales with $P_e$, self-focusing with $1/P_e$, and a threshold $P_e<P_c(H_0,\tau_h)$ depends jointly on lower-layer enthalpy forcing and residence time. We then invert the framework with raw ERA5 in storm-relative coordinates for Rai, Hinnamnor, and Mawar and summarize 33 supported western North Pacific RI cases from 2018 to 2023. Across these cases, weakly positive annular gate states are common during RI windows, whereas energetic response varies widely and is strongest where the flattened gate coincides with finite lower-layer enthalpy forcing and resolved baroclinic contrast. The combined theory and reanalysis therefore support a restrained conclusion: a weakly positive annular PV-gradient state appears to be permissive, but not sufficient, for early RI onset.