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Vishnu Nair, Thijs Heus, and Maarten van Reeuwijk

Abstract

The dynamics of a subsiding shell at the edges of actively growing shallow cumulus clouds with updrafts is analyzed using direct numerical simulation. The actively growing clouds have a fixed in-cloud buoyancy and velocity. Turbulent mixing and evaporative cooling at the cloud edges generate a subsiding shell that grows with time. A self-similar regime is observed for first- and second-order moments when normalized with respective maximum values. Internal scales derived from integral properties of the flow problem are identified. A self-similarity analysis using these scales reveals that contrary to classical self-similar flows, the turbulent kinetic energy budget terms and velocity moments scale according to the buoyancy and not with the mean velocity. The shell thickness is observed to increase linearly with time. The buoyancy scale remains time invariant and is set by the initial cloud–environment thermodynamics. The shell accelerates ballistically with a magnitude set by the saturation value of the buoyancy of the cloud–environment mixture. In this regime, the shell is buoyancy driven and independent of the in-cloud velocity. Relations are obtained for predicting the shell thickness and minimum velocities by linking the internal scales with external flow parameters. The values thus calculated are consistent with the thickness and velocities observed in typical shallow cumulus clouds. The entrainment coefficient is a function of the initial state of the cloud and the environment, and is shown to be on the same order of magnitude as fractional entrainment rates calculated for large-scale models.

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Dick Abma, Thijs Heus, and Juan Pedro Mellado

Abstract

This study investigates the dynamics of the subsiding shell at the lateral boundary of cumulus clouds, focusing on the role of evaporative cooling. Since the size of this shell is well below what large-eddy simulations can resolve, the authors have performed direct numerical simulations of an idealized subsiding shell. The system develops a self-similar, Reynolds number–independent flow that allows for the determination of explicit scaling laws relating the characteristic length, time, and velocity scales of the shell. It is found that the shell width grows quadratically in time, linearly with the traveled distance. The magnitude of these growth rates shows that evaporative cooling, in its most idealized form, is capable of producing a fast-growing shell with numbers that are consistent with observations of the subsiding shell around real shallow cumulus clouds: for typical thermodynamic conditions in cumulus clouds, a velocity on the order of 1 m s−1 and a thickness on the order of 10 m are established in about 2 min. This fits well within the typical cloud lifetime, suggesting that this idealization is an adequate framework for the analysis of relevant aspects in the subsiding shell associated with buoyancy reversal. It also indicates that the scaling laws derived here can be used to estimate the potential strength of a subsiding shell and the mean lateral entrainment associated with it, once an estimate of the local thermodynamical state of the cloud boundary is provided. It is shown that the dominant parameter of this system is the saturation buoyancy, whereas the effect of the saturation mixing fraction is minor.

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Thijs Heus and Harm J. J. Jonker

Abstract

In this study large-eddy simulations (LES) are used to gain more knowledge on the shell of subsiding air that is frequently observed around cumulus clouds. First, a detailed comparison between observational and numerical results is presented to better validate LES as a tool for studies of microscale phenomena. It is found that horizontal cloud profiles of vertical velocity, humidity, and temperature are in good agreement with observations. They show features similar to the observations, including the presence of the shell of descending air around the cloud. Second, the availability of the complete 3D dataset in LES has been exploited to examine the role of lateral mixing in the exchange of cloud and environmental air. The origin of the subsiding shell is examined by analyzing the individual terms of the vertical momentum equation. Buoyancy is found to be the driving force for this shell, and it is counteracted by the pressure-gradient force. This shows that evaporative cooling at the cloud edge, induced by lateral mixing of cloudy and environmental air, is the responsible mechanism behind the descending shell. For all clouds, and especially the smaller ones, the negative mass flux generated by the subsiding shell is significant. This suggests an important role for lateral mixing throughout the entire cloud layer. The role of the shell in these processes is further explored and described in a conceptual three-layer model of the cloud.

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Mohamed S. Ghonima, Joel R. Norris, Thijs Heus, and Jan Kleissl

Abstract

A detailed derivation of stratocumulus cloud thickness and liquid water path tendencies as a function of the well-mixed boundary layer mass, heat, and moisture budget equations is presented. The derivation corrects an error in the cloud thickness tendency equation derived by R. Wood to make it consistent with the liquid water path tendency equation derived by J. J. van der Dussen et al. The validity of the tendency equations is then tested against the output of large-eddy simulations of a typical stratocumulus-topped boundary layer case and is found to be in good agreement.

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Mohamed S. Ghonima, Thijs Heus, Joel R. Norris, and Jan Kleissl

Abstract

The breakup of stratocumulus clouds over coastal land areas is studied using a combination of large-eddy simulations (LESs) and mixed-layer models (MLMs) with a focus on mechanisms regulating the timing of the breakup. In contrast with stratocumulus over ocean, strong sensible heat flux over land prevents the cloud layer from decoupling during day. As the cloud thins during day, turbulence generated by surface flux becomes larger than turbulence generated by longwave cooling across the cloud layer. To capture this shift in turbulence generation in the MLM, an existing entrainment parameterization is extended. The MLM is able to mimic cloud evolution for a variety of Bowen ratios, but only after this modification of the entrainment parameterization. Cloud lifetime depends on a combination of the cloud-top entrainment flux, the Bowen ratio of the surface, and the strength of advection of cool ocean air by the sea breeze. For dry land surface conditions, the authors’ MLM suggests a breakup time a few hours after sunrise. For relatively wet land surface conditions, the cloud layer briefly breaks into partly cloudy conditions during midday, and the stratocumulus cloud reforms in the evening.

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Jeannine Katzwinkel, Holger Siebert, Thijs Heus, and Raymond A. Shaw

Abstract

High-resolution measurements of the turbulent, thermodynamic, and microphysical structure of the edges of trade wind cumuli have been performed with the Airborne Cloud Turbulence Observation System. Lateral entrainment of subsaturated air into the cloud region leads to an evaporative cooling effect. The negatively buoyant air partly enhances the compensating downdraft, forming a subsiding shell at cloud edge. Based on the presented observations, the subsiding shell is divided into a turbulent and humid inner shell adjacent to the cloud interior and a nonbuoyant, nonturbulent outer shell. In the trade wind region, continuous development of shallow cumuli over the day allows for an analysis of the properties of both shells as a function of different cloud evolution stages. The shallow cumuli are divided into actively growing, decelerated, and dissolving based on cloud properties. As the cumuli evolve from actively growing to dissolving, the subsaturated environmental air is mixed deeper and deeper into the cloud region and the subsiding shell grows at the expense of the cloud. This measured evolution of the subsiding shell compares favorably with the predictions of a direct numerical simulation of an idealized subsiding shell. The thickness of the measured outer shell decreases with the evolution of the cumuli while the intensity of the downdraft is nearly constant.

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Thijs Heus, Gertjan van Dijk, Harm J. J. Jonker, and Harry E. A. Van den Akker

Abstract

Mixing between shallow cumulus clouds and their environment is studied using large-eddy simulations. The origin of in-cloud air is studied by two distinct methods: 1) by analyzing conserved variable mixing diagrams (Paluch diagrams) and 2) by tracing back cloud-air parcels represented by massless Lagrangian particles that follow the flow. The obtained Paluch diagrams are found to be similar to many results in the literature, but the source of entrained air found by particle tracking deviates from the source inferred from the Paluch analysis. Whereas the classical Paluch analysis seems to provide some evidence for cloud-top mixing, particle tracking shows that virtually all mixing occurs laterally. Particle trajectories averaged over the entire cloud ensemble also clearly indicate the absence of significant cloud-top mixing in shallow cumulus clouds.

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Virendra P. Ghate, Pavlos Kollias, Susanne Crewell, Ann M. Fridlind, Thijs Heus, Ulrich Löehnert, Maximilian Maahn, Greg M. McFarquhar, Dmitri Moisseev, Mariko Oue, Manfred Wendisch, and Christopher Williams
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