The analyses of individual case studies of complete and partial secondary eye-wall replacement have revealed two modes of tropical cyclone structure changes. These two modes are represented by the conceptual radial wind profiles in Fig. 85.
Figure 85 Conceptual radial profiles of tangential winds for tropical cyclones during complete or partial secondary eyewall replacement. The dashed and solid curves represent the azimuthal-average wind profiles at time (t) and t+∆t, respectively.
The first mode (Fig. 85a) was observed during complete and partial secondary eyewall replacement for Stage IIa and Stage III of the life cycle as defined in Fig. 9. This mode was specifically observed for complete eyewall replacement in the one Fabian (2003) case, the fourth Ivan (2004) case, and the first Wilma (2005) case (the second Wilma case was not used since the eyewall was over land). Additionally, this first
mode was observed for the partial eyewall replacement cases of Emily (2005) and Rita (2005). For this mode, the Rmax increases and Vmax (denoted as maximum tangential wind speed, Vt, in the discussions of Chapters III and IV) decreases in association with a complete or partial eyewall replacement cycle. The outer-core structure (R34) also expands during the complete or partial eyewall replacement cycle, which includes a small and time-lagged R34 increase following the inner-core (Rmax) change. This first mode is consistent with the traditional explanation for concentric eyewall replacement by Willoughby et al. (1982) as presented in Chapter I.A.3.
In these first mode cases (Fig. 85a), the average decrease in Vt was 7 m s−1 with a range of 6 m s−1 to 11 m s−1. The Rmax approximately doubled during these first mode cases, except for the Fabian eyewall replacement cycle that had a three-fold Rmax
increase and for the first Wilma eyewall replacement cycle that had a five-fold Rmax
increase. The average Rmax increase was 28 km with a range from 6 km to 56 km.
The average R34 increase for these first mode cases (Fig. 85a) was 59 km with a range from 20 km to 109 km. The R34 increases for the first mode were generally larger than those of the second mode (discussed below) since the exponent x remains nearly constant. Indeed, the average exponent x increase was only 0.08 with a range of −0.02 to 0.21 during these first mode cases. Applying Eq. (20) to the partial eyewall replacement of Rita, the Vt decrease by 10 m s−1 has a 1-to-1 impact on the right side of the equation, whereas the 26 km increase in Rmax with an exponent x = 0.47 has an approximate 2.4-to-1 impact. Thus, the Rmax increase compensates for the Vtdecrease and the resultant effect is a R34increase of 52 km. These R34increases are considerable outward expansions, especially when a tropical cyclone is approaching landfall.
Except for the partial eyewall replacement of Ivan, the second mode (Fig. 85b) was only observed during complete secondary eyewall replacement and for Stage IIa of the life cycle as defined in Fig. 9. This mode was specifically observed for both Frances (2004) cases, the first three Ivan (2004) cases, the one Katrina (2005) case, and the Ivan (2004) partial eyewall replacement case. For this mode, the Rmax and Vmax both increase in association with a eyewall replacement cycle. The outer-core structure (R34) also expands during this eyewall replacement cycle, and often continues to expand in a time-lagged response of 6 h or more following the inner-core (Rmax) change.
For the second mode (Fig. 85b), the observed average increase in Vt was 8 m s−1 with a range of 2 m s−1 to 13 m s−1. Rapid intensification occurred during an eyewall replacement cycle when strong spiral rainband convection was in close proximity to the secondary eyewall. This was the case for the first eyewall replacement of Frances (Figs.
50c—e), the second and third eyewall replacements of Ivan (Figs. 58e—f and 61c—e), the eyewall replacement of Katrina (Figs. 67b—c), and the partial eyewall replacement of Ivan (Figs. 55a—b). Although, these convective asymmetries were not present or were much weaker for the remainder of the case studies in the second mode, the cases with convective asymmetries suggest that the process of axisymmetrization may be a potential mechanism for rapid storm intensification during eyewall replacement. The Rmax doubled or tripled (e.g., Hurricane Katrina) during eyewall replacement for the second mode. The observed average Rmax increase was 23 km with a range from 12 km to 37 km, which is very similar to the first mode.
The observed average R34 increase during eyewall replacement for the second mode (Fig. 85b) was 45 km with a range from 7 km to 99 km. The largest R34
increases occurred when rapid intensification (i.e., large Vt increases) was combined with a Rmax increase. Indeed, this is consistent with Eq. (20) since increases in Vt
and Rmax on the left side of the equation are expected to result in an increase in R34
on the right side. However, the other unknown in Eq. 20 is the exponent x, which in the pre-eyewall replacement period for Katrina was equal to 0.31. If this exponent also applied after the eyewall replacement and using the Hour 18 values of Vt = 46 m s−1 and Rmax = 34 km, the resulting R34 would be 807 km, which would be a 539 km increase in the outer-core radius. In reality, the observed R34 increase was limited to 71 km, which still represents a considerable outward expansion in less than 24 h for a tropical cyclone approaching landfall. This R34 increase of 539 km did not occur because the exponent for the outer profile during the eyewall replacement was much larger (0.64 versus 0.31), which implies a more rapid decrease in wind with radius. During eyewall replacement for all cases in the second mode (Fig. 85b), the post-replacement exponent x on average was increased by 0.19 with a range between 0.07 and 0.33. The smallest change in exponent x (0.07 increase) occurred for Ivan’s second eyewall replacement, and R34 increased by 99 km in 18 h and then continued to increase by 120 km in 24 h. Thus, a “flatter-than-average” outer wind profile existed prior to the second mode of secondary eyewall formation that then became
“sharper-than-average” following secondary eyewall formation. This time change in
the profile shapes demonstrates that accurately predicting the change in the R34 with a fixed value for exponent x during eyewall replacement is not plausible.
For all cases of complete and partial eyewall replacement with the exception of Wilma, the outward (inward) ∆KEanom was correlated with an expansion (contrac-tion) of the Rmax radius. Indeed, the correlation coefficients for the Fabian, Frances, Ivan, and Katrina cases (0.709, 0.743, 0.642, and 0.775, respectively) suggest a linear relationship between ∆KEanom and Rmax. Additionally, the correlation coefficients for the Emily and Rita cases (0.460, and 0.399, respectively) suggest a positive corre-lation between the ∆KEanom and the Rmax changes, albeit with a larger spread in the values. Large increases in the radial inflow variance were often observed when strong asymmetric spiral rainband convection existed in close proximity to the primary or secondary eyewall. However, an increase in the R34 value was not always observed 6 h or more after the increased radial inflow variance.
The formation of a secondary eyewall was frequently observed as a tropical cy-clone approached land, e.g., for Ivan at Hours 92, 164.5, and 212.5 (Figs. 58d, 64a, and 65d, respectively) as the storm center approached land within 130 km, 150 km, and 240 km, respectively. Additional examples include Hour 43 of Katrina (Fig. 67f) and Hour 65.5 of Wilma (Fig. 72c) where these storm centers experienced land inter-action within 230 km and 180 km, respectively. The impacts of tropical cyclone land interaction will be further explored in a later section of this chapter.