The Horizontal Spectrum of Vertical Velocities near the Tropopause from Global to Gravity Wave Scales

Abstract

Vertical motions are fundamental for atmospheric dynamics. Compared to horizontal motions, the horizontal spectrum of vertical velocity w is less well known. Here, w spectra are related to spectra of horizontal motions in the free atmosphere near the tropopause from global to gravity wave scales. At large scales, w is related to vertically averaged horizontal divergent motions by continuity. At small scales, the velocity energy spectra reach anisotropy as in stably stratified turbulence. Combining these limits approximates the w spectrum from global to small scales. The w spectrum is flat at large scales when the divergent spectrum shows a −2 slope, reaches a maximum at mesoscales after transition to −5/3 slopes, and then approaches a fraction of horizontal kinetic energy. The ratio of vertical kinetic energy to potential energy increases quadratically with wavenumber at large scales. It exceeds unity at small scales in stratified turbulence. Global and regional simulations and two recent aircraft measurement field campaigns support these relationships within 30% deviations. Energy exchange between horizontal and vertical motions may contribute to slope changes in the spectra. The model allows for checking measurement validity. Isotropy at large and small scales varies between the datasets. The fraction of divergent energy is 40%–70% in the measurements, with higher values in the stratosphere. Spectra above the tropopause are often steeper over mountains than over oceans, partly with two −5/3 subranges. A total of 80% of w variance near the tropopause occurs at scales between about 0.5 and 80 km.

Model intercomparison of COSMO 5.0 and IFS 45r1 at kilometer-scale grid spacing

“…deep convection seems to be even more drastic for the vertical than for the horizontal winds: The amplitude is clearly reduced throughout all wavelengths for both models. The amplitude and shape of the power spectral densities of w from the explicit runs seem to mostly agree with values from other observational and numerical studies (Bacmeister et al, 1996;Gao and Meriwether, 1998;Callies et al, 2016;Schumann, 2019;Panosetti et al, 2019). The spectra of the configurations used in this study all follow a slope of roughly k −1/5 .…”

Far‐Ranging Impact of Mountain Waves Excited Over Greenland on Stratospheric Dehydration and Rehydration

“…The model top is at 0.01 hPa and 137 vertical hybrid levels are used. Here we use the updated In the spirit of Dörnbrack et al (2017), temperature perturbations T′ are calculated as the difference between the temperature field retrieved at full spectral resolution and the spectrally truncated fields T CO 106 (Malardel & Wedi, 2016;Wedi, 2014); the total horizontal wave number 106 is selected as it can be used to separate large-scale synoptic processes from inertia gravity waves (Schumann, 2019;Žagar et al, 2017). Figure 3 displays the magnitude of the horizontal wind V H and the temperature perturbations T′ related to mesoscale gravity waves resolved by the ERA5 data.…”

“…In the spirit of Dörnbrack et al. (2017), temperature perturbations T ′ are calculated as the difference between the temperature field retrieved at full spectral resolution and the spectrally truncated fields T CO 106 (Malardel & Wedi, 2016; Wedi, 2014); the total horizontal wave number 106 is selected as it can be used to separate large‐scale synoptic processes from inertia gravity waves (Schumann, 2019; Žagar et al., 2017).…”

Spatial spectrum of temperature fluctuations in buoyancy driven chaotic and turbulent atmosphere

“…In a recent paper Ref. [33] a spectral analysis of the data obtained during the long-distance flights over the South Pacific near New Zealand (the DEEPWAVE experiment [34]) was performed. The measurements were made in the lowermost stratosphere.…”

“…Figures 12 and 13 shows the horizontal power spectra of the temperature fluctuations for high and small dissipation rates respectively (the spectral data were taken from Fig. 4b of the Ref [33]). The dashed curve is drawn to indicate the stretched exponential Eq.…”