The persistence of a tropical cyclone seed vortex depends on its structure

Tropical cyclones (TC) are often generated from pre-existing ``seed" vortices. Seeds with higher persistence might have a higher chance to undergo TC genesis. What controls seed persistence remains unclear. This study proposes that planetary Rossby wave drag is a key factor that affects seed persistence. Using recently developed theory for the response of a vortex to the planetary vorticity gradient, a new parameter given by the ratio of the maximum wind speed ($V_{max}$) to the Rhines speed at the radius of maximum wind ($R_{max}$), here termed ``vortex compactness" ($C_v$), is introduced to characterize the vortex weakening by planetary Rossby wave drag. The relationship between vortex compactness and weakening rate is tested via barotropic $\beta$-plane experiments. The vortex's initial $C_v$ is varied by systematically varying their initial $V_{max}$ and $R_{max}$ in idealized wind profile models. Experiments using vorticity distributions from real-world seeds possessing are also taken from reanalysis. The weakening rate depends strongly on the vortex's initial $C_v$ across both idealized and real-world experiments, and the asymmetry introduces minor differences. Experiments doubling the size of seed vortices cause them to weaken more rapidly in line with other experiment sets. The dependence of the weakening rate on initial compactness can be predicted from a simple theory, which is more robust for more compact vortices. Our results suggest that a seed's structure strongly modulates how long it can persist in the presence of a planetary vorticity gradient. Connections to real seeds on Earth are discussed.