The Rotational and Divergent Kinetic Energy Spectra of Geostrophic Vortices and Inertia-Gravity Waves

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 10 <= l <= 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. The atmospheric horizontal kinetic energy (HKE) spectrum exhibits a mysterious -5/3 slope at mesoscales, but underlying physical mechanisms are still not fully understood. Evaluating the contributions of geostrophic vortices and inertia-gravity waves to the HKE spectrum helps us understand this issue. Combining the normal-mode and Helmholtz decompositions, we investigate the rotational and divergent kinetic energy (RKE and DKE) spectra of geostrophic vortices and inertia-gravity waves in the global atmosphere with ERA5 reanalysis. Our results verify that the RKE approximates the HKE of the vortex well, but the DKE underestimates the HKE of the wave, especially at larger scales. The HKE of vortices and waves is dominated by their respective rotational and divergent components. However, unlike the negligible divergent component in vortices, the contribution of the rotational component in waves is significant. In the vertically integrated HKE over three selected layers in the upper troposphere and stratosphere, the average percentage of RKE at l = 10-100 exceeds 25%. When using the intersection of RKE and DKE spectra to diagnose the mesoscale transition, it should be noted that the crossing scale of the HKE spectra of waves and vortices may be larger. The total rotational kinetic energy (RKE) spectra can be well approximated to the horizontal kinetic energy (HKE) spectra of Rossby waves The total divergent kinetic energy (DKE) spectra closely resemble the DKE spectra of inertia-gravity waves rather than their HKE spectra On average, the RKE component accounts for more than 25% in the HKE of inertia-gravity waves at wavenumbers 10-100