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In this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers. [ABSTRACT FROM PUBLISHER]

In this survey we consider the impact of turbulence on cloud formation from the cloud scale to the droplet scale. We assess progress in understanding the effect of turbulence on the condensational and collisional growth of droplets and the effect of entrainment and mixing on the droplet spectrum. The increasing power of computers and better experimental and observational techniques allow for a much more detailed study of these processes than was hitherto possible. However, much of the research necessarily remains idealized and we argue that it is those studies which include such fundamental characteristics of clouds as droplet sedimentation and latent heating that are most relevant to clouds. Nevertheless, the large body of research over the last decade is beginning to allow tentative conclusions to be made. For example, it is unlikely that small-scale turbulent eddies (i.e. not the energy-containing eddies) alone are responsible for broadening the droplet size spectrum during the initial stage of droplet growth due to condensation. It is likely, though, that small-scale turbulence plays a significant role in the growth of droplets through collisions and coalescence. Moreover, it has been possible through detailed numerical simulations to assess the relative importance of different processes to the turbulent collision kernel and how this varies in the parameter space that is important to clouds. The focus of research on the role of turbulence in condensational and collisional growth has tended to ignore the effect of entrainment and mixing and it is arguable that they play at least as important a role in the evolution of the droplet spectrum. We consider the role of turbulence in the mixing of dry and cloudy air, methods of quantifying this mixing and the effect that it has on the droplet spectrum. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office [ABSTRACT FROM AUTHOR]

Although predictability represents one of the fundamental problems in atmospheric science, gaps in our knowledge remain. Theoretical understanding of the inverse error cascade is limited mostly to homogeneous, isotropic turbulence, whereas numerical simulations have focused on highly complex numerical weather prediction models. These results cannot be easily reconciled. This paper describes selected aspects of the predictability behavior of rotating stratified turbulence. The objective is to determine how the predictability varies with scale when the dynamics are more realistic than the idealized models that underlie the classical picture of predictability and yet are free of the parameterizations that complicate interpretation of NWP models. Using a numerical model of the nonhydrostatic Boussinesq equations, it is shown that the predictability decay, as diagnosed by the relative error, is slower for subsynoptic flow. The dependence on the deformation radius, differences between balanced and unbalanced modes, and implications for NWP models are discussed. [ABSTRACT FROM AUTHOR]

The authors present simulations of cloud-free and cloudy, nonprecipitating, convective turbulence at spatial resolutions down to Δx = 2.6 m for a domain size of (1 km)3. The runs are analyzed with attention focused on the dynamical differences between resolutions and the presence or absence of moisture, as well as on the small-scale variability of the liquid water spectra in the cloudy cases. Because of evaporation and condensation, liquid water content does not act like a passive scalar. Much of the evaporation occurs in highly turbulent cloud-top mixing where differences in variances and kurtoses of real-space vorticity probability density functions between cloudy and cloud-free runs are also found. The cloudy cases have higher variance and lower kurtosis values than their cloud-free counterparts. The lower kurtosis values mean fewer high-intensity vortices for the cloudy cases, which is most likely due to the loss of buoyancy as evaporation occurs during entrainment events. This effect is associated with a change in the liquid water content spectra found in regions of cloud decay. Conditional sampling of these regions shows increased small-scale variability, above the background increase due to the bottleneck effect, of liquid water content spectra; this is not found in other cloudy regions. This may help explain recent measurements of enhanced small-scale liquid water content variability in aircraft measurements of stratocumulus clouds. [ABSTRACT FROM AUTHOR]

Although it is now accepted that imbalance in the atmosphere and ocean is generic, the feedback of the unbalanced motion on the balanced flow has not received much attention. In this work the parameterization problem is examined in the context of rotating stratified turbulence, that is, with a nonhydrostatic Boussinesq model. Using the normal modes as a first approximation to the balanced and unbalanced flow, the growth of ageostrophic perturbations to the quasigeostrophic flow and the associated feedback are studied. For weak stratification, there are analogies with the three-dimensionalization of decaying 2D turbulence: the growth rate of the ageostrophic perturbation follows a linear estimate, geostrophic energy is extracted from the base flow, and the associated damping on the geostrophic base flow (the “eddy viscosity”) is peaked at large horizontal scales. For strong stratification, the transfer spectra and eddy viscosities maintain this structure if there is synoptic-scale motion and the buoyancy scale is adequately resolved. This has been confirmed for global Rossby and Froude numbers of O(0.1). Implications for atmospheric and oceanic modeling are discussed. [ABSTRACT FROM AUTHOR]

There is a growing interest in understanding the role that moisture plays in atmospheric dynamics, particularly in its effect on predictability. Current research indicates that when moisture effects are added to an atmospheric model, the error growth produced by the new moist dynamics reduces the predictability times, especially at the scales of moist convection. The issue of moist convection’s effect on predictability is addressed herein. By performing high-resolution large-ensemble runs, it is shown that although nonprecipitating moist convection is less predictable than dry convection resulting from the same forcing, this effect can be explained by the energy injected into the system through the latent heating and cooling arising from the convective motion. This extra energy is spread evenly over most scales of the convective dynamics. When the predictability times are scaled to account for the extra kinetic energy, and the resulting earlier growth of error energy, wet and dry convection have very similar error growth characteristics. Sensitivity tests are performed to ensure that the results from the large ensembles have converged and that they are consistent with either changing resolution, diffusion levels, initial error energy length scales, or forcing amplitude. [ABSTRACT FROM AUTHOR]

The influence of the aspect ratio on the three-dimensionalization and subsequent saturation of freely decaying two-dimensional turbulence is studied numerically. We show that the aspect ratio strongly affects the saturation level of the perturbation and its feedback on the base flow. The saturation level scales linearly with the aspect ratio, as does the total damping exerted by the perturbation. In spectral space the feedback yields a positive eddy viscosity at large scales and a small eddy viscosity at small scales. A surprising result is the persistence of coherent vortices even after the saturation of the perturbation. [ABSTRACT FROM AUTHOR]

The three-dimensionalization of freely-decaying two-dimensional turbulence is studied numerically. Using two different basic states, it is shown that the hyperbolic instability of steady mixing layers generalizes to unsteady flow. The growth of three-dimensional (3D) perturbations is interpreted in terms of a “pressureless” analysis in which horizontal pressure gradients are neglected and the underlying physical mechanism is advective in nature. For a steady, pressureless base flow the (asymptotic) growth rate is exactly determined, in a few special cases, by variants of the so-called Weiss criterion; more generally, local growth rate estimates are obtained. For freely-decaying two-dimensional turbulence there is analogous behavior: while the 3D perturbation remains small the pressureless approximation holds at large horizontal scales and local growth rate estimates apply. The pressureless modes have a determining influence on the growth (the damping effect of the horizontal pressure gradient is small). © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The goal of this work is to answer the question of whether nonuniformity in the spatial distribution of sizes and positions of cloud droplets and/or variable vertical velocity in a turbulent medium can contribute to the broadening of the droplet size distribution. A numerical approach to simulate the growth and trajectory of several tens of thousands of cloud droplets in a turbulent environment whose properties vary from droplet to droplet is used. The finite inertia of particles in a turbulent fluid causes particles to diverge from regions of high vorticity and to converge preferentially in regions of low vorticity, thus creating strong deviations in particle concentration. As a first step, the inertia effect was examined in the context of nongrowing, sedimenting, or nonsedimenting droplets. It was found that statistically significant preferential concentration is possible in conditions typical of cloud droplets in cumulus clouds. In the absence of sedimentation, preferential concentration increases as a function of the Stokes number S[sub t]. Allowing the droplets to sediment decreases preferential concentration to a degree that increases with the velocity ratio S[sub υ]. A series of experiments including condensational growth of droplets was then performed. It was found that while the increasing preferential concentration of droplets, as a result of increasing eddy dissipation rate, does result in increases in the instantaneous dispersion of the supersaturation perturbation distribution, the width of the size distribution of droplets, which is a function of the dispersion in the time integral of the supersaturation perturbations, decreases. This result is a consequence of the decrease in decorrelation time of the supersaturation perturbations as the turbulence intensity increases. Comparison of the results herein with the observations made in quasi-adiabatic cloud cores leads one to the conclusion that the microscopic approach, even under... [ABSTRACT FROM AUTHOR]

No Abstract available. [ABSTRACT FROM AUTHOR]