This paper presents a simple theoretical argument to isolate the conditions under which a tropical cyclone can rapidly develop a warm-core thermal structure and subsequently approach a steady state. The theoretical argument is based on the balanced vortex model and, in particular, on the associated transverse circulation equation and the geopotential tendency equation. These second-order partial differential equations contain the diabatic forcing and three spatially varying coefficients: the static stability A, the baroclinity B, and the inertial stability C. Thus, the transverse circulation and the temperature tendency in a tropical vortex depend not only on the diabatic forcing but also on the spatial distributions of A, B, and C. Experience shows that the large radial variations of C are typically the most important effect. Under certain simplifying assumptions as to the vertical structure of the diabatic forcing and the spatial variability of A, B, and C, the transverse circulation equation and the geopotential tendency equation can be solved via separation of variables. The resulting radial structure equations retain the dynamically important radial variation of C and can be solved in terms of Green’s functions. These analytical solutions show that the vortex response to a delta function in the diabatic heating depends critically on whether the heating occurs in the low-inertial-stability region outside the radius of maximum wind or in the high-inertial-stability region inside the radius of maximum wind. This result suggests that rapid intensification is favored for storms that have at least some of the eyewall convection inside the radius of maximum wind. The development of an eye partially removes diabatic heating from the high-inertial-stability region of the storm center; however, rapid intensification may continue if the eyewall heating continues to become more efficient. As the warm core matures and static stability increases over the inner core, conditions there become less favorable for deep upright convection and the storm tends to approach a steady state.

Two hurricane eye features that have yet to be adequately explained are the clear-air moat that forms at the outer edge of the eye and the hub cloud that forms near the circulation centre. To investigate whether these features can be explained by the spatial distribution of the subsidence field, we have derived an analytical solution of the Sawyer-Eliassen transverse circulation equation for a three-region approximation with an unforced central eye region of intermediate or high inertial stability, a diabatically-forced eyewall region of high inertial stability, and an unforced far-field of low inertial stability. This analytical solution isolates the conditions under which the subsidence is concentrated near the edge of the eye. The crucial parameter is the dimensionless dynamical radius of the eye, defined as the physical radius of the eye divided by the characteristic Rossby length in the eye. When this dimensionless dynamical radius is less than 0.6, there is less than 10% horizontal variation in the subsidence rate across the eye; when it is greater than 1.8, the subsidence rate at the edge of the eye is more than twice as strong as at the centre of the eye. When subsidence is concentrated at the edge of the eye, the largest temperature anomalies occur near there rather than at the vortex centre. This warm-ring structure, as opposed to a warm-core structure, is often observed in the lower troposphere of intense hurricanes.

In the widely accepted convective ring model of tropical cyclone intensification, the intensification of the maximum winds and the contraction of the radius of maximum winds (RMW) occur simultaneously. This study shows that in idealized numerical simulations, contraction and intensification commence at the same time, but that contraction ceases long before peak intensity is achieved. The rate of contraction decreases with increasing initial size, while the rate of intensification does not vary systematically with initial size. Utilizing a diagnostic expression for the rate of contraction, it is shown that contraction is halted in association with a rapid increase in the sharpness of the tangential wind profile near the RMW and is not due to changes in the radial gradient of the tangential wind tendency. It is shown that a number of real storms exhibit a relationship between contraction and intensification that is similar to what is seen in the idealized simulations. In particular, the statistical distribution of intensifying tropical cyclones indicates that, for major hurricanes, most contraction is completed prior to most intensification.By forcing a linearized vortex model with the diabatic heating and frictional tendencies from a simulation, it is possible to qualitatively reproduce the simulated secondary circulation and separately examine the vortex responses to heating and friction. It is shown that heating and friction both contribute substantially to boundary layer inflow. They also both contribute to the contraction of the RMW, as the positive wind tendency from heating-induced inflow is maximized inside of the RMW, while the net negative wind tendency from friction and frictionally induced inflow is maximized outside of the RMW.

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This study seeks to reconcile discrepancies between previous studies analyzing the relationship between lightning and tropical cyclone (TC) intensity change. Inner-core lightning bursts (ICLBs) were identified from 2005 to 2014 in North Atlantic (NA) and eastern North Pacific (ENP) TCs embedded in favorable environments (e.g., vertical wind shear ≤ 10 m s−1; sea surface temperatures ≥ 26.5°C) using data from the World Wide Lightning Location Network (WWLLN) transformed onto a regular grid with 8-km grid spacing to replicate the expected nadir resolution of the Geostationary Lightning Mapper (GLM). Three hypothesized factors that could impact the 24-h intensity change after a burst were tested: 1) prior intensity change, 2) azimuthal burst location, and 3) radial burst location. Most ICLBs occurred in weak TCs (tropical depressions and tropical storms), and most TCs intensified (remained steady) 24 h after burst onset in the NA (ENP). TCs were more likely to intensify 24 h after an ICLB if they were steady or intensifying prior to burst onset. Azimuthally, 75% of the ICLBs initiated downshear, with 92% of downshear bursts occurring in TCs that remained steady or intensified. Of the ICLBs that initiated or rotated upshear, 2–3 times more were associated with TC intensification than weakening, consistent with recent studies finding more symmetric convection in intensifying TCs. The radial burst location relative to the radius of maximum wind (RMW) provided the most promising result: TCs with an ICLB inside (outside) the RMW were associated with intensification (weakening).