Local similarity in the stable boundary layer and mixing-length approaches: consistency of concepts

In stably stratified flows vertical movement of eddies is limited by the fact that kinetic energy is converted into potential energy, leading to a buoyancy displacement scale z B . Our new mixing-length concept for turbulent transport in the stable boundary layer follows a rigid-wall analogy, in the sense that we assume that the buoyancy length scale is similar to neutral length scaling. This implies that the buoyancy length scale is: ¿ B = ¿ B z B , with ¿ B ¿ ¿, the von Karman constant. With this concept it is shown that the physical relevance of the local scaling parameter z/¿ naturally appears, and that the ¿ coefficient of the log-linear similarity functions is equal to c/¿ 2, where c is a constant close to unity. The predicted value ¿ ¿ 1/¿ 2 = 6.25 lies within the range found in observational studies. Finally, it is shown that the traditionally used inverse linear interpolation between the mixing length in the neutral and buoyancy limits is inconsistent with the classical log-linear stability functions. As an alternative, a log-linear consistent interpolation method is proposed

Turbulent dispersion in cloud-topped boundary layers

Compared to dry boundary layers, dispersion in cloud-topped boundary layers has received less attention. In this LES based numerical study we investigate the dispersion of a passive tracer in the form of Lagrangian particles for four kinds of atmospheric boundary layers: 1) a dry convective boundary layer (for reference), 2) a "smoke" cloud boundary layer in which the turbulence is driven by radiative cooling, 3) a stratocumulus topped boundary layer and 4) a shallow cumulus topped boundary layer. We show that the dispersion characteristics of the smoke cloud boundary layer as well as the stratocumulus situation can be well understood by borrowing concepts from previous studies of dispersion in the dry convective boundary layer. A general result is that the presence of clouds enhances mixing and dispersion ¿ a notion that is not always reflected well in traditional parameterization models, in which clouds usually suppress dispersion by diminishing solar irradiance. The dispersion characteristics of a cumulus cloud layer turn out to be markedly different from the other three cases and the results can not be explained by only considering the well-known top-hat velocity distribution. To understand the surprising characteristics in the shallow cumulus layer, this case has been examined in more detail by 1) determining the velocity distribution conditioned on the distance to the nearest cloud and 2) accounting for the wavelike behaviour associated with the stratified dry environmen

Stochastic parameterization of shallow cumulus convection estimated from high-resolution data

In this paper, we report on the development of a methodology for stochastic parameterization of convective transport by shallow cumulus convection in weather and climate models. We construct a parameterization based on Large-Eddy Simulation (LES) data. These simulations resolve the turbulent fluxes of heat and moisture and are based on a typical case of non-precipitating shallow cumulus convection above sea in the trade-wind region. Using clustering, we determine a finite number of turbulent flux pairs for heat and moisture that are representative for the pairs of flux profiles observed in these simulations. In the stochastic parameterization scheme proposed here, the convection scheme jumps randomly between these pre-computed pairs of turbulent flux profiles. The transition probabilities are estimated from the LES data, and they are conditioned on the resolved-scale state in the model column. Hence, the stochastic parameterization is formulated as a data-inferred conditional Markov chain (CMC), where each state of the Markov chain corresponds to a pair of turbulent heat and moisture fluxes. The CMC parameterization is designed to emulate, in a statistical sense, the convective behaviour observed in the LES data. The CMC is tested in single-column model (SCM) experiments. The SCM is able to reproduce the ensemble spread of the temperature and humidity that was observed in the LES data. Furthermore, there is a good similarity between time series of the fractions of the discretized fluxes produced by SCM and observed in LES

Stochastic Parameterization of Convective Area Fractions with a Multicloud Model Inferred from Observational Data

Observational data of rainfall from a rain radar in Darwin, Australia, are combined with data defining the large-scale dynamic and thermodynamic state of the atmosphere around Darwin to develop a multicloud model based on a stochastic method using conditional Markov chains. The authors assign the radar data to clear sky, moderate congestus, strong congestus, deep convective, or stratiform clouds and estimate transition probabilities used by Markov chains that switch between the cloud types and yield cloud-type area fractions. Cross-correlation analysis shows that the mean vertical velocity is an important indicator of deep convection. Further, it is shown that, if conditioned on the mean vertical velocity, the Markov chains produce fractions comparable to the observations. The stochastic nature of the approach turns out to be essential for the correct production of area fractions. The stochastic multicloud model can easily be coupled to existing moist convectio

Variability of Optical Counterparts in the Chandra Galactic Bulge Survey

Contains fulltext : 132445.pdf (preprint version ) (Open Access

Lagrangian Droplet Dynamics in the Subsiding Shell of a Cloud Using Direct Numerical Simulations

This study investigates the droplet dynamics at the lateral cloud–environment interface in shallow cumulus clouds. A mixing layer is used to study a small part of the cloud edge using direct numerical simulation combined with a Lagrangian particle tracking and collision algorithm. The effect of evaporation, gravity, coalescence, and the initial droplet size distribution on the intensity of the mixing layer and the evolution of the droplet size distribution is studied. Mixing of the droplets with environmental air induces evaporative cooling, which results in a very characteristic subsiding shell. As a consequence, stronger horizontal velocity gradients are found in the mixing layer, which induces more mixing and evaporation. A broadening of the droplet size distribution is observed as a result of evaporation and coalescence. Gravity acting on the droplets allows droplets in cloudy filaments detrained from the cloud to sediment and remain longer in the unsaturated environment. While this effect of gravity did not have a significant impact in this case on the mean evolution of the mixing layer, it does contribute to the broadening of the droplet size distribution and thereby significantly increases the collision rate. Although more but smaller droplets result in more evaporative cooling, more droplets also increase small-scale fluctuations and the production of turbulent dissipation. For the smallest droplets considered with a radius of 10 mm, the authors found that, although a more pronounced buoyancy dip was present, the increase in dissipation rate actually led to a decrease in the turbulent intensity of the mixing layer. Extrapolation of the results to realistic clouds is discussed.Geoscience and Remote SensingCivil Engineering and Geoscience

Preferred location of droplet collisions in turbulent flows

This study investigates the local flow characteristics near droplet-droplet collisions by means of direct numerical simulation of isotropic cloudlike turbulence. The key finding is that, generally, droplets do not collide where they preferentially concentrate. Preferential concentration is found to happen as expected in regions of low enstrophy (vorticity magnitude), but collisions tend to take place in regions with significantly higher dissipation rates (up to a factor of 2.5 for Stokes unity droplets). Investigation of the droplet history reveals that collisions are consistently preceded by dissipative events. Based on the droplet history data, the following physical picture of a collision can be constructed: Enstrophy makes droplets preferentially concentrate in quiescent flow regions, thereby increasing the droplet velocity coherence, i.e., decreasing relative velocities between droplets. Strongly clustered droplets thus have a low collision probability, until a dissipative event accelerates the droplets towards each other. We study the relation between the local dissipation rate and the local collision kernel and vary the averaging scale to relate the results to the globally averaged collision and dissipation rates. It is noted that, unlike enstrophy, there is a positive correlation between the dissipation rate and collision efficiency that extends from the largest to the smallest scales of the flow.Geoscience & Remote SensingCivil Engineering and Geoscience