Critical Saturation Dynamics and Scaling Laws in Tropical Cyclones

We propose a nonlinear saturation model for tropical cyclone intensification based on a reaction–diffusion critical dynamics framework. The model describes hurricane evolution through an effective scalar field χ(x, t) representing convective saturation density. The resulting dynamics naturally produces threshold behavior, rapid intensification, finite saturation, and scaling laws for maximum wind velocity. Near the critical sea-surface temperature threshold Tc, the model predicts a universal scaling relation Vmax ∼ (Ts − Tc) β with critical exponent β = 12 . This exponent matches the scaling structure appearing in thermodynamic maximum potential intensity theories and suggests that tropical cyclones may belong to a broader universality class of driven dissipative critical systems. We discuss the physical justification for the energy–saturation coupling, the regime of validity of the near-threshold expansion, and the observational signatures of the predicted scaling law.