The rotational and divergent kinetic energy (RKE and DKE) spectra of geostrophic vortices (Rossby waves; RWs) and inertia-gravity waves (IGWs) in the global atmosphere are investigated with ERA5 reanalysis. The separation of RWs and IGWs in physical space is based on the normal-mode decomposition, and the Helmholtz decomposition produces their RKE and DKE spectra at different layers, with a focus on spherical wavenumbers l=10-100. In the upper troposphere and the middle and lower stratosphere, the RKE spectra of the total mode closely resemble the horizontal kinetic energy (HKE) spectra of RWs over most wavenumbers; the DKE spectra of the total mode are more comparable to the DKE spectra rather than the HKE spectra of IGWs, although their slopes are similar. The HKE of RWs is dominated by its rotational component, accounting for more than 80% of the HKE in most ranges of concern. Although the HKE of IGWs is dominated by its divergent component, its rotation component is also significant, with an average percentage exceeding 25% in all three vertical layers analyzed. Care must be taken when employing divergence as a proxy of IGWs, as the DKE may underestimate the HKE of IGWs. With the increase of altitude and the decrease of scale, the contribution of the divergent component increases in the horizontal circulation of both RWs and IGWs.

Geostrophic Vortices,Inertia-gravity Waves,Kinetic Energy Spectra,Normal-mode decomposition