In this first part of a two-part study, the mechanisms that accomplish the warming in the eye of tropical cyclones are investigated through a potential temperature budget analysis of an idealized simulation. The spatial structure of warming varies substantially with time. During rapid intensification (RI), the warming is maximized at midlevels, and as a consequence, the perturbation temperature is always maximized in this region. At the start of RI, total advection of potential temperature is the only significant term contributing to warming the eye. However, for a substantial portion of RI, the region of most rapid warming actually undergoes mean ascent. The net advective warming is shown to be a result of eddy radial advection of potential temperature, dominated by a wavenumber~(-1) feature that is likely due to a dynamic instability. At a sufficient intensity, mean vertical advective warming becomes concentrated in a narrow zone just inward of the eyewall. In agreement with prior studies, this advective tendency is largely canceled by diabatic cooling. Subgrid-scale horizontal diffusion of potential temperature plays a surprisingly large role in the maintenance of the warmcore structure, and when the storm is intense, yields a negative tendency that can be of the same magnitude as advective warming.
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