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- Author or Editor: Raymond A. Shaw x
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Abstract
It is hypothesized that bursts of high supersaturation are produced in turbulent, convective clouds through interactions between cloud droplets and the small-scale structure of atmospheric turbulence. This hypothesis is based on the observation that intermittency in the energy dissipation of turbulence at small scales is, in part, related to the presence of rare but intense vortex tubes. Scaling relationships for the size, lifetime, and intensity of vortex tubes observed in numerical simulations and laboratory studies of turbulence are presumed to hold at the high Reynolds numbers encountered in the atmosphere. Under this assumption a scale analysis shows that the tubes are sufficiently intense and persistent as to cause large flux divergences in the local concentrations of cloud droplets. When embedded in a mean updraft, a vortex tube will become a localized region of high supersaturation due to the low number concentration of cloud droplets (condensation sites). For typical cumulus conditions, water supersaturations may reach values of over 10% in the core of a vortex tube. Upon vortex breakdown, the localized regions of high supersaturation will lead to the formation of small concentrations of“superadiabatic” droplets in clouds. Finally, a threshold condition for this mechanism is derived and shown to be related to the droplet size distribution and the turbulent kinetic energy dissipation rate, both of which are commonly measured or calculated quantities in cloud field studies and cloud models. When the threshold condition is met, the concentration of superadiabatic droplets is expected to increase approximately linearly with height above cloud base.
Abstract
It is hypothesized that bursts of high supersaturation are produced in turbulent, convective clouds through interactions between cloud droplets and the small-scale structure of atmospheric turbulence. This hypothesis is based on the observation that intermittency in the energy dissipation of turbulence at small scales is, in part, related to the presence of rare but intense vortex tubes. Scaling relationships for the size, lifetime, and intensity of vortex tubes observed in numerical simulations and laboratory studies of turbulence are presumed to hold at the high Reynolds numbers encountered in the atmosphere. Under this assumption a scale analysis shows that the tubes are sufficiently intense and persistent as to cause large flux divergences in the local concentrations of cloud droplets. When embedded in a mean updraft, a vortex tube will become a localized region of high supersaturation due to the low number concentration of cloud droplets (condensation sites). For typical cumulus conditions, water supersaturations may reach values of over 10% in the core of a vortex tube. Upon vortex breakdown, the localized regions of high supersaturation will lead to the formation of small concentrations of“superadiabatic” droplets in clouds. Finally, a threshold condition for this mechanism is derived and shown to be related to the droplet size distribution and the turbulent kinetic energy dissipation rate, both of which are commonly measured or calculated quantities in cloud field studies and cloud models. When the threshold condition is met, the concentration of superadiabatic droplets is expected to increase approximately linearly with height above cloud base.
Abstract
Water phase transitions are central to climate and weather. Yet it is a common experience that the principles of phase equilibrium are challenging to understand and teach. A simple mechanical analogy has been developed to demonstrate key principles of liquid evaporation and the temperature dependence of equilibrium vapor pressure. The system is composed of a circular plate with a central depression and several hundred metal balls. Mechanical agitation of the plate causes the balls to bounce and interact in much the same statistical way that molecules do in real liquid–vapor systems. The data, consisting of the number of balls escaping the central well at different forcing energies, exhibit a logarithmic dependence on the reciprocal of the applied energy (analogous to thermal energy k B T) that is similar to that given by Boltzmann statistics and the Clausius–Clapeyron equation. These results demonstrate that the enthalpy (i.e., latent heat) of evaporation is well interpreted as the potential energy difference between molecules in the vapor and liquid phases, and it is the fundamental driver of vapor pressure increase with temperature. Consideration of the uncertainties in the measurements shows that the mechanical system is described well by Poisson statistics. The system is simple enough that it can be duplicated for qualitative use in atmospheric science teaching, and an interactive animation based on the mechanical system is available online for instructional use (http://phy.mtu.edu/vpt/).
Abstract
Water phase transitions are central to climate and weather. Yet it is a common experience that the principles of phase equilibrium are challenging to understand and teach. A simple mechanical analogy has been developed to demonstrate key principles of liquid evaporation and the temperature dependence of equilibrium vapor pressure. The system is composed of a circular plate with a central depression and several hundred metal balls. Mechanical agitation of the plate causes the balls to bounce and interact in much the same statistical way that molecules do in real liquid–vapor systems. The data, consisting of the number of balls escaping the central well at different forcing energies, exhibit a logarithmic dependence on the reciprocal of the applied energy (analogous to thermal energy k B T) that is similar to that given by Boltzmann statistics and the Clausius–Clapeyron equation. These results demonstrate that the enthalpy (i.e., latent heat) of evaporation is well interpreted as the potential energy difference between molecules in the vapor and liquid phases, and it is the fundamental driver of vapor pressure increase with temperature. Consideration of the uncertainties in the measurements shows that the mechanical system is described well by Poisson statistics. The system is simple enough that it can be duplicated for qualitative use in atmospheric science teaching, and an interactive animation based on the mechanical system is available online for instructional use (http://phy.mtu.edu/vpt/).
Abstract
On time scales that are long compared to the phase relaxation time, a quasi-steady supersaturation s qs is expected to exist in clouds. On shorter time scales, however, turbulent fluctuations of temperature and water vapor concentration should generate fluctuations in supersaturation. The variability of temperature, water vapor, and supersaturation has been measured in situ with submeter resolution in warm, continental, shallow cumulus clouds. Several cumuli with horizontal extents of order 100 m were sampled during their first appearance and development to depths of ~100 m in a growing boundary layer. Fluctuations of the saturation ratio are observed to be approximately normally distributed with standard deviations on the order of 1%. This variability is almost one order of magnitude larger than s qs calculated using simultaneous measurements of the vertical velocity component and the droplet size distribution. It is argued that, depending on the ratio of the phase relaxation and the turbulent mixing time, substantial fluctuations in the supersaturation field can exist on small spatial scales, centered on s qs for the mean state. The observations also suggest that, on larger scales, fluctuations of the supersaturation field are damped by cloud droplet growth. Droplets with diameters of up to 20 μm were observed in the shallow cumulus clouds, whereas the adiabatic diameter was less than 10 μm. Such large droplets may be explained by a few droplets experiencing the highest observed supersaturations for a certain time. Consequences for aerosol activation and droplet size dispersion in a highly fluctuating supersaturation field are briefly discussed.
Abstract
On time scales that are long compared to the phase relaxation time, a quasi-steady supersaturation s qs is expected to exist in clouds. On shorter time scales, however, turbulent fluctuations of temperature and water vapor concentration should generate fluctuations in supersaturation. The variability of temperature, water vapor, and supersaturation has been measured in situ with submeter resolution in warm, continental, shallow cumulus clouds. Several cumuli with horizontal extents of order 100 m were sampled during their first appearance and development to depths of ~100 m in a growing boundary layer. Fluctuations of the saturation ratio are observed to be approximately normally distributed with standard deviations on the order of 1%. This variability is almost one order of magnitude larger than s qs calculated using simultaneous measurements of the vertical velocity component and the droplet size distribution. It is argued that, depending on the ratio of the phase relaxation and the turbulent mixing time, substantial fluctuations in the supersaturation field can exist on small spatial scales, centered on s qs for the mean state. The observations also suggest that, on larger scales, fluctuations of the supersaturation field are damped by cloud droplet growth. Droplets with diameters of up to 20 μm were observed in the shallow cumulus clouds, whereas the adiabatic diameter was less than 10 μm. Such large droplets may be explained by a few droplets experiencing the highest observed supersaturations for a certain time. Consequences for aerosol activation and droplet size dispersion in a highly fluctuating supersaturation field are briefly discussed.
Abstract
The helicopter-borne instrument payload known as the Airborne Cloud Turbulence Observation System (ACTOS) was used to study the entrainment and mixing processes in shallow warm cumulus clouds. The characteristics of the mixing process are determined by the Damköhler number, defined as the ratio of the mixing and a thermodynamic reaction time scale. The definition of the reaction time scale is refined by investigating the relationship between the droplet evaporation time and the phase relaxation time. Following arguments of classical turbulence theory, it is concluded that the description of the mixing process through a single Damköhler number is not sufficient and instead the concept of a transition length scale is introduced. The transition length scale separates the inertial subrange into a range of length scales for which mixing between ambient dry and cloudy air is inhomogeneous, and a range for which the mixing is homogeneous. The new concept is tested on the ACTOS dataset. The effect of entrained subsaturated air on the droplet number size distribution is analyzed using mixing diagrams correlating droplet number concentration and droplet size. The data suggest that homogeneous mixing is more likely to occur in the vicinity of the cloud core, whereas inhomogeneous mixing dominates in more diluted cloud regions. Paluch diagrams are used to support this hypothesis. The observations suggest that homogeneous mixing is favored when the transition length scale exceeds approximately 10 cm. Evidence was found that suggests that under certain conditions mixing can lead to enhanced droplet growth such that the largest droplets are found in the most diluted cloud regions.
Abstract
The helicopter-borne instrument payload known as the Airborne Cloud Turbulence Observation System (ACTOS) was used to study the entrainment and mixing processes in shallow warm cumulus clouds. The characteristics of the mixing process are determined by the Damköhler number, defined as the ratio of the mixing and a thermodynamic reaction time scale. The definition of the reaction time scale is refined by investigating the relationship between the droplet evaporation time and the phase relaxation time. Following arguments of classical turbulence theory, it is concluded that the description of the mixing process through a single Damköhler number is not sufficient and instead the concept of a transition length scale is introduced. The transition length scale separates the inertial subrange into a range of length scales for which mixing between ambient dry and cloudy air is inhomogeneous, and a range for which the mixing is homogeneous. The new concept is tested on the ACTOS dataset. The effect of entrained subsaturated air on the droplet number size distribution is analyzed using mixing diagrams correlating droplet number concentration and droplet size. The data suggest that homogeneous mixing is more likely to occur in the vicinity of the cloud core, whereas inhomogeneous mixing dominates in more diluted cloud regions. Paluch diagrams are used to support this hypothesis. The observations suggest that homogeneous mixing is favored when the transition length scale exceeds approximately 10 cm. Evidence was found that suggests that under certain conditions mixing can lead to enhanced droplet growth such that the largest droplets are found in the most diluted cloud regions.
Abstract
The use of a hot-wire anemometer for high-resolution turbulence measurements in a two-phase flow (e.g., atmospheric clouds) is discussed. Experiments in a small wind tunnel (diameter of 0.2 and 2 m in length) with a mean flow velocity in the range between 5 and 16 m s−1 are performed. In the wind tunnel a spray with a liquid water content of 0.5 and 2.5 g m−3 is generated. After applying a simple despiking algorithm, power spectral analysis shows the same results as spectra observed without spray under similar flow conditions. The flattening of the spectrum at higher frequencies due to impacting droplets could be reduced significantly. The time of the signal response of the hot wire to impacting droplets is theoretically estimated and compared with observations. Estimating the fraction of time during which the velocity signal is influenced by droplet spikes, it turns out that the product of liquid water content and mean flow velocity should be minimized. This implies that for turbulence measurements in atmospheric clouds, a slowly flying platform such as a balloon or helicopter is the appropriate instrumental carrier. Examples of hot-wire anemometer measurements with the helicopter-borne Airborne Cloud Turbulence Observation System (ACTOS) are presented.
Abstract
The use of a hot-wire anemometer for high-resolution turbulence measurements in a two-phase flow (e.g., atmospheric clouds) is discussed. Experiments in a small wind tunnel (diameter of 0.2 and 2 m in length) with a mean flow velocity in the range between 5 and 16 m s−1 are performed. In the wind tunnel a spray with a liquid water content of 0.5 and 2.5 g m−3 is generated. After applying a simple despiking algorithm, power spectral analysis shows the same results as spectra observed without spray under similar flow conditions. The flattening of the spectrum at higher frequencies due to impacting droplets could be reduced significantly. The time of the signal response of the hot wire to impacting droplets is theoretically estimated and compared with observations. Estimating the fraction of time during which the velocity signal is influenced by droplet spikes, it turns out that the product of liquid water content and mean flow velocity should be minimized. This implies that for turbulence measurements in atmospheric clouds, a slowly flying platform such as a balloon or helicopter is the appropriate instrumental carrier. Examples of hot-wire anemometer measurements with the helicopter-borne Airborne Cloud Turbulence Observation System (ACTOS) are presented.
After the initial rapid growth by condensation, further growth of a cloud droplet is punctuated by coalescence events. Such a growth process is essentially stochastic. Yet, computational approaches to this problem dominate and transparent quantitative theory remains elusive. The stochastic coalescence problem is revisited and it is shown, via simple back-of-the-envelope results, that regardless of the initial size, the fastest one-in-a-million droplets, required for warm rain initiation, grow about 10 times faster than the average droplet. While approximate, the development presented herein is based on a realistic expression for the rate of coalescence. The results place a lower bound on the relative velocity of neighboring droplets, necessary for warm rain initiation. Such velocity differences may arise from a variety of physical mechanisms. As an example, turbulent shear is considered and it is argued that even in the most pessimistic case of a cloud composed of single-sized droplets, rain can still form in 30 min under realistic conditions. More importantly, this conclusion is reached without having to appeal to giant nuclei or droplet clustering, only occasional “fast eddies.” This is so because, combined with the factor of 10 accelerated growth of the one-in-a-million fastest droplets, the traditional turbulent energy cascade provides sufficient microshear at interdroplet scales to initiate warm rain in cumulus clouds within the observed times of about 30 min. The simple arguments presented here are readily generalized for a variety of time scales, drizzle production, and other coagulation processes.
After the initial rapid growth by condensation, further growth of a cloud droplet is punctuated by coalescence events. Such a growth process is essentially stochastic. Yet, computational approaches to this problem dominate and transparent quantitative theory remains elusive. The stochastic coalescence problem is revisited and it is shown, via simple back-of-the-envelope results, that regardless of the initial size, the fastest one-in-a-million droplets, required for warm rain initiation, grow about 10 times faster than the average droplet. While approximate, the development presented herein is based on a realistic expression for the rate of coalescence. The results place a lower bound on the relative velocity of neighboring droplets, necessary for warm rain initiation. Such velocity differences may arise from a variety of physical mechanisms. As an example, turbulent shear is considered and it is argued that even in the most pessimistic case of a cloud composed of single-sized droplets, rain can still form in 30 min under realistic conditions. More importantly, this conclusion is reached without having to appeal to giant nuclei or droplet clustering, only occasional “fast eddies.” This is so because, combined with the factor of 10 accelerated growth of the one-in-a-million fastest droplets, the traditional turbulent energy cascade provides sufficient microshear at interdroplet scales to initiate warm rain in cumulus clouds within the observed times of about 30 min. The simple arguments presented here are readily generalized for a variety of time scales, drizzle production, and other coagulation processes.
Supplement to: Fluctuations and Luck in Droplet Growth by Coalescence
Obtaining the Drop Size Distribution
Abstract
The entrainment of clear air and its subsequent mixing with a filament of cloudy air, as occurs at the edge of a cloud, is studied in three-dimensional direct numerical simulations that combine the Eulerian description of the turbulent velocity, temperature, and vapor fields with a Lagrangian cloud droplet ensemble. Forced and decaying turbulence is considered, such as when the dynamics around the filament is driven by larger-scale eddies or during the final period of the life cycle of a cloud. The microphysical response depicted in n d − 〈r 3〉 space (where n d and r are droplet number density and radius, respectively) shows characteristics of both homogeneous and inhomogeneous mixing, depending on the Damköhler number. The transition from inhomogeneous to homogeneous mixing leads to an offset of the homogeneous mixing curve to larger dilution fractions. The response of the system is governed by the smaller of the single droplet evaporation time scale and the bulk phase relaxation time scale. Variability within the n d − 〈r 3〉 space increases with decreasing sample volume, especially during the mixing transients. All of these factors have implications for the interpretation of measurements in clouds. The qualitative mixing behavior changes for forced versus decaying turbulence, with the latter yielding remnant patches of unmixed cloud and stronger fluctuations. Buoyancy due to droplet evaporation is observed to play a minor role in the mixing for the present configuration. Finally, the mixing process leads to the transient formation of a pronounced nearly exponential tail of the probability density function of the Lagrangian supersaturation, and a similar tail emerges in the droplet size distribution under inhomogeneous conditions.
Abstract
The entrainment of clear air and its subsequent mixing with a filament of cloudy air, as occurs at the edge of a cloud, is studied in three-dimensional direct numerical simulations that combine the Eulerian description of the turbulent velocity, temperature, and vapor fields with a Lagrangian cloud droplet ensemble. Forced and decaying turbulence is considered, such as when the dynamics around the filament is driven by larger-scale eddies or during the final period of the life cycle of a cloud. The microphysical response depicted in n d − 〈r 3〉 space (where n d and r are droplet number density and radius, respectively) shows characteristics of both homogeneous and inhomogeneous mixing, depending on the Damköhler number. The transition from inhomogeneous to homogeneous mixing leads to an offset of the homogeneous mixing curve to larger dilution fractions. The response of the system is governed by the smaller of the single droplet evaporation time scale and the bulk phase relaxation time scale. Variability within the n d − 〈r 3〉 space increases with decreasing sample volume, especially during the mixing transients. All of these factors have implications for the interpretation of measurements in clouds. The qualitative mixing behavior changes for forced versus decaying turbulence, with the latter yielding remnant patches of unmixed cloud and stronger fluctuations. Buoyancy due to droplet evaporation is observed to play a minor role in the mixing for the present configuration. Finally, the mixing process leads to the transient formation of a pronounced nearly exponential tail of the probability density function of the Lagrangian supersaturation, and a similar tail emerges in the droplet size distribution under inhomogeneous conditions.
