## 4 Discussion and Conclusions  
In this paper, the intensification of Typhoon Lekima is simulated for the purpose of investigating the evolution and characteristics of HKE spectra and diagnosing the corresponding spectral HKE budgets for real TC. Accompanied with the intensification of Lekima, the HKE spectra at various heights vary remarkably. After the completion of the intensification, the spectra reproduce the canonical atmospheric spectrum to some extent, but also exhibit significant differences from the canonical spectrum. In the troposphere, the spectrum is in perfect agreement with the canonical spectrum before the intensification of Lekima; while accompanied with the intensification, the spectrum is gradually modified, and an arc-like spectral shape forms over the central mesoscale and extends to smaller scales. The investigation on RKE and DKE shows that the appearance of the arc-like shape is a direct result of the increasing vorticity during the intensification of Lekima. Combined with the idealized TC simulation of WZ2018 and the observational hurricane study of [PERSON] and [PERSON] [32], this arc-like shape is a unique and robust feature for atmospheric HKE spectrum associated with TC. The stronger the TC, the more pronounced this feature is and the smaller scale it extends to. In the lower stratosphere, the spectrum is in perfect agreement with the canonical spectrum at the mesoscale with a slope of \(-5/3\), but the \(-3\) slope at the synoptic scale does not appear. The canonical atmospheric spectrum is obtained by averaging numerous of observations, and is considered representative and universal to the earth's atmosphere. However, the results in this study demonstrate that the canonical spectrum does not always apply to all cases. In fact, the evolution of HKE spectrum here in the troposphere directly reflects the modification of the spectrum by the development of Lekima. It is thus a reasonable inference that weather systems with unique structure and vibrant energy activity have the potential of modifying the canonical atmospheric spectrum during their development and evolution. Future investigations on the atmospheric energy spectrum should focus upon the spectral feature associated with specific weather systems, and seek to determine the formation mechanism behind the potential difference from the canonical spectrum. For example, why does the enhancement of rotational mode of TC lead to the swelling of HKE spectrum over the central mesoscale? The predictability of TC indicated by the energy spectra, which has not been discussed here, also deserves to be explored. According to [PERSON] [35], atmospheric system governed by a \(k^{-p}\) power law has limited predictability when \(p<3\) and unlimited predictability when \(p\geq 3\). The arc-likeshape of HKE spectrum over the central mesoscale means that \(p\) for TC system changes dramatically over a relatively narrow scale range, which may imply that the predictability of TC is complicated at the mesoscale. By diagnosing the spectral HKE budget, the roles various physical processes play during the intensification of Lekima are investigated. Some processes, such as the buoyancy forcing, vertical transportation of IGWs, nonlinear interactions, and vertical transportation of convection, make remarkable contributions at almost all heights from lower troposphere to lower stratosphere. Other processes, by contrast, only make significant contributions at specific heights. The results for various budget terms here are qualitatively consistent with those in WZ2018, which both verifies the reasonability and authenticity of results from the idealized TC simulation and also suggests that the roles of various physical processes play during the intensification of TC are relatively steady. The dependence of budget terms on scale and height is intriguing. For example, from the pressure vertical flux and its divergence, it can be found that upward- and downward-propagating IGWs with broad horizontal-wavelength range are excited near the tropopause.