AUTHOR=Schubert Wayne H. , Taft Richard K. , Slocum Christopher J. 

TITLE=Baroclinic effects on the distribution of tropical cyclone eye subsidence

JOURNAL=Frontiers in Earth Science

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2022.1062465

DOI=10.3389/feart.2022.1062465

ISSN=2296-6463

ABSTRACT=<p>Solutions of the secondary (transverse) circulation equation for an axisymmetric, gradient balanced vortex are used to better understand the distribution of subsidence in the eye of a tropical cyclone. This secondary circulation equation is derived using both the physical radius coordinate <italic>r</italic> and the potential radius coordinate <italic>R</italic>. In the <italic>R</italic>-coordinate version, baroclinic effects are implicit in the coordinate transformation and are recovered in the final step of transforming the solution for the streamfunction Ψ back from <italic>R</italic>-space to <italic>r</italic>-space. Two types of elliptic problems for Ψ are formulated: 1) the full secondary circulation problem, which is formulated on 0 ≤ <italic>R</italic> &lt; <italic>∞</italic>, with the diabatic forcing due to eyewall convection appearing on the right-hand side of the elliptic equation; 2) the restricted secondary circulation problem, which is formulated on 0 ≤ <italic>R</italic> ≤ <italic>R</italic><sub>ew</sub>, where the constant <italic>R</italic><sub>ew</sub> is the potential radius of the inside edge of the eyewall, with no diabatic forcing but with the streamfunction specified along <italic>R</italic> = <italic>R</italic><sub>ew</sub>. The restricted secondary circulation problem can be solved semi-analytically for the case of vertically sheared, Rankine vortex cores. The solutions identify the conditions under which large values of radial and vertical advection of <italic>θ</italic> are located in the lower troposphere at the outer edge of the eye, thereby producing a warm-ring thermal structure.</p>