## 1 Introduction  
For the past few decades, despite large improvement in the track forecast of tropical cyclone (TC), there is almost no substantial improvement in the intensity forecast for all lead times [1]. Model skill in predicting TC formation and rapid intensification is still very limited [2]. One reason why TC intensity is so poorly predicted lies in that, compared to track, which is more dependent on the environmental conditions, TC intensity can be more strongly dependent on internal dynamics and moist convection, which occur on smaller scales, and are more chaotic, less well understood, and intrinsically less predictable [3]. In this context, a better understanding of TC internal dynamics associated with its intensity variation is essential for improving intensity forecasts [4; 5]. Among various methods, energy spectrum analysis is known to reveal signals at different scales. It is thus particularly suitable for investigating physical processes associated with TC, which is known as a typical multiscale system. Atmospheric energy spectrum refers to the distribution (i.e., variance) of atmospheric energy with wavenumber and/or frequency, which can intuitively reflect the scale characteristics of energy. Since the pioneering work of [PERSON] and [PERSON] [6], based on data from aircraft flights, many researchers have examined the horizontal wavenumber (\(k_{h}\)) spectrum of the atmospheric energy, especially for the mesoscale range. Numerous observational studies have reached a consensus--the atmospheric horizontal kinetic energy (HKE) spectrum as a function of \(k_{h}\) possesses robust canonical shape, which follows a \(k_{h}^{-3}\) power law at the synoptic scale and a \(k_{h}^{-5/3}\) power law at the mesoscale, with a transition scale between these two power-law dependence around horizontal wavelength (\(\lambda_{h}=2\pi\)/\(k_{h}\)) of -500 km [7,8]. Up to now, the underlying mechanism for the formation of the canonical shape of atmospheric energy spectrum, especially for the mesoscale -5/3 spectral slope, is still under explored [9, 10, 11, 12]. Although the mechanism is not clear, the observed atmospheric spectrum has already been reproduced by many numerical models and even becomes an indicator for verifying models [13, 14, 15, 16]. In addition to studying the pattern of the energy spectrum, the contributions of various physical processes at different scales to the energy budget to the atmosphere can also be investigated by means of spectral energy budget formulation. As it is difficult for observational methods to provide the comprehensive data needed for budget diagnosis, the relevant studies are always performed based on results from high-resolution numerical simulation [17, 18, 19, 20, 21, 22, 23]. [PERSON] et al. [22] (hereafter [PERSON]), to our knowledge, were the first to investigate the energy spectrum associated with TC using high-resolution numerical model. Using an idealized simulation, they studied the distribution of mesoscale HKE spectrum and corresponding spectral budget as a function of \(k_{h}\) at different vertical heights during the intensification and mature stage of TC, and revealed the specific roles of various physical processes, such as energy cascade, buoyancy effect, convection, and vertical propagation of inertia-gravity waves (IGWs). In particular, they found that unlike the canonical atmospheric spectrum, the HKE spectrum in their simulation displays an arc-like shape at the mesoscale in the troposphere. Although they have achieved some conclusions, the research of WZ2018 was entirely based on idealized simulation, which suffered lots of simplification. For example, the simulation is performed on the \(f\) plane, which does not take the real geography and terrain into account; the initial vortex is artificial and assumed to be axisymmetric; the background atmosphere is specified as motionless, which does not contain any system except for the initial vortex; and the radiation processes are neglected.