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Szymon P. Malinowski and Isztar Zawadzki

Abstract

The cloud–environment mixing process is considered in terms of fractal properties of the cloud-clear air interface. The fractal dimension of the cloud surface is estimated from high-resolution airborne data. The value obtained is D = 2.55 in a range of scales from at least 10 m to over 1000 m with the possibility of even greater extension. This differs significantly from values obtained in shear-generated, well-developed, and homogeneous turbulence. The distribution of filament sizes of cloudy and clear air and estimates of the cloud surface and characteristic time of mixing process are given.

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Szymon P. Malinowski and Hanna Pawlowska-Mankiewicz

Abstract

The existence small-scale inhomogeneities in cumulus clouds leads to a reinterpretation of the experimental data on total water mixing ratio Q and wet equivalent potential temperature θq. This reinterpretation indicates that the height of the level of entrained air may be sometimes overestimated.

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H. Gerber, Szymon P. Malinowski, and Haflidi Jonsson

Abstract

Buoyancy reversal by evaporative cooling in entrainment holes has a minimal influence on stratocumulus (Sc) observed during the Physics of Stratocumulus Top (POST) aircraft field study held off the California coast in 2008. High-resolution temperature and microphysics measurements show only small differences for Sc with and without buoyancy reversal predicted by mixing fraction analysis that relates mixtures of cloudy air and free-atmospheric air to buoyancies of the mixtures. The reduction of LWC due to evaporation in the holes is a small percentage (average ~12%) of liquid water diluted in the Sc by entrainment from the entrainment interface layer (EIL) located above unbroken cloud top where most mixing, evaporation, and reduction of the large buoyancy jump between the cloud and free atmosphere occur. Entrainment is dominated by radiative cooling at cloud top.

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Szymon P. Malinowski, Monique Y. Leclerc, and Darrel G. Baumgardner

Abstract

Fractal analyses of individual cloud droplet distributions using aircraft measurements along one-dimensional horizontal cross sections through clouds are performed. Box counting and cluster analyses are used to determine spatial scales of inhomogeneity of cloud droplet spacing. These analyses reveal that droplet spatial distributions do not exhibit a fractal behavior. A high variability in local droplet concentration in cloud volumes undergoing mixing was found. In these regions, thin filaments of cloudy air with droplet concentration close to those observed in cloud cores were found. Results suggest that these filaments may be anisotropic. Additional box counting analyses performed for various classes of cloud droplet diameters indicate that large and small droplets are similarly distributed, except for the larger characteristic spacing of large droplets.

A cloud-clear air interface defined by a certain threshold of total droplet count (TDC) was investigated. There are indications that this interface is a convoluted surface of a fractal nature, at least in actively developing cumuliform clouds. In contrast, TDC in the cloud interior does not have fractal or multifractal properties. Finally a random Cantor set (RCS) was introduced as a model of a fractal process with an ill-defined internal scale. A uniform measure associated with the RCS after several generations was introduced to simulate the TDC records. Comparison of the model with real TDC records indicates similar properties of both types of data series.

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Miroslaw Andrejczuk, Wojciech W. Grabowski, Szymon P. Malinowski, and Piotr K. Smolarkiewicz

Abstract

This note presents an analysis of several dozens of direct numerical simulations of the cloud–clear air mixing in a setup of decaying moist turbulence with bin microphysics. The goal is to assess the instantaneous relationship between the homogeneity of mixing and the ratio of the time scales of droplet evaporation and turbulent homogenization. Such a relationship is important for developing improved microphysical parameterizations for large-eddy simulation of clouds. The analysis suggests a robust relationship for the range of time scale ratios between 0.5 and 10. Outside this range, the scatter of numerical data is significant, with smaller and larger time scale ratios corresponding to mixing scenarios that approach the extremely inhomogeneous and homogeneous limits, respectively. This is consistent with the heuristic argument relating the homogeneity of mixing to the time scale ratio.

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Miroslaw Andrejczuk, Wojciech W. Grabowski, Szymon P. Malinowski, and Piotr K. Smolarkiewicz

Abstract

This paper extends the previously published numerical study of Andrejczuk et al. on microscale cloud–clear air mixing. Herein, the primary interest is on microphysical transformations. First, a convergence study is performed—with well-resolved direct numerical simulation of the interfacial mixing in the limit—to optimize the design of a large series of simulations with varying physical parameters. The principal result is that all conclusions drawn from earlier low-resolution (Δx = 10−2 m) simulations are corroborated by the high-resolution (Δx = 0.25 × 10−2 m) calculations, including the development of turbulent kinetic energy (TKE) and the evolution of microphysical properties. This justifies the use of low resolution in a large set of sensitivity simulations, where microphysical transformations are investigated in response to variations of the initial volume fraction of cloudy air, TKE input, liquid water mixing ratio in cloudy filaments, relative humidity (RH) of clear air, and size of cloud droplets. The simulations demonstrate that regardless of the initial conditions the evolutions of the number of cloud droplets and the mean volume radius follow a universal path dictated by the TKE input, RH of clear air filaments, and the mean size of cloud droplets. The resulting evolution path only weakly depends on the progress of the homogenization. This is an important conclusion because it implies that a relatively simple rule can be developed for representing the droplet-spectrum evolution in cloud models that apply parameterized microphysics. For the low-TKE input, when most of the TKE is generated by droplet evaporation during mixing and homogenization, an inhomogeneous scenario is observed with approximately equal changes in the dimensionless droplet number and mean volume radius cubed. Consistent with elementary scale analysis, higher-TKE inputs, higher RH of cloud-free filaments, and larger cloud droplets enhance the homogeneity of mixing. These results are discussed in the context of observations of entrainment and mixing in natural clouds.

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Emmanuel O. Akinlabi, Marta Wacławczyk, Juan Pedro Mellado, and Szymon P. Malinowski

Abstract

In this work, direct numerical simulation (DNS) of the stratocumulus cloud-top mixing layer is used to test various approaches to estimate the turbulence kinetic energy (TKE) dissipation rate ε from one-dimensional (1D) intersections that resemble experimental series. Results of these estimates are compared with “true” (DNS) values of ε in buoyant and inhomogeneous atmospheric flows. We focus on recently proposed methods of the TKE dissipation-rate retrievals based on zero crossings and recovering the missing part of the spectrum. These methods are tested on fully resolved turbulence fields and compared to standard retrievals from power spectra and structure functions. Anisotropy of turbulence due to buoyancy is shown to influence retrievals based on the vertical velocity component. TKE dissipation-rate estimates from the number of crossings correspond well to spectral estimates. The method based on the recovery of the missing part of the spectrum works best for Pope’s model of the dissipation spectrum and is sensitive to external intermittency. This allows for characterization of external intermittency by the Taylor-to-Liepmann scale ratio. Further improvements of this method are possible when the variance of the velocity derivative is used instead of the number of zero crossings per unit length. In conclusion, the new methods of TKE dissipation-rate retrieval from 1D series provide a valuable complement to standard approaches.

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Yong-Feng Ma, Szymon P. Malinowski, Katarzyna Karpińska, Hermann E. Gerber, and Wojciech Kumala

Abstract

The authors have analyzed the scaling behavior of marine boundary layer (MBL) clouds using high-resolution temperature (T) and liquid water content (LWC) fluctuations from aircraft measurements collected over the Pacific Ocean during the Physics of Stratocumulus Top (POST) research campaign in summer of 2008. As an extension of the past studies for scale-invariant properties of MBL clouds, the authors studied the variability of scaling exponents with height. The results showed that both LWC and T have two distinct scaling regimes: the first one displays scale invariance over a range from about 1–5 m to at least 7 km, and the second one goes from about 0.1–1 to 1–5 m. For the large-scale regime (r > 1–5 m), turbulence in MBL clouds is multifractal, while scale break and scaling exponents vary with height, most significantly in the cloud-top region. For example, LWC spectral exponent β increases from 1.42 at cloud base to 1.58 at cloud top, while scale break decreases from ~5 m at cloud base to 0.8 m at cloud top. The bifractal parameters (H 1, C 1) for LWC increase from (0.14, 0.02) at cloud base to (0.33, 0.1) at cloud top while maintaining a statistically significant linear relationship C 1 ≈ 0.4H 1 − 0.04 in MBL clouds. From near surface to cloud top, (H 1, C 1) for T also increase with height, but above cloud top H 1 increases and C 1 decreases with height. The results suggest the existence of three turbulence regimes: near the surface, in the middle of the boundary layer, and in the cloud-top region, which need to be distinguished.

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MirosŁaw Andrejczuk, Wojciech W. Grabowski, Szymon P. Malinowski, and Piotr K. Smolarkiewicz

Abstract

This paper discusses results from a series of direct numerical simulations of the microscale cloud–clear air mixing, set forth in the idealized scenario of decaying moist turbulence. In the moist case, kinetic energy of microscale motions comes not only from the classical downscale energy cascade, but it can also be generated internally due to the evaporation of cloud droplets. Three sets of numerical simulations are performed for three intensities of initial large-scale eddies. In each set, a control dry simulation is performed, as well as two moist simulations applying either bulk or detailed representation of cloud microphysics.

Model results suggest that, as far as the evolutions of enstrophy and turbulent kinetic energy are concerned, the most significant impact of moist processes occurs at the low intensity of initial large-scale eddies (the input turbulent kinetic energy of 2 × 10−4 m2 s−2 resulting in the maximum eddy dissipation rate of 5 × 10−4 m2 s−3). In such a case, mixing and homogenization are dominated by the kinetic energy generated as a result of evaporation of cloud water and its impact on the microscale buoyancy. Detailed microphysics, which explicitly treat the size dependence of cloud droplet sedimentation and evaporation, appear to have a comparatively small effect, although this result might be an artifact of a coarse grid resolution used in the simulations. High anisotropy, also observed in laboratory experiments with mixing between cloudy and cloud-free air, prevails even at the high intensity of initial large-scale eddies (the input turbulent kinetic energy of 2 × 10−2 m2 s−2, the maximum eddy dissipation rate of 7 × 10−3 m2 s−3), despite the fact that mixing and homogenization proceed in a similar manner in moist and dry simulations.

Impact on cloud microphysics is also quantified. Cloud droplet spectra at the end of simulations correspond to neither the extremely inhomogeneous nor homogeneous mixing scenarios—the two asymptotic limits where, respectively, either the cloud droplet size or the number of cloud droplets remain constant. The shift from low to high intensity of initial large-scale eddies shifts the mixing scenario toward the homogeneous case, corroborating the classical argument based on scale analysis.

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