Lower limit of the radius of maximum winds in a diagnostic model

Lowest eyewall size with eyewall replacement cycle as constraint

Yu Liu ¹, Yanluan Lin¹

¹Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 100084, China

Abstract

This study investigates the constraint on the tropical cyclone inner-core structure imposed by the eyewall replacement cycle using the theoretical model of radial profile of tangential wind established by Chavas et al. (2015) (referred to as C15). Previous studies have emphasized the role of vorticity gradient discontinuity in the boundary layer process of secondary eyewall formation (Huang et al. 2012; Kepert 2013). However, the theoretical determination of the location and magnitude of the vorticity gradient discontinuity remains lacking. In this study, we demonstrate that in the C15 model, the vorticity gradient discontinuity inherently occurs at the connection point, with its magnitude primarily determined by the inner Rossby number. Consequently, our findings suggest that eyewall replacement cycles may impose an upper limit on the inner Rossby number, thereby implying the existence of a lower limit for the eyewall size. Moreover, we highlight the connection point as the most probable location for the formation of secondary eyewall, which provides a partial explanation for the most frequent observation of secondary eyewalls being located near 3 times the size of the primary eyewall. The presence of the connection point serves as a significant structural disparity between the C15 model and the theoretical model proposed by Emanuel and Rotunno (2011) (referred to as ER11). In light of Wang and Lin's (2020) assertion that the ER11 model acts as a prototype for a reversible moist tropical cyclone, the connection point could be regarded as originating from irreversible entropy sources. Thus, we posit a close association between the eyewall replacement cycle and irreversible entropy sources, implying that the occurrence of eyewall replacement cycles is intrinsic for real-world tropical cyclones that inevitably possess irreversible entropy sources.

Key words: Tropical cyclones, Eyewall size, Eyewall replacement cycle, C15 model