Universal Scaling of Tangential Wind Fields in Axisymmetric Tropical Cyclone Vortices: Empirical Evidence for V²R Conservation

Imagine tropical cyclones (TCs) as the most perfectly structured and dynamically powerful rotating vortex systems at the interface of Earth’s oceans and atmosphere—much like celestial planets in the sky, they exhibit extraordinary structural order and hidden dynamical laws. For decades, scientists have relied on the modified Rankine (mRankine) vortex model to parameterize TC wind fields, yet the critical decay parameter α has remained purely empirical, with no clear underlying physical constraints. Our global observational analysis of nearly circular TCs finally unlocks this mystery: we reveal that the primary circulation region of these storms strictly adheres to a V²R conservation law—where V is the tangential wind speed and R is the radial distance from the storm center. Analyzing 59 observational data points across multiple ocean basins—the Western North Pacific, Atlantic, and South Pacific—we find that V²R remains nearly invariant across 64 kt, 50 kt, and 34 kt wind radii at identical observation times. Statistical validation confirms this robustness with an overall standard deviation of just 6.6%. From this conservation law, we further derive a fundamental mathematical relation: R³/T² = K (a constant), where R is the rotational radius and T is the rotation period. This striking parallel to Kepler’s third law of planetary motion hints at an inherent dynamical symmetry within stable TC vortices. Our findings not only resolve the long-standing enigma of the empirical decay parameter α but also lay a new theoretical foundation for vortex dynamics and wind field modeling, offering fresh insights into the fundamental laws governing these "planets of the atmosphere."