To understand the basic mechanism governing the size evolution of tropical cyclones (TCs), we systematically perform numerical experiments using the primitive equation system on an f-plane. A simplified, TC-like vortex is initially given and an external forcing mimicking cumulus heating is applied to an annular region at a prescribed distance from the vortex center. Moist process and surface friction are excluded for simplification. We focus on the sensitivity of size evolution to the location of the forcing. The vortex size is defined as the radius of 15 m s–1 lowest-level wind speed (R15). The evolution of R15 depends on the forcing location, and its dependence can be understood by considering radial transport of the absolute angular momentum (AAM) at R15 due to the heat-induced secondary circulation (SC), whose structure is governed by the distribution of inertial stability. When the forcing is applied to the outer part of a vortex but still inside R15, where inertial stability is weak, the SC extends to the outside of R15 and carries AAM inward. Thus, R15 increases. Conversely, when the forcing is applied near the center of the vortex, where inertial stability is strong, the SC closes inside R15 and R15 hardly increases. These results indicate that extension of the heat-induced SC to the outside of R15 is important for the evolution of the vortex size. Moreover, the further beyond R15 the SC extends, the more the vortex size increases. This relationship is consistent with the result of the parcel trajectory analysis; the larger the extent of SC, the longer distances the parcels cover, conserving larger AAM. Finally, when the forcing is applied to the outside of R15, smaller AAM is carried outward by the SC on the inward side of the heating location, resulting in the decrease of R15.
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