The authors investigate the mesoscale dynamics that produce the lower-stratospheric energy spectra in idealized moist baroclinic waves, using the moist nonhydrostatic formulation of spectral energy budget of kinetic energy and available potential energy by J. Peng et al. The inclusion of moist processes energizes the lower-stratospheric mesoscale, helping to close the gap between observed and simulated energy spectra. In dry baroclinic waves, the lower-stratospheric mesoscale is mainly forced by weak downscale cascades of both horizontal kinetic energy (HKE) and available potential energy (APE) and by a weak conversion of APE to HKE. At wavelengths less than 1000 km, the pressure vertical flux divergence also has a significant positive contribution to the HKE; however, this positive contribution is largely counteracted by the negative HKE vertical flux divergence. In moist baroclinic waves, the lower-stratospheric mesoscale HKE is mainly generated by the pressure and HKE vertical flux divergences. This additional HKE is partly converted to APE and partly removed by diffusion. Another negative contribution to the mesoscale HKE is from the forcing of a visible upscale HKE cascade. Besides the conversion of HKE, however, the three-dimensional divergence also has a significant positive contribution to the mesoscale APE. With these two direct APE sources, the lower-stratospheric mesoscale also undergoes a much stronger upscale APE cascade. These results suggest that both downscale and upscale cascades through the mesoscale are permitted in the real atmosphere and the direct forcing of the mesoscale is available to feed the upscale energy cascade.
A high-resolution cloud-permitting simulation with the Weather Research and Forecasting (WRF) Model is performed to investigate the mesoscale horizontal kinetic energy (HKE) spectra of a tropical cyclone (TC). The spectrum displays an arc-like shape in the troposphere and a quasi-linear shape in the lower stratosphere for wavelengths below 500 km during the mature period of the TC, while they both develop a quasi −5/3 slope. The total HKE spectrum is dominated by its rotational component in the troposphere but by its divergent component in the lower stratosphere. Further spectral HKE budget diagnosis reveals a generally downscale cascade of HKE, although a local upscale cascade gradually forms in the lower stratosphere. However, the mesoscale energy spectrum is not only governed by the energy cascade, but is evidently influenced also by other physical processes, among which the buoyancy effect converts available potential energy (APE) to HKE in the mid- and upper troposphere and converts HKE to APE in the lower stratosphere, the vertically propagating inertia–gravity waves transport the HKE from the upper troposphere to lower and higher layers, and the vertical transportation of convection always transports HKE upward.
The intensification of Typhoon Lekima (2019) is simulated with the Weather Research and Forecasting model to study the atmospheric horizontal kinetic energy (HKE) spectra and corresponding spectral HKE budgets under the control of real tropical cyclone (TC). The results show that the TC has the ability to modify the canonical atmospheric energy spectrum during its evolution, which is dominated by its rotational mode. With the intensification of Lekima, the HKE spectrum in the troposphere swells over the central mesoscale and develops an arc-like shape. The stronger the TC, the more pronounced the arc-like shape is and the smaller scale it extends to. The roles various physical processes play at different heights and horizontal scales during the intensification of Lekima are investigated and the dependence of the effect of physical processes on scale and height is revealed. Meanwhile, the potential relationship between the intensification of TC, the activation of energy activity at smaller scales, and the downscale extension of the arc-like spectral shape is found.
The mesoscale kinetic energy (KE) spectra of the mei-yu front system are investigated through idealized numerical simulations. In the mature stage, the upper-tropospheric KE spectrum resembles a −3 power law for wavelengths between 1000 and 400 km and shallows to a slope of approximately − at smaller wavelengths. A similar behavior can be observed in the lower stratosphere. At both levels, the rotational KE spectrum shallows nearly to the same extent as the divergent KE spectrum at smaller wavelengths, accounting for the transition in the total KE spectrum. About 12 h after the latent heating is turned off, the mesoscale KE spectra hardly show the distinct spectral transition, especially in the upper troposphere. The spectral KE budget for various height ranges is analyzed and compared. In the upper troposphere, the mesoscale KE is deposited through the buoyancy flux and removed by the advective nonlinearity and vertical pressure flux divergence. The buoyancy flux spectrum in the mature phase has a peak at scales of around 300 km and a plateau throughout the mesoscale, which suggests a significant injection of KE in the mesoscale. The negative contribution of the advective nonlinearity demonstrates that to some extent the mesoscale KE derives from a nonlinear upscale cascade, with the buoyancy-produced energy source located at the lower end of mesoscale spectrum. In the lower stratosphere, the mesoscale KE is deposited through the advective nonlinearity and vertical pressure flux divergence and removed by the buoyancy flux. This suggests that the lower-stratospheric KE spectrum is influenced by both the downscale energy cascade and vertically propagating IGWs.
In this second part of a two-part study, a newly developed moist nonhydrostatic formulation of the spectral energy budget of both kinetic energy (KE) and available potential energy (APE) is employed to investigate the dynamics underlying the mesoscale upper-tropospheric energy spectra in idealized moist baroclinic waves. By calculating the conservative nonlinear spectral fluxes, it is shown that the inclusion of moist processes significantly enhances downscale cascades of both horizontal KE and APE. Moist processes act not only as a source of latent heat but also as an “atmospheric dehumidifier.” The latent heating, mainly because of the depositional growth of cloud ice, has a significant positive contribution to mesoscale APE. However, the dehumidifying reduces the diabatic contribution of the latent heating by 15% at all scales. Including moist processes also changes the direction of the mesoscale conversion between APE and horizontal KE and adds a secondary conversion of APE to gravitational energy of moist species. With or without moisture, the vertically propagating inertia–gravity waves (IGWs) produced in the lower troposphere result in a significant positive contribution to the upper-tropospheric horizontal KE spectra at the large-scale end of the mesoscale. However, including moist processes generates additional sources of IGWs located in the upper troposphere; the upward propagation of the convectively generated IGWs removes much of the horizontal KE there. Because of the restriction of the anelastic approximation, the three-dimensional divergence has no significant contribution. In view of conflicting contributions of various direct forcings, finally, an explicit comparison between the net direct forcing and energy cascade is made.
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