# Elliptical Structures of Gravity Waves Produced by Typhoon Soudelor in 2015 near Taiwan
## 4 Results
In addition, the activity of energy density spread outward along the eyewall and \(E_{p}\) became large and dominant in the UT. In particular, a significant activity of \(E_{p}\) was observed above the CMR. A comparison between Figure 9c,e revealed different distributions of wave energy density. The maximum wave energy density was mostly localized at a longitude of about 124.5\({}^{\circ}\) E and 23.5\({}^{\circ}\) N in the LS above the location of the RMW in the UT (Figure 9e,f, respectively). The values of the mean total energy density \(E_{t}\) over the domain D2 were estimated at about 4.4 J kg\({}^{-1}\), 13.36 J kg\({}^{-1}\) and 10.3 J kg\({}^{-1}\) at heights of 3-10 km, 8-15 km and 18-25 km, respectively. in quadrature in the UT and LS, whereas temperature and meridional wind perturbations were out of phase (Figure 10b). Thus, the phase relationships between perturbations were in agreement with the linear theory of GW polarization, which sketched elliptically polarized structures on the hodograph of horizontal wind perturbations [24]. Indeed, the hodographic analysis confirmed the presence of elliptical structures of GWs at 12:00 UTC on 7 August. Significant amplitudes of horizontal wind perturbation were retrieved from 100 m interpolated vertical profiles of perturbations in Regions A, B, C and D (Figure 11). The variation of the axis ratio, vertical length of the ellipses and direction of the major axis indicated GWs of different natures. The axis ratios and perimeters of the two ellipses on Figure 11c,d indicated the presence of similar GWs with a vertical wavelength of about 2.6 km, but propagating southwestward and southeastward in Regions B and C, respectively, which was consistent with the direction of the wavelike patterns observed in Figure 8b. Figure 11e,d revealed some GWs with a vertical wavelength of about 2 km, which propagated northeastward and eastward at the upper border and within Region D, respectively. Such results supported the presence of the mesoscale semi-circular GWs propagating dominantly eastward at the rear of the TC. For these last cases, cyclonic rotation (anticyclonic) of the ellipse with height at altitudes \(<\)15 km (\(>\)15 km) indicated downward (upward) propagation of wave energy density in the troposphere (LS) and suggested the presence of a GW source located near the tropopause. Elliptically polarized structures of GWs were also observed ahead of TC Soudelor in the UT and LS above Taiwan when the TC was approaching the island as far as a distance of 1100 km from 6 August at 00:00 UTC (not shown). In comparison, Reference [12] reported TC-induced GWs on high-resolution radiosonde profiles in the UT and LS above Tromelin Island (16.1\({}^{\circ}\) S, 54.3\({}^{\circ}\) E) when TC Hudah (2000) at a distance less than 2000 km east. Besides, simulated profiles of horizontal wind perturbations revealed the presence of quasi-inertial GWs in the TC eye with large amplitudes of perturbations (Figure 12a,c) where the two warm anomalies were located at about 5 km and 15 km heights (Figure 6d). The inertial period was estimated at about 30.7 h at the latitude of the TC eye. Figure 12a indicates that the hodograph is cyclonic (anticyclonic) below (above) 5 km height. Similar observations were reported below and above 15 km height (Figure 12b,c). The two elliptically polarized GWs had the same intrinsic periods of about 20 h (\(\omega\#\approx 1.5\)). The vertical and horizontal wavelengths were estimated at about 1.4 km (2.6 km) and 254 km (328 km), respectively, in the lower troposphere (UT). A destructive interference between upward and downward inertio-GWs might explain the presence of an intermediate GW with an intrinsic period of about 10 h (\(\omega\#\approx 2.8\)), and horizontal and vertical wavelengths of about 150 km and 1.9 km respectively, located at heights of 6.5-10.5 km between the two anomalies.