Towards Relaxing the Symmetric Neutrality Assumption of the Potential Intensity Theory of Tropical Cyclones

The potential intensity (PI) theory of tropical cyclones (TCs) provides a reasonable estimate of the maximum intensity that a TC can achieve in a quiescent environment. The traditional PI theory relies on the symmetric neutrality assumption, where the isolines of absolute angular momentum (M) are parallel to the saturation entropy (s*) surfaces within the eyewall updraft. However, there is currently no quantitative theory that describes how these surfaces directly relate to the maximum tangential wind (v_max) near the surface when the symmetric neutrality is not valid.

In this study, I revisited the PI theory without making the symmetric neutrality assumption and identified a new equipartition principle between the mechanical and thermal energies of a balanced vortex, which has several important implications on the TC vortex structure. This energetic principle admits a generalized v_max equation, which captures both the balanced and unbalanced components within the TC boundary layer. It is shown that this v_max equation is the natural extension of the traditional PI v_max expression into the non-symmetrically neutral state. Specifically, it explicitly shows how the gradient between s* and M should be computed in order to dynamically link to the balanced v_max component of a non-symmetrically neutral vortex. Verifying against axisymmetric model simulations, it is found that the generalized v_max equation can accurately quantify the contributions of various processes to v_max during the rapid intensification. The implications of these findings on the TC intensification, such as the TC inner-core structure and the upper-tropospheric mixing, will be discussed.