On the Dynamical and Thermodynamic Constraints of Axisymmetric Tropical Cyclones under Non-Symmetric-Neutrality

Abstract

The potential intensity (PI) theory of tropical cyclones (TCs) provides a reasonable estimate of the steady-state intensity in a quiescent environment. The theory relies on the symmetric neutrality (SN) assumption, where absolute angular momentum (M) surfaces are parallel to the saturation entropy (s*) surfaces within the eyewall above the boundary layer. However, existing theories do not explain how these variables constrain the vortex structure and maximum tangential wind (vmax) under non-symmetric neutrality (non-SN) conditions. This study relaxes the SN assumption to derive a generalized vmax formula that summarizes the dynamical and thermodynamic constraints on the vortex structure and intensity under non-SN conditions. It is proven that under non-SN conditions, the gradient of s* with respect to M holding temperature (T) constant constrains the curvature of the M surfaces throughout the saturated eyewall, thereby determining the balanced intensity above the TC boundary layer. In addition, generalized expressions for the unbalanced and frictional contributions to vmax are also derived. Verifying against axisymmetric simulations, this generalized formula accurately quantifies the balanced, unbalanced, and frictional contributions during the rapid intensification (RI). Despite being diagnostic, it offers valuable insights into TC intensification under non-SN conditions: (1) before reaching SN, the s* gradient should be computed holding T fixed to quantify the balanced wind component. (2) During TC intensification, the s* gradient distinctly increases with height along the eyewall updraft, confirming that SN assumption is not valid during RI. The implications of these findings on the vortex structure and the upper-tropospheric mixing during RI are examined.