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1. Introduction
Secondary eyewalls are structures concentric to the primary eyewall of tropical cyclones and are characterized by maxima in tangential winds and convective activity. Given their frequency of occurrence (Hawkins and Helveston 2004, 2008; Kuo et al. 2008), their relationship with intensity change (e.g., Willoughby et al. 1982; Houze et al. 2007; Yang et al. 2013), their association with longer duration of higher storm intensity (Kuo et al. 2009), and their linkage to storm growth (Maclay et al. 2008), there is great interest in developing secondary eyewall forecasting tools. Today, the valuable and sophisticated forecasting tools tend to rely on empirical relationships (e.g., Kossin and Sitkowski 2009) and do not necessarily directly incorporate the physical processes of secondary eyewall formation.
Secondary eyewall formation dynamics have been the subject of intense contemporary research and contrasting views of the azimuthally averaged dynamics prevail. One line of thought suggests that the boundary layer contributes to the formation of secondary eyewalls by its participation in a feedback between a local enhancement of the radial vorticity gradient above the boundary layer, a corresponding frictional updraft, and increased convective intensity (Kepert 2013). This view is based on the conception that linearized idealizations of the boundary layer of the hurricane inner core are useful representations of the dynamics of such regions of the storm (Kepert 2001; Kepert and Wang 2001). In this view, supergradient winds are a result of the existence of eyewalls and not precursors of them.
Another view of the role of boundary layer dynamics in secondary eyewall formation envisions the Eliassen axisymmetric balanced vortex dynamics being an appropriate framework to describe secondary eyewall formation and evolution (e.g., Zhu and Zhu 2014). In this view, proposed initially by Shapiro and Willoughby (1982), the boundary layer plays a role only as a sink of tangential momentum. In this model, the boundary layer acts to spin down the tangential wind in the layer. Studies, like that of Rozoff et al. (2012), focus on the balanced aspects of the problem.
In contrast with the two foregoing lines of thought, another perspective suggests that nonlinear boundary layer dynamics are essential to secondary eyewall formation and evolution (Huang et al. 2012; Abarca and Montgomery 2013, 2015). Huang et al. (2012) proposed that secondary eyewall...