A new formulation of the spectral energy budget of kinetic and available potential energies of the atmosphere is derived, with spherical harmonics as base functions. Compared to previous formulations, there are three main improvements: (i) the topography is taken into account, (ii) the exact three-dimensional advection terms are considered, and (iii) the vertical flux is separated from the energy transfer between different spherical harmonics. Using this formulation, results from two different high-resolution GCMs are analyzed: the Atmospheric GCM for the Earth Simulator (AFES) T639L24 and the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) T1279L91. The spectral fluxes show that the AFES, which reproduces quite realistic horizontal spectra with a k(-5/3) inertial range at the mesoscales, simulates a strong downscale energy cascade. In contrast, neither the k(-5/3) vertically integrated spectra nor the downscale energy cascade are produced by the ECMWF IFS.

The EOLE experiment is revisited to study turbulent processes in the lower stratosphere circulation from a Lagrangian viewpoint and to resolve a discrepancy on the slope of the atmospheric energy spectrum between the work of Morel and Larcheveque and recent studies using aircraft data. Relative dispersion of balloon pairs is studied by calculating the finite-scale Lyapunov exponent, an exit-time-based technique that is particularly efficient in cases in which processes with different spatial scales are interfering. The main goal is to reconciliate the EOLE dataset with recent studies supporting a k(-5/3) energy spectrum in the 100-1000-km range. The results also show exponential separation at smaller scales, with a characteristic time of order 1 day, and agree with the standard diffusion of about 10(7) m(2) s(-1) at large scales. A remaining question is the origin of a k(-5/3) spectrum in the mesoscale range between 100 and 1000 km.

Recently, it has been discussed whether the mesoscale energy spectra in the upper troposphere and lower stratosphere are generated by weakly or strongly nonlinear dynamics. A necessary condition for weak non- linearity is that the Rossby number Ro vertical bar zeta(z)vertical bar/f << 1, where zeta(z) is the vertical vorticity and f is the Coriolis parameter. First, it is shown that Ro can be estimated by integration of the rotational wavenumber energy spectrum E-r. Then divergence and rotational energy spectra and their ratio, R E-d/E-r, are calculated from the Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) dataset, and it is shown that at least 1000 flight segments are needed to obtain converged results. It is found that R < 1 in the upper troposphere, ruling out the hypothesis that the spectra are produced by inertia-gravity waves with frequencies larger than f. In the lower stratosphere R is slightly larger than unity. An analysis separating between land and ocean data shows that E-d and temperature spectra have somewhat larger magnitude over land compared to ocean in the upper troposphere-a signature of orographically or convectively forced gravity waves. No such effect is seen in the lower stratosphere. At midlatitudes the Rossby number is on the order of unity and at low latitudes it is larger than unity, indicating that strong nonlinearities are prevalent. Also the temperature spectra, when converted into potential energy spectra, have larger magnitude than predicted by the weakly nonlinear wave hypothesis.

We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high-resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water vapor mixing ratio, and the resulting supersaturation fields together with the Navier-Stokes equation. We find that the droplet size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation-fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (nonturbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation.

The author shows that the horizontal two-point correlations of vertical vorticity and the associated vorticity wavenumber spectrum can be constructed from previously measured velocity structure functions in the upper troposphere and lower stratosphere. The spectrum has a minimum around k = 10(-2) cycles per kilometer (cpkm) corresponding to wavelengths of 100 km. For smaller wavenumbers it displays a k(-1) range and for higher wavenumbers, corresponding to mesoscale motions, it grows as k(1/3). The two-point correlation of horizontal divergence of horizontal velocity and the associated horizontal spectrum is also constructed. The horizontal divergence spectrum is of the same order of magnitude as the vorticity spectrum in the mesoscale range and show similar inertial range scaling. It is argued that these results show that the mesoscale motions are not dominated by internal gravity waves. Instead, the author suggests that the dynamic origin of the k(1/3) range is stratified turbulence. However, in contrast to Lilly, the author finds that stratified turbulence is not a phenomenon associated with an upscale energy cascade, but with a downscale energy cascade.

The horizontal wavenumber spectra of wind and temperature in the upper troposphere and lower stratosphere display a narrow k(-3) range at scales on the order of 1000 km and a broad k(-5/3) range at mesoscales on the order of 1 to 500 km. Recently, Tulloch and Smith suggested that a surface quasigeostrophic (SQG) turbulence model can explain the observed spectra. Here, it is first argued that the mesoscale spectra are not likely to be explained by any quasigeostrophic model because the Rossby number corresponding to the mesoscale dynamics is on the order of unity or larger. Then it is argued that the SQG model in particular cannot explain the observations because its mesoscale spectrum displays a k(-5/3) dependence only in a very thin layer just below the tropopause. The thickness of this layer can be estimated to be of the order of 10 m, whereas aircraft measurements are typically performed several hundred meters away from the tropopause.

Several existing sets of smaller-scale ocean and atmospheric data appear to display Kolmogorov-Obukov-Corrsin inertial ranges in horizontal spectra for length scales up to at least a few hundred meters. It is argued here that these data are inconsistent with the assumptions for these inertial range theories. Instead, it is hypothesized that the dynamics of stratified turbulence explain these data. If valid, these dynamics may also explain the behavior of strongly stratified flows in similar dynamic ranges of other geophysical flows.

KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Centra, SeRC - Swedish e-Science Research Centre. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.

Brandt, Luca

KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Centra, SeRC - Swedish e-Science Research Centre. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.

The authors study the condensational growth of cloud droplets in homogeneous isotropic turbulence by means of a large-eddy simulation (LES) approach. The authors investigate the role of a mean updraft velocity and of the chemical composition of the cloud condensation nuclei (CCN) on droplet growth. The results show that a mean constant updraft velocity superimposed onto a turbulent field reduces the broadening of the droplet size spectra induced by the turbulent fluctuations alone. Extending the authors' previous results regarding stochastic condensation, the authors introduce a new theoretical estimation of the droplet size spectrum broadening that accounts for this updraft velocity effect. A similar reduction of the spectra broadening is observed when the droplets reach their critical size, which depends on the chemical composition of CCN. The analysis of the square of the droplet radius distribution, proportional to the droplet surface, shows that for large particles the distribution is purely Gaussian, while it becomes strongly non-Gaussian for smaller particles, with the left tail characterized by a peak around the haze activation radius. This kind of distribution can significantly affect the later stages of the droplet growth involving turbulent collisions, since the collision probability kernel depends on the droplet size, implying the need for new specific closure models to capture this effect.