# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 4 Results
Reference [28] previously proposed a conceptual model of the TC inner core including GWs above the warmer core interacting with the weak subsidence in the eye and stronger descent at the inner edge of the eyewall. The FFT was applied on the vertical profiles of zonal and meridional wind perturbations at latitude of 23\({}^{\circ}\) N and longitudes between 119\({}^{\circ}\) E and 133\({}^{\circ}\) E to compute the energy distribution as a function of vertical wavelength for height layers of 3-10 km, 8-15 km and 18-25 km (Figure 13a). The energy density was normalized by the maximum value produced by zonal wind perturbations at heights of 8-15 km. Wave perturbations were dominant in the zonal wind, especially in the UT. The mean vertical wavelength peaked in both zonal and meridional wind perturbations at about 4 km in the UT and LS. It was shorter in the lower troposphere (2-4 km). The vertical profiles of intrinsic frequencies \(\omega\) derived from the method of variance and were calculated at 3-25 km heights and latitude 23\({}^{\circ}\) N. Figure 13b visualizes the mean longitude-height distribution of the normalized intrinsic frequencies \(\omega\#\) at longitudes between 119\({}^{\circ}\) E and 129\({}^{\circ}\) E. The analysis captured low-frequency GWs with normalized intrinsic frequencies up to 6 (period of 5 h) with a mean value of 2.5-3.5 (periods of 8-13 h). Large normalized intrinsic frequencies were mostly localized at the rear of the TC. They were mostly present from the bottom up to heights of 10-11 km and also below the tropopause where the TC outflows are located. Finally, the observations identified the tangential wind asymmetry below the tropopause as possible locations of GW sources. Figure 13c indicates that the mean value of normalized intrinsic frequencies decreased from 4.6 (T = 7 h) in the lowest level at 2 km height to 2.8 (T = 12 h) at about 12 km height and ranged between 2.4 and 3 (T = 10-13 h) in the UT and LS. The occurrence distributions of periods, normalized by the maximum value at heights of 3-25 km, highlighted weighted mean values ranging between 12.5 h and 14.5 h for the three height layers with a mean value of 13.4 h for the layer of 3-25 km (Figure 13d). Structures with short periods \(<\)5 h were dominant at heights \(<\)10 km. In comparison, the observations of [PERSON] (2008) revealed dominant low-frequency GWs with periods of 4 h and 6-8 h in the UT and longer periods of 13 h in the LS and the simulation produced GWs with periods of 4-12 h during TC intensification in the UT and LS. Considering the respective dominant parameters \(\lambda_{v}\) and \(\omega\)_ff_ of 2-5 km and 2.5-3.7 (periods of 9-13 h) at 5-25 km heights. Equation (2) provided dominant horizontal wavelengths of 116-708 km in the troposphere and LS. Figure 9: Mean kinetic energy distribution \(E_{k}\) (J kg\({}^{-1}\)) from horizontal wind perturbations (grey shading) at heights of (**a**) 3–10 km, (**c**) 8–15 km and (**e**) 18–25 km on 7 August 12:00 UTC. Contours of mean energy density (J kg\({}^{-1}\)) derived from potential temperature (\(E_{p}\), red), zonal wind (\(E_{\mu}\), green) and meridional (\(E_{v}\), blue) perturbations are superimposed. Longitudinal cross-sections of mean energy density distributions: (**b**) 3–10 km, (**d**) 8–15 km and (**f**) 18–25 km at latitude 23\({}^{\circ}\) N.  
Figure 11: Hodographs of horizontal wind perturbations on 7 August 12:00 UTC. In the LS (**a**) at (23\({}^{\circ}\) N, 125\({}^{\circ}\) E) in the UT and (**b**) at (22\({}^{\circ}\) N, 126.4\({}^{\circ}\) E) in Region A; in the middle troposphere (**c**) at (23\({}^{\circ}\) N, 122\({}^{\circ}\) E) in Region B, (**d**) at (22\({}^{\circ}\) N, 124.9\({}^{\circ}\) E) in Region C; (**e**) at (25.5\({}^{\circ}\) N, 125.3\({}^{\circ}\) E) and (**f**) at (21\({}^{\circ}\) N, 128.8\({}^{\circ}\) E) in the UT in Region D respectively. Crosses visualize the vertical step of 100 m height.