Microphysics of Aerodynamic Contrail Formation Processes

VOLUME 72 JOURNAL OF THE ATMOSPHERIC SCIENCES SEPTEMBER 2015

JOACHIM JANSEN Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, Netherlands

ANDREW J. HEYMSFIELD National Center for Atmospheric Research, Boulder, Colorado

(Manuscript received 2 December 2014, in ﬁnal form 9 April 2015)

ABSTRACT

Aerodynamic condensation is a result of intense adiabatic cooling in the airflow over aircraft wings and behind propeller blades. Out of cloud, condensation appears as a burstlike fog (jet aircraft during takeoff and landing, propellers) or as an iridescent trail visible from the ground behind the trailing edge of the wing (jet aircraft in subsonic cruise flight) consisting of a monodisperse population of ice particles that grow to sizes comparable to the wavelength of light in ambient humidities above ice saturation. In this paper, the authors focus on aerodynamic contrail ice particle formation processes over jet aircraft wings. A 2D compressible flow model is used to evaluate two likely processes considered for the initial ice particle formation: homogeneous droplet nucleation (HDN) followed by homogeneous ice nucleation (HIN) and condensational growth of ambient condensation nuclei followed by their homogenous freezing. The model shows that the more numerous HDN particles outcompete frozen solution droplets for water vapor in a 0.5–1-m layer directly above the wing surface and are the only ice particles that become visible. Experi- mentally verified temperature and relative humidity–dependent parameterizations of rates of homogeneous droplet nucleation, growth, and freezing indicate that visible aerodynamic contrails form between T 52208 and 2508CandRH$ 80%. By contrast, combustion contrails require temperatures below 2388C and ice-saturated conditions to persist. Therefore, aerodynamic and combustion contrails can be observed simultaneously.

1. Introduction become an area of scientific interest because they can occur at much higher temperatures than combustion Combustion condensation trails, commonly associated contrails (Gierens et al. 2009; Kärcher et al. 2009). with ‘‘contrails,’’ are due to combustion of aircraft fuel and The phenomenon of aerodynamic condensation can be have been widely studied (e.g., the series of articles in the linked to the formation of aircraft produced ice particles April 2010 issue of the Bulletin of the American Meteoro- logical Society). These contrails generally occur at temper- (APIPs), first reported by Rangno and Hobbs (1983, 1984). atures colder than 2388C(Jensen et al. 1998) resulting Cooling behind the blades of propeller aircraft can produce from the offsetting effects of vapor and heat emitted visible aerodynamic condensation. During research flights during combustion (Schmidt 1941; Schumann 1996). In that measured cloud microphysical properties, Rangno and contrast, aerodynamic condensation is produced by Hobbs documented the production of ice crystals from the adiabatic expansion and the resulting cooling of moist passage of propeller aircraft through clouds at tempera- air over aircraft wings. These puffs of condensation are tures as warm as 288C. Ice particle concentrations were most readily seen by a passenger on an aircraft as con- more than 100 times greater than the expected concentra- densation over the wings during aircraft landing or tions of ambient ice nuclei at this temperature. Vonnegut takeoff (Fig. 1, left). Aerodynamic contrails have recently (1986), commenting on the APIP observations, suggested that adiabatic expansion in the flow over the propeller tips was sufficient to cool the cloud droplets to the temperature for homogeneous ice nucleation (HIN), ;2398C, if cloud Corresponding author address: Andrew Heymsfield, NCAR, 2 8 3450 Mitchell Lane, Boulder, CO 80301. temperatures were only a few degrees below 8 C, and E-mail: [email protected] that this could produce abundant numbers of ice crystals.

DOI: 10.1175/JAS-D-14-0362.1

Ó 2015 American Meteorological Society 3293 3294 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

FIG. 1. Examples of overwing condensation. (left) A Boeing 777-F1B cargo aircraft landing at Schiphol Airport, Netherlands, on 4 Jun 2012 (the photograph was taken by J. Schäfer and is used with his permission). (right) An Embraer-190 two-engine jet aircraft ﬂying over Milan, Italy, on 25 Jun 2012, heading southwest at ;10.6-km altitude, showing both combustion and iridescent aerodynamic contrails [the photograph is from Santacroce (2012) and is used with the permission of M. Santacroce].

Following up on the Vonnegut suggestion, Foster was sufficient for HDN to occur. In unfiltered air, high 2 and Hallett (1993) carried out laboratory measure- concentrations of ice crystals (;104 cm 3) were gener- ments of HIN via rapid expansion of moist, cool air ated at temperatures a few degrees warmer than for in a cloud chamber. After the injection of droplets, ice clean air. The warmer onset of HIN may have resulted crystals were readily observed at temperatures colder from the presence of ice nuclei present in the unfiltered than 2408C, with concentrations, although not mea- laboratory air but could also be interpreted as due to sured, significantly greater than the concentration of condensation on larger CN, followed by HDN, and condensation nuclei (CN) present in the ambient air. finally by HIN. This is an important and relevant observation that we To gain a better understanding of the APIP for- will address later. mation process(es), Woodley et al. (1991, 2003) Foster and Hallett (1993) found the onset conditions studied APIP generation from the University of for ice nucleation to be consistent with HIN theory as Wyoming King Air research aircraft in supercooled long as the cloud droplets were exposed to the HIN fog at temperatures between about 258 and 2128C onset temperature with sufficient time to freeze. With- with almost no natural ice nuclei during the Mono out any cloud present initially, the onset temperature Lake Experiments (MOLAS). APIP generation from dropped below 2488C, dependent on the initial chamber nine different propeller aircraft, including the King temperature, rather than 2408C typically associated Air, was studied and interpreted. Adiabatic expan- with droplets freezing homogeneously. The homoge- sion at the propeller tips achieves a cooling of 2408C, neous freezing temperature is warmer as the droplet sufficient for HIN. Woodley et al. (2003) estimated volume increases (Pruppacher and Klett 1997 and ref- that the ice concentrations generated at the propeller 2 erences therein) and in this case the droplets were likely tips was .105 cm 3 and suggested from laboratory to be very small. Foster and Hallett interpreted the experiments that the HDN process is involved in process of APIP generation to be due to homogeneous APIP generation. droplet nucleation (HDN) from vapor, which typically Conditions conducive to APIP generation over pro- produces large numbers of submicron-size droplets— peller blades are analogous to those generating ice and ice crystals after HIN. particles during the cooling of air over aircraft wings at An earlier study by Maybank and Mason (1959) re- sufficiently low temperatures. Gierens et al. (2009) ported on expansions of a small volume of moist air from quantified adiabatic cooling over a generic, idealized temperatures of 2108 and 2208C to final temperatures airfoil at an ambient temperature of 2228C for a com- of 2458C and colder. It was concluded that ice crystals, mercial jet aircraft flying at subsonic speed and observed 2 in concentrations ; 106 cm 3, formed in clean air first by an overwing temperature drop exceeding 208C. In this HDN followed by HIN. This HIN pathway occurred only highly supersaturated environment, activation of ambi- when the temperature drop and thus the supersaturation ent CN and growth of the resulting droplets could be SEPTEMBER 2015 J A N S E N A N D H E Y M S F I E L D 3295 followed by their homogeneous freezing at ambient light. The color changes are due to particle growth temperatures colder than 2208C. (Sassen 1979; Kärcher et al. 2009). Using the wingspan 2 Using Gierens’s model, Kärcher et al. (2009) modeled (28.7 m) and the cruising speed (245 m s 1) to estimate the process of aerodynamic contrail formation from the distance of the contrail behind the wing trailing edge, ambient solution droplets at temperatures from 2388 we show in the next section that the particles grow to to 2688C and a pressure range of 150 to 300 hPa. They visible sizes in a time of 60–80 ms, depending on their initialized the particles with supercooled aqueous solu- point of origin at the wing root or tip. In the extremely tions of sulfuric acid (H2SO4) and other components low temperatures reached over the wing (T 2388C), that were positioned just upstream of the wing. These the homogeneous ice nucleation rate is sufficiently high solution droplets then swelled by condensation in the to freeze all but the most concentrated solution droplets supersaturated air in the flow over the wings, while some (Koop et al. 2000; Kärcher et al. 2009). It is therefore froze homogeneously, dependent on their size. Sub- almost certain that the particles in aerodynamic con- sequent growth of the crystals produced was driven by trails are ice and that they can occur simultaneously with the difference between ambient and ice saturation vapor combustion contrails. pressure, which, at water saturation, increases with de- Case studies can provide some insight into atmospheric creasing temperature (for temperatures of 2158C and conditions conducive of aerodynamic contrail formation. colder). Homogeneous droplet nucleation—the gener- Published case studies by Kärcher et al. (2009) and ation of droplets without the need for cloud condensa- Gierens et al. (2011) combine photos of aerodynamic tion nuclei—has not been considered previously in the contrail-generating aircraft and corresponding radio- study of aerodynamic contrails. sonde measurements and indicate formation tempera- This study aims to identify the process(es) responsible tures of approximately 2328 and 2348C, respectively. For for aerodynamic condensation and quantify the tem- Fig. 1 (right), radiosonde measurements from Milano peratures, pressures, and humidities when aerodynamic Linate Airport (LIML) recorded 4 h before the photo contrails form and to estimate the conditions under was taken display an ambient temperature (T0) of about which these contrails occur simultaneously with com- 2468C and an ambient saturation ratio with respect to ice bustion contrails at temperatures conducive to combus- (Si,0) between 0.49 and 0.56. The humidity values are lower tion contrail generation. We first present an overview of than required for APIPs persistence, although radiosonde observations of aerodynamic condensation and labora- measurements of relative humidity are known to have a tory experiments in section 2 and in section 3 discuss the dry bias at cold temperatures (Miloshevich et al. 2009). development of a numerical model to evaluate the rela- These observations indicate that visible condensation tive importance of the various processes that might be trails may occur over a much wider range of T0 and S0 involved. In section 4, we conduct a sensitivity study to than previously thought. quantify ambient atmospheric conditions conducive of For cases where combustion and aerodynamic contrails visible aerodynamic contrail formation. In section 5 we are observed simultaneously, the combustion contrail discuss the validity of our model results using recent ob- diameter at the point where it first becomes visible behind servations. We summarize our work and draw conclu- the engine, when Scontrail . Sw,sat (Schumann 1996), can sions in section 6. provide an alternative estimate of the saturation ratio.

The initial diameter DL1 is a function of environmental 2. Overview of conditions conducive of parameters P0, T0, and S0 and ﬂight parameters that aerodynamic contrail formation govern the mixing of heat and moisture in the trail. We use the wingspan of the aircraft in Fig. 1 (28.7 m) to

In this section, we use observations of aerodynamic estimate DL1 5 3.3 6 0.3 m. The photo in Fig. 1 is part condensation and laboratory studies to establish the of a series depicting cruising jet aircraft that show both atmospheric and overwing conditions that we think are contrail types, taken in the afternoon of 25 June 2012 in potentially conducive of aerodynamic condensation and Milan, Italy (Santacroce 2012). For each photo the time, the subsequent generation of ice crystals. aircraft type, and altitude were known from ﬂight

The right panel in Fig. 1 shows an Embraer-190 two- tracker data. Estimating DL1 6 10% for two more air- engine jet aircraft ﬂying over Milan, Italy, at an altitude craft, and using P0 from radiosonde measurements we of approximately 10.6 km. The white trails behind each use Schumann’s method to constrain T0 between 245.68 engine are due to combustion, cooling, and ice growth. (S 5 Sw,sat) and 253.58C(S 5 Si,sat), consistent with The iridescent trail is instead caused by overwing cool- radiosonde measurements. The radiosonde-derived ing and condensation, and the colors are due to particle temperature is at the higher end of this spectrum, and sizes that are comparable to the wavelength of visible we estimate that the ambient relative humidity must 3296 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

about 0.6], the crystals in Fig. 1 right can survive to much lower saturation ratios in the downstream part of the flow over the wing than the water droplets in Fig. 1 (left). Together with the ambient temperature and relative humidity, aerodynamic condensation is controlled by the amount and duration of adiabatic expansion ach- ieved over the wing. To homogeneously freeze deliquesced CN or HDN at ambient temperatures $ 2388C and produce a visible trail, the overwing expansion must induce a temperature drop sufficient to cause HIN. Figure 2 shows a model simulation of the air temperature and supersaturation with respect to water and ice during the flow of air over an idealized (Joukowski) airfoil in several configurations. In this example we used an ambient temperature of 2408C and an initial satura- FIG. 2. Evolution of the temperature and saturation ratio with tion ratio of 0.9 with respect to water or 1.0 with respect to respect to ice (Si) and water (Sw) in laminar compressible flow over ice. Without condensation or freezing, the 115-hPa peak an idealized Airbus A340 (root) airfoil. Values were calculated pressure deficit over the wing leads to about 308Cof 5 along a streamline 0.4 m (at x 0 m) above the wing surface. cooling and a resulting water saturation ratio about 22. Airflow velocity corresponds to jet aircraft cruise velocity 2 (243 m s 1) at an angle of attack of 18. Variations of the overwing It is important to note that the pressure deficit (and temperature with angle of attack and chord length are also shown. therefore T and RH) and time scale of overwing flow The pressure altitude is 300 hPa and the ambient temperature and scales with the chord length (Gierens et al. 2009) but also ice supersaturation are 2408C and 1, respectively. The blue region with the airspeed and angle of attack of the aircraft. along the x axis indicates the horizontal extent of the wing, directly An increased angle of attack will generate extra lift at the fuselage (11.70 m) and midwing (7.9 m, dotted line). Detailed model and airfoil description can be found in Gierens et al. (2009). through a higher pressure difference (up to the stall angle of attack, approximately 158 for the airfoil considered here), driven by a greater expansion over the top have been closer to water saturation than the radiosonde of the wing (Fig. 2, dashed black line). Scaling the airfoil measurements would suggest. to decrease the chord length, analogous to a wing section Aerodynamic contrails at cruise altitude obviously farther from the root (Fig. 2, dotted black line), will only differ from instantaneously visible condensation nor- reduce the time scale of overwing flow. We outline our mally seen over the wings of aircraft on takeoff or assumptions regarding the wing configuration and air- landing at temperatures $08C. The left panel of Fig. 1 craft speed during subsonic cruise flight in the model shows aerodynamic condensation over the wings of a development section. Boeing 777-F1B cargo aircraft landing on Schiphol Given the high supersaturations generated over Airport, the Netherlands, on 4 June 2012. Similar to the wings, and its apparent relevance to APIPs formation aerodynamic contrail in the right panel, the thickness of over propellers, the homogeneous droplet nucleation the condensation layer is proportional to the chord process must be considered. The relevance of homoge- length (wing depth), reaching a maximum at the wing neous condensation is supported by expansion chamber root. Airport meteorological records for the day the experiments. For example, Wölk et al. (2002) observed 5 10 23 21 picture was taken show daily mean values of T0 5 8.98C high rates of HDN (from 10 to 10 cm s ) in ex- and Sw,0 5 0.87. Thus, depending on overwing tempera- pansion chamber experiments in clean air at a range of tures conducive of homogeneous freezing, aerodynamic temperatures (from 2138 to 2438C) and saturation ratios condensation particles may be either liquid or ice. (from 6 to 22)—conditions similar to those occurring in The examples shown in Fig. 1 provide insight into the modeled overwing flow (Fig. 2). Laboratory experiments processes involved in aerodynamic contrail formation (Table 1) indicate a strong, nonlinear dependence of the and their visual appearance. As air flows over the wing nucleation rate on the saturation ratio and of the initial of the aircraft, it expands, cools, and the vapor con- cluster size on temperature. In the next section we com- denses, and on the aft side of the wing, it warms, combine Gierens’s compressible flow model from Fig. 2 with presses, and the condensate evaporates. Because ice empirical characterization of the homogeneous nucle- particles survive to much lower vapor saturation ratios ation rate based on the experiments of Table 1 in order to than water droplets, especially at 2508C [at ice satura- quantify the role of the HDN process in aerodynamic tion (Si 5 1), the saturation ratio with respect to water is contrail formation. SEPTEMBER 2015 J A N S E N A N D H E Y M S F I E L D 3297

TABLE 1. Overview of studies determining homogeneous nucleation rate J of water and critical cluster size n* with different experi- mental techniques, as a function of temperature T and saturation ratio S. Critical cluster sizes are calculated from the slopes of the nucleation rate isotherms.

2 2 Study Technique T (K) SJ(cm 3s 1) n* Heist and Reiss (1973) Thermal diffusion cloud chamber 280–330 2–4 ;1 Mikheev et al. (2002) Laminar-ﬂow tube reactor 210–250 2.4–5.2 102–103 17–39 2 Brus et al. (2009) Thermal diffusion cloud chamber 295–320 2.5–3.6 2 3 10 2–5 3 101 47–78 2 Brus et al. (2008) Thermal diffusion cloud chamber 290–320 2.7–4.3 3 3 10 1–3 3 102 45–55 Allen and Kassner (1969) Expansion cloud chamber 268–274 4–6 101–104 Miller et al. (1983) Expansion cloud chamber 230–290 4–13 102–106 23–40 Manka et al. (2010) Laminar-ﬂow diffusion chamber 240–270 5–11 102–106 29–45 Wagner and Strey (1981) Two-piston expansion chamber 275–300 6–15 105–109 Wölk et al. (2002) Nuclear pulse chamber 220–260 6–22 105–1010 Viisanen et al. (1993, 2000) Nuclear pulse chamber 220–260 6–23 105–1010 27–42 Wölk and Strey (2001) Nuclear pulse chamber 220–260 6–25 105–1010 20–34 Dobbins et al. (1980) Expansion cloud chamber 260 7–8 106–108 Lee (1977) Shock tube 230–255 8–17 ;1010 Luijten et al. (1997) Pulse expansion wave tube 230–250 8–18 108–1011 14–25 Peters and Paikert (1989) Shock tube 200–260 10–17 107–109 Holten et al. (2005) Pulse expansion wave tube 200–240 10–58 107–1011 10–30 Streletzky et al. (2002) Shaped supersonic nozzle 230 29–32 4–6 3 1015 Heath et al. (2002, 2003) Supersonic nozzle 190–240 40–190 1017 16 17 Kim et al. (2004) Shaped supersonic nozzle (D2O) 210–230 46–143 4 3 10 –3 3 10

3. Model development attack for the pressure deficit, we derived these values from the Airbus A340 flight operations manual and In this section, we develop a model that considers two historical flight track data. We assumed the true air- pathways to aerodynamically produced condensation: 2 speed increasing linearly from 218 (5.4 km) to 245 m s 1 1) homogeneous droplet nucleation from the vapor phase (cruise altitude . 9.4 km). The angle of attack was taken and 2) condensation on ambient condensation nuclei. constant at 58 during climb and 38 during cruise. The Each of these pathways can lead to ice production via HIN pressure deficit over the wing decreases from 210 to if the temperatures during cooling over the wings are 170 hPa during climb, resulting from the decreasing sufficiently low. Because so little is known about het- weight of the aircraft combusting fuel and a lower climb erogeneous ice nucleation under these conditions, and rate aloft. As a result, the magnitude of the average relatively low concentrations of ice nuclei are present temperature drop in the layer 0.16–3.0 m above the wing compared to liquid aerosol that can homogenously increases with decreasing ambient temperature: freeze, this process will be ignored here. ›(T 2 T )/›T 520:2. Ambient pressures and tem- The evolution of pressure and temperature over a 0 min 0 peratures were derived from a standard atmosphere; for commercial jet aircraft wing was simulated using a two- example, we assume that the ambient temperature and dimensional potential flow model developed by Gierens pressure are 158C and 1013 hPa, respectively, at ground et al. (2009, kindly provided by K. Gierens for use in this level and 2538C and 220 hPa at cruising altitude. study) for compressible flow. We used an idealized Joukowski airfoil, with parameters chosen as to match a. Homogeneous condensation the shape of an Airbus A340 wing at the root (H 5 1.6 m, L 5 11.7 m), where condensation is most visible. Rele- Homogeneous droplet nucleation is a process whereby vant quantities were calculated along 20 streamlines liquid droplets condense directly from the vapor phase, vertically spaced 0.1 m apart. The trajectory closest to without the need for cloud condensation nuclei. Good the wing surface was taken above the turbulent bound- examples are seen in everyday life, including condensa- ary layer, which scales withpffiffiffi chord length L and measures tion from warm water sprayed from a shower head and on the order of 0:3 3 L c, with the drag factor c ’ 0.002 steam produced from a kettle boiling water (Carlon (Landau and Lifshitz 1987) or about 0.16 m for L 5 11.7 m. 1984). In each case, the supersaturation generated from To evaluate the different aerodynamic contrail for- the cooling of the heated vapor can be very large—a sat- mation processes for a wide range of atmospheric con- uration ratio of 10 or more. ditions, we modeled the overwing flow of a jet aircraft Homogeneous droplet nucleation was first quantified ascending from about 5 to 11 km (cruise altitude). by Becker and Döring (1935) by calculating the free Considering the importance of airspeed and angle of energy required to form a critical cluster of water 3298 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

FIG. 3. Homogeneous droplet nucleation rate as a function of temperature and saturation ratio. Expansion chamber experiments (symbols) closely match the parameterization of Wölk et al. (2002) (dashed blue lines). Figure adapted from Manka et al. (2010). molecules (nucleus) in unstable equilibrium with the for the surface tension of small clusters by Merikanto surrounding vapor. Later corrections of the Becker– et al. (2007). Values of the latent heat of evaporation– Döring classical nucleation theory by Girshick and Chiu sublimation, saturation vapor pressure, and surface (1990)—who included the formation-free energy of a tension were approximated by empirical parameteriza- monomer—and Wölk et al. (2002)—whodevisedanem- tions. The interdependent quantities of vapor pressure, pirical correction based on cloud chamber experiments— (droplet) temperature, and droplet radii were resolved have significantly improved nucleation rate predictions. using an ordinary differential equation solver. We use this theoretical framework to model the HDN The critical cluster size of newly formed droplets is process, guided by the laboratory observations. given by the Gibbs–Thomson equation, which has been A comparison between the Wölk et al. (2002) pa- experimentally verified for temperatures from 2708 2 2 rameterization of the nucleation rate J (cm 3 s 1) and to 2158C(Manka et al. 2010). Newly formed clusters of experiments is shown in Fig. 3. The overall agreement water proceed rapidly through different growth stages. between measurements and classical nucleation theory Small droplets first enter the free molecule regime is good along the 2538–1478C isotherms. Large dis- (radii # 10 nm), where droplets are smaller than the crepancies exist for temperatures # 2538C(Mikheev mean free path of water molecules in air and the mass et al. 2002), which may have been the result of homo- flux to the droplet depends on the number of collisions. geneous freezing of droplets directly after their nucle- Rapid growth takes place as the mass flux continuously ation (Wölk et al. 2013). changes to the diffusion controlled continuum regime (radii . 200 nm), where droplets grow to visible size. b. Droplet growth Fladerer and Strey (2003) experimentally verified a Growth of homogeneously nucleated droplets is de- commonly used droplet growth model for homoge- termined using heat and mass flux calculations between neously nucleated droplets (Seinfeld and Pandis 1998). the droplet and gas phases. We use a commonly used They measured the time evolution of homogeneously droplet growth model described in Heymsfield and nucleated droplet size in a supersaturated environ- Sabin (1989), based on Fukuta and Walter (1970) for- ment. Their experiments show that at low temperatures mulations for heat and vapor transport, in which cur- (2438 to 2238C) and high saturation ratios (from 8 to vature effects are considered. We applied a correction 13) HDN droplets grow exponentially to visible sizes SEPTEMBER 2015 J A N S E N A N D H E Y M S F I E L D 3299

(radii $ 0.6 mm) in under 10 ms. In Fig. 4 we compared our small cluster growth calculations with their measurements. For mass and thermal accommodation coefficients of 0.75 and 0.96, respectively, the model shows good agreement with the data. c. Ambient CN initialization and growth The initial solution droplet composition and size distribution is controlled by a prescribed CN dry mass spectrum and the ambient relative humidity, which governs deliquescence. Heymsfield (1973) measured ambient activated CN (dry) mass spectra and concentrations from an aircraft at 7–8-km altitude. Following his observations, we use lognormal mass distribution 217 212 (mmin 5 1 3 10 and mmax 5 1 3 10 g) with an 23 ambient CN concentration of 260 cm . We assume that FIG. 4. Calculated growth of homogeneously nucleated droplets at cruising altitude the CN are ammonium sulfate, using the Fukuta and Walter (1970) formulations for heat and va- 5 3 3 23 5 consistent with the observations of Twomey (1971). The por transport. Initial parameters are nd 4.2 10 cm , Tinit 8 5 52 8 5 particle growth model described in the previous section 20.0 C, Pinit 722 hPa, Tmin 39.5 C, Ptot,min 409 hPa, and 5 5 is applied to resolve the growth and evaporation rate of Py,min 170.6 Pa (Sw,max 8.2). Circles correspond to measured droplet radii (Fladerer and Strey 2003); the solid line is the the solution droplets. For liquid particles we consider modeled evolution of the droplet radius. both solute and curvature effects through the modified vapor diffusion and heat conduction coefficients (Fukuta solute and curvature effects and with different parame- and Walter 1970; Fitzgerald 1972). terizations specific for the solid phase (e.g., density, equilibrium vapor pressure, and latent heat). This ap- d. Homogeneous freezing and ice crystal growth proach implies that we assume ice particles are initially Because temperatures over the wing of a cruising jet spherical: the extremely high vapor flux driving the initial aircraft reach well below 2408C, it is likely that some growth phase is likely to produce amorphous ice rather deliquesced ambient CN and HN droplets can freeze than fully developed crystalline structures (Kärcher et al. homogeneously.1 However, because the droplet vol- 2009). The habit and optical properties of aged APIPs umes are small and the cooling occurs over a time scale are a subject of ongoing research. In situ measurements of of milliseconds, it is important to quantify this process. ice crystal size (effective radii, reff) and habit in young Bartell and Chushak (2003) and Manka et al. (2012) combustion contrails suggest that small hexagonal plates, measured the homogeneous freezing rate of small columns, and triangles (reff # 2 mm) are abundant 1 min (#6 nm) pure water droplets at temperatures relevant after formation (Goodman et al. 1998). However, ice for APIPs formation (2808 to 2558C). The measured particles aged 2–20 min are initially near spherical 2 2 rates (J ’ 1023 cm 3 s 1) can be approximated by clas- (Schröder et al. 2000; Gayet et al. 2012) and only grow sical nucleation theory, adapted for cubic ice (Murray into larger (reff $ 5 mm), quasi-spherical particles as the et al. 2010). Homogeneous freezing of supercooled so- contrail transitions into cirrus (.20 min; Febvre et al. lution droplets is modeled using the empirical parame- 2009). In situ observations of aged (reff $ 150 mm) ice terization by Koop et al. (2000), which includes the crystals from aircraft-induced virga below a supercooled depression of the melting point by the solutes in water cloud by a C-130 research aircraft equipped with the drop. The formation of ice particles directly from the particle imaging probes show hexagonal and columnar vapor phase or via deposition nucleation is not consid- crystals develop at a later stage (Heymsfield et al. 2010). ered here, for reasons discussed in Kärcher et al. (2009). Ice crystal growth rates were calculated using the 4. Model results droplet growth model described in section 3b without The purpose of this study is to identify the dominant processes responsible for creating out-of-cloud overwing condensation and aerodynamic contrails; we do 1 In the remainder of this paper, we will refer to homogeneously nucleated (condensed) droplets as ‘‘HN droplets’’ and to HN not consider the processes occurring within a cloud. droplets that subsequently freeze homogeneously as ‘‘HN ice First, we examine the relative importance of the fol- particles.’’ lowing overwing processes for generation of the APIPs: 3300 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

1) deliquescence of water vapor on CN leading to solution droplet growth, followed by homogeneous freezing and 2) homogeneous condensation followed by homogeneous freezing. Because aerodynamic contrails appear to form in relatively warm (T0 $ 2388C) and humid (S0 $ Si,sat) conditions (case study; Gierens et al. 2011), both liquid droplets and ice crystals can contribute to the generation of a visible trail. We have therefore included both the liquid water content (LWC) and ice water content (IWC) at different ambient temperatures in our model. Figure 5 shows the modeled liquid water content over an Airbus A340 wing at temperatures of 2458, 2358, and 2258C, at near water saturation (Sw,0 5 0.9) along trajectories 0.3 and 3.0 m above the wing surface. The initial decrease in solution droplet LWC is caused by evaporation in compressed and heated air at the stag- nation point in front of the leading edge of the wing, followed directly by adiabatic expansion, cooling, and freezing midwing. Not all solution droplets freeze: initial evaporation increases the molality of the larger ($1 mm) solution droplets and decreases their water activity and homogeneous freezing rate (Koop et al. 2000). Compression and evaporation prevail closer to thewingsurfaceandatlowambienttemperatures, because we assume increasing airspeed with altitude. At higher temperatures and farther from the wing surface, the homogeneous freezing rate is temperature controlled. The droplets that remain are allowed to grow in the supersaturated environment, causing an increase in the LWC, but evaporate behind the wing where S0 # Sw,sat. FIG. 5. Modeled evolution of the LWC along two trajectories The homogeneous formation of liquid droplets occurs (a) 0.3 and (b) 3.0 m above an Airbus A340 airfoil due to growth of over a very short time scale and is only observed in tra- solution droplets with (blue lines) and without (orange lines) the # jectories close ( 1 m) to the wing surface, where the su- HDN process enabled at Sw,0 5 0.9 and different ambient tem- 52 8 2 8 2 8 persaturation is sufﬁciently high (Tmin 52808 to 2608C, peratures [T0 45 (solid lines), 35 (dashed), and 25 C (dotted)]. Evolution of the overwing temperature is shown in Sw,max 5 18 to 61). From Fig. 3, we ﬁnd that these con- 2 2 green. The wing leading edge is located at t 5 0, the trailing edge at ditions are highly conducive of HDN (J # 1014 cm 3 s 1). t 5 0.05 s. For each T0, we calculated the airspeed (TAS 5 233, 224, 2 It is important to note, however, that because S in- and 220 m s 1) and airfoil angle of attack (a 5 4.08, 5.08, and 5.08) creases exponentially with decreasing T (Fig. 2), the using altitude-dependent approximations (see text), while the 5 supersaturations conducive to HDN are only present ambient pressure (P0 296, 371, and 460 hPa) was derived from over a small fraction of the wing, where T approximates a standard atmosphere.

Tmin within 58C. In the very short time frame (6 ms) within which HDN can occur, temperatures and su- Solution droplets can take up significantly more water persaturations are relatively constant, resulting in a vapor above the layer where homogeneous droplet nu- highly monodisperse population of particles (i.e., a par- cleation dominates. For trajectories within the overwing ticle size distribution with a geometric standard deviation HDN layer (h 5 0.3 m; Fig. 5a), the solution droplet 4 6 23 sG of ,1.25). Although numerous [10 –10 cm com- LWC increases when the HDN process is disabled (or- 2 pared to 102–103 cm 3 for upper-tropospheric cloud ange lines), compared to model runs where homoge- condensation nuclei (CCN) (Heymsfield 1973)], these neous condensation is enabled (blue lines). Much higher droplets freeze within 5 ms after formation (Manka et al. above the wing (h 5 3.0 m; Fig. 5b), the temperature 2012) and the liquid phase is likely to remain subvisible drop (green lines) is insufficient for the HDN process to over the wing (r 5 0.1–1 nm; Fig. 4) during cruise flight. occur. Here, the LWC is determined solely by growth SEPTEMBER 2015 J A N S E N A N D H E Y M S F I E L D 3301 and freezing of solution droplets, resulting in identical values for the HDN-disabled and -enabled model runs. To explain the formation of visible aerodynamic contrails behind the wing trailing edge, we need to know the fate of ambient solution and HN droplets after freezing. Figure 6 shows the ice water content over the same idealized A340 airfoil used in Fig. 5. Upon cooling, the excess water vapor is distributed over growing HN ice particles and frozen solution droplets. As the HN ice particles are more numerous by three orders of magnitude or more (albeit smaller) than the frozen solution droplets, they form the largest contribution to the IWC despite the higher volumetric growth rate of the latter. The large number of growing particles rapidly depletes the excess water vapor to near-equilibrium values (S 5

Si,sat). Toward the trailing edge of the wing the air is heated adiabatically by recompression, and the particle growth rate is limited by the decreasing relative humidity. FIG. 6. Modeled evolution of the peak IWC over an Airbus A340 As the relatively dry air is recompressed further, a vapor airfoil due to freezing and growth of solution droplets (black lines) and homogeneous droplet nucleation followed by homogeneous deﬁcit replaces a vapor excess (S , 1), and sublimation i freezing (red lines) at Sw,0 5 0.9 and different ambient tempera- lowers the IWC. During recompression the ice particles tures [T0 52458 (solid lines), 2358 (dashed), and 2258C (dotted)]. either decrease in size, or sublimate entirely, depending The ice saturation ratio in the trajectory with maximum total IWC r on their size and the vapor density. Surviving ice parti- is shown in green. The ambient vapor densities y,0(T0) are shown in blue. The wing leading edge is located at t 5 0 and the trailing cles will grow until an equilibrium with the ambient 5 5 edge at t 0.05 s. Ambient pressures, ﬂow velocities, and airfoil water vapor is reached (Si,0 1) and a visible trail angles of attack are as in Fig. 5. is formed. The model shows a clear increase in overwing IWC and LWC with increasing ambient temperature. The 2012). With the ice particle number concentration ni, the limiting factor appears to be the excess water vapor; optical depth t can be calculated: the ambient vapor density increases with temperature at constant RH. There is a minor effect of recompres- t 5 p 2 D r Qext(r)ni z. (2) sion on air density and the liquid and ice water content

(ra,0/ra,min # 1.2). For simplicity, we assume that the observer is looking at the condensation trail from directly below. We calculated a. Aerodynamic contrail visibility the extinction along 40 stacked trajectories (streamlines) From Figs. 5 and 6, it appears that homogeneous equally distributed vertically up to 5 m from the wing droplet nucleation followed by homogeneous freezing surface, a conservative estimate of the thickness of the creates large numbers of APIPs that could form a visible condensation layer observed over the wings of landing jet trail. To assess contrail visibility, the optical depth of the aircraft (Fig. 1). The optical depth was obtained by population of HN ice particles and frozen solution summation through all trajectories, taking their vertical droplets can be used. First, the Mie extinction efﬁciency separation as Dz. We here assume a visibility threshold

Qext is calculated from the particle radius r and re- of ty $ 0.01 for visual detection of contrails. Lidar fractive index n—we assume a monodisperse population studies by Sassen and Cho (1992) estimated the optical of spherical particles and a scattering wavelength l of depth of visible cirrus at 0.03 # ty # 3.0, and ty ’ 0.01 at 0.589 mm(Van de Hulst 1957): low angular distances from the sun, because the scattering phase function has a strong forward peak. 4 1 2 cos(q) 4pr(n 2 1) ä Q 5 2 2 sin(q) 2 , q 5 . K rcher et al. (2009) performed detailed radiative ext q q l transfer simulations for monodisperse populations of (1) spherical ice particles with sizes similar to the wavelength of visible light (l 5 390–700 nm) and found that

The error in Qext introduced by this approximation iridescence is only observed within 308 angular distance equals a factor of 0.9 for r ’ 1.0 mm and a factor of 2.0 for from the sun, resulting in a similar threshold value r ’ 0.1 mm compared to an exact Mie routine (Thomas (ty 5 0.01–0.03). 3302 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

below 2408C(Fig. 5) and the homogeneous freezing rate is high enough to freeze the majority of liquid particles. When the model is run with HDN disabled (Fig. 7b), growth and freezing of solution droplets produce a visible trail (as in Kärcher et al. 2009), while liquid droplets remain invisible. Droplet salinity increase during compression and evaporation at the leading edge reduces the freezing rate and results in a lower optical depth at higher temperatures. Kärcher et al. (2009), who did not include the solute effect in their droplet freezing parameterization, reported a reverse temperature dependency. It is apparent that growth and freezing of ambient solution droplets do not produce visible condensation. As detailed in the previous section, this is because growing HN ice particles use up most of the excess water vapor. Visible overwing condensation and aerodynamic contrails originate solely from the HDN process followed by HIN. This ﬁnding is new: to our knowledge, vapor depletion from the homogeneous nucleation process has not been considered previously in the study of aerodynamic condensation. b. Sensitivity study Figures 6 and 7 show a direct relationship between the IWC, the visibility of aerodynamic condensation, and ambient temperature and saturation ratio. To assess the atmospheric relevance of aerodynamic condensation we need to establish in more detail the T and S boundary conditions. Since we have shown in the previous section that solution droplet growth and freezing is unlikely to produce a visible contrail at temperatures from 2508

to 2208C and Sw,0 5 0.9, we will only consider the HDN 1 HIN process here. Figure 8 shows the peak concentration of HN ice FIG. 7. Modeled evolution of the optical depth over an Airbus particles and their effective radius (Fig. 8a) and aero- A340 airfoil with the HDN process (a) enabled and (b) disabled at dynamic contrail optical depth (Fig. 8b) 30 m behind near water saturation (Sw,0 5 0.9) and different ambient temperatures [T0 52458 (solid lines), 2358 (dashed), and 2258C (dot- the wing trailing edge for air temperatures between ted)]. Colors refer to processes of homogeneous droplet nucleation 2528 and 2208C and a saturation ratio between that of followed by homogeneous freezing (red lines) and liquid (blue ice (Si,sat) and water (Sw.sat). The distance was chosen to lines) and homogeneously frozen solution droplets (black lines). t 5 match the observed wing–contrail separation in Fig. 1. The visibility threshold value ( y 0.01) is plotted in green. The 8 wing leading edge is located at t 5 0 and the trailing edge at t 5 We applied a linear decrease of the angle of attack (6.6 – 21 0.05 s. Ambient pressures, ﬂow velocities, and airfoil angles of at- 1.48) and an increase of true airspeed (207–249 m s ) tack are as in Fig. 5. from an altitude of 5.4 to 10.5 km—within ranges prescribed in Airbus A320 ﬂight operation manuals—in order to enable condensation of homogeneous droplets In Fig. 7, a time series of the aerodynamic contrail at a constant height of 0.2 m above the wing surface at all optical depth is shown for solution droplets (ice and temperatures. liquid) and HN ice crystals for air temperatures Figure 8a demonstrates that the HN ice particle ef- between 2458 and 2258C and an ambient water satu- fective radius is nearly independent of the relative ration ratio of 0.9. No visible contrails originate from humidity. The reason is that the excess vapor density— growth of liquid solution or HN droplets because even at water vapor available for particle growth—is de-

T0 52258C, the minimum temperature reaches well termined for the most part by the ambient vapor density, SEPTEMBER 2015 J A N S E N A N D H E Y M S F I E L D 3303

FIG. 8. Sensitivity study of the HDN–HIN processes to different initial temperatures and saturation ratios, 30 m behind the trailing edge of the wing. (a) Concentration and effective radius of homogeneously nucleated droplets. (b) Optical depth. The green contour represents the visibility threshold. Schmidt–Appleman visibility threshold for combustion contrails (high-pass turbofan jet engine, standard atmosphere) is shown in blue. Combustion and

aerodynamic contrails are only persistent if S0 $ Si,sat (dashed gray line, both panels). which varies an order of magnitude with ambient tem- et al. 2012 and our Fig. 1), we can evaluate the threshold perature (Fig. 6). Variations in relative humidity have a visibility temperature of the trails using the well- minor impact on the vapor density (factor , 1.5), as does established Schmidt–Appleman criteria (Schmidt 1941; the halving of the temperature drop by increasing Appleman 1953). Visible combustion contrails can form

T0 from 2508 to 2208C (factor , 1.6). The number below temperatures as high as 2378C, but the precise concentration increases with both saturation ratio and threshold temperature depends on the ambient vapor temperature, because the nucleation rate depends on mixing ratio and fuel properties, such as amount of the relative, rather than absolute humidity. There is a water vapor and heat produced (Schumann 1996) as well 2 maximum number of ice particles (2 3 106 cm 3) that is as the engine propulsion efﬁciency (Schumann 2000). not apparent in expansion chamber experiments per- In Fig. 8b we have added the environmental conditions formed under similar conditions. This is an important for visible combustion trails for a commercial jet aircraft model result that we will address in the next section. ﬂying at cruise speed in a standard atmosphere (blue Aerodynamic contrails are generated within a broad line) by calculating the threshold temperature corre- range of atmospheric conditions. When water saturation sponding to each P0–Sw,0 combination and using engine is assumed in the model, visible aerodynamic contrails parameters for a B747 burning kerosene listed in

(Fig. 8b, green contour) are generated at T0 $ 2498C, Schumann (1996). From T0 52518 to 2388C and Sw,0 $ but in reality water saturation is not expected at tem- 0.8, aerodynamic and combustion contrails can be ob- peratures colder than 2388C. When we lower the rela- served simultaneously. tive humidity closer to ice saturation, a visible trail forms 2 8 at about 20 C. Aerodynamic contrails are not visible 5. Discussion at a water saturation ratio below 0.76. Comparing both panels it appears that contrail visibility is highly corre- Validation of our model results remains a challenge, lated with the number of homogeneous droplets that are because observations are limited to individual cases generated over the wings: the higher the temperature where the contrail angular distance to the sun is less than and saturation ratio, the more HN droplets nucleate and 308 (Gierens et al. 2011) and characteristic irisation can the more visible a contrail is. This may explain the high be distinguished (Fig. 1) or where the ambient temper- visibility of aerodynamic condensation near the ground. ature is clearly too high for combustion contrails. Fur- The effective particle radius varies across one order of thermore, determining the atmospheric conditions magnitude and is important only as a lower limit for the associated with an observation relies on accurate ra- optical depth. diosonde measurements or reanalysis data often not Because aerodynamic contrails are sometimes ob- resolved at high temporal (,1 h) and spatial (,1 km) served coexisting with combustion trails (Unterstrasser resolutions associated with (aerodynamic) contrail 3304 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72

FIG. 9. Time evolution of the HN ice particle effective radius, mean number concentration (nm), and the particle size distribution geometric standard deviation (sg) at increments of 10 m from the wing leading edge. Trajectories are shown in gray. A 2D cross section of the wing is shown in red. The wing leading edge is located at x 5 0 and the trailing edge at x 5 11.7 m. Ambient temperature and water saturation ratio were 2308C and 0.9, respectively. The airfoil 2 angle of attack was 5.08 and the true airspeed 222 m s 1 [calculated using an altitude-dependent linear approximation (see text)], while the ambient pressure was derived from a standard atmosphere. formation and ageing (Schumann 1996). Finally, even if similar to the wavelength of light in 3) high enough con- the aircraft type and ground speed are known, assump- centrations to produce a layer with optical depth $ 0.01. To tions have to be made about the true airspeed (de- be consistent with the observations in Fig. 1 the required pendent on the wind speed and direction) and angle of optical depth and particle size must be reached within attack. Given these uncertainties, our model adequately 30 m after leaving the wing. Figure 9 shows the evolution predicts visible aerodynamic contrail formation in of the ice particle effective radius behind the wing for the 2328 to 2558C temperature range derived from the T0 52308C and Sw,0 5 0.9. Between 20 and 50 m behind observations in Fig. 1, Kärcher et al. (2009), and Gierens the leading edge of the wing, the peak effective particle et al. (2011), as well as the coexistence of aerodynamic radius increases from 0.5 to 0.9 mm, with a geometric and combustion trails. standard deviation (sg) that remains well below the If the radiosonde measurements associated with Fig. 1 monodispersity threshold value of 1.25. The optical are representative of the air mass in which the contrail depth reaches $0.03 during the initial growth phase formed, they suggest that aerodynamic contrails could directly over the wing (Fig. 7). Fulﬁlling all the listed be visible at a lower water saturation ratio than the 0.76 requirements, it is likely that the HDN 1 HIN process limit value we calculated. Possibly the moisture from the can produce an iridescent trail. engine exhaust could contribute to additional particle Conspicuously, particles in the layer directly above growth (not modeled). Conversely, the HN ice particles the wing do not grow to visible size but instead evapo- generated over the wing are of minor importance as rate during recompression. The number of HN droplets condensation nuclei in combustion contrail formation, peaks closest to the wing surface because the saturation because the number of ultraﬁne particles that could act ratio and thus the temperature drop largely determines as CN (Kärcher et al. 1998) in the exhaust stream 30– the homogeneous nucleation rate. At a threshold tem- 2 50 m behind the wing is much higher (n 5 107 cm 3; perature drop, the number of ice particles becomes so Schröder et al. 1998; corrected for dilution using large that the maximum crystal size reached prior to Schumann et al. 1998) than the peak number of HN ice recompression is limited by vapor depletion. This hap- 2 particles (n 5 106 cm 3), especially after mixing with pens when the number of homogeneously nucleated 2 ambient air. droplets exceeds 2 3 106 cm 3. During the 40 ms of re-

An alternative model validation method is to check compression, S decreases below Si,sat (Fig. 2) and sur- whether the aerodynamic contrails’ iridescent appear- vival of HN ice crystals depends on their sublimation ance can be reproduced. A detailed analysis of aero- rate, which scales inversely with particle size. Smaller dynamic contrails’ optical properties was performed by particles and an extremely low vapor density ensure Kärcher et al. (2009). Iridescence requires 1) a mono- faster sublimation. Closest to the wing surface, ice par- disperse population of 2) particles with diameters ticles are just small enough to sublimate entirely within SEPTEMBER 2015 J A N S E N A N D H E Y M S F I E L D 3305 the recompression timespan. This process explains the and an average overwing temperature of Twing # 2388C polydisperse particle size distribution (sg 5 1.73) and for the formation conditions. They found that where the peaking number concentration prior to recompression majority of commercial jet aircraft flight time is spent— (the smallest particles have not yet evaporated) as well at cruise altitude (150–350 hPa) outside the tropical as the HN ice particle concentration maximum behind belt (6308)—the annual probability of ice supersatu- the wing trailing edge found in the sensitivity study rated conditions is less than 20%. With the added ele- (Fig. 8a). vated relative humidity constraint imposed by this The model predicts the formation of aerodynamic study, the probability of aerodynamic contrail forma- contrails at water saturation ratios of $0.8, well above tion is further reduced. Combustion contrails, on the ice saturation. It is therefore likely that aerodynamic contrary, are only constrained by the ambient tem- condensation frequently occurs in, or directly above or perature because the engine exhaust supplies nearly all below, supercooled water or mixed-phase clouds with of the water vapor needed for particle growth temperatures between 288 and 2388C(Rangno and (Schumann 1996). We underwrite the conclusion of Hobbs 1983; Woodley et al. 1991, 2003). The ice parti- Gierens and Dilger (2013) that the frequency of oc- cles produced may subsequently grow at the expense of currence of aerodynamic contrails is unlikely to exceed preexisting cloud droplets through the Wegener– that of combustion contrails. Bergeron–Findeisen process and precipitate from the The homogeneous droplet nucleation and freezing cloud as visible streamers and—if the cloud is thin—may process may explain both aerodynamic contrails formed leave a visible hole where the liquid water droplets during cruise flight and overwing condensation visible have either frozen and precipitated or evaporated during landing and takeoff. However, speed and other (Heymsfield et al. 2010). Near airports, inadvertent parameters differ strongly between cruise and landing or cloud seeding can lead to local intensification of snow- takeoff: for example, the magnitude and location of the fall, clearly visible in radar imagery as bands of en- pressure minimum over the wings changes during hanced reflectivity correlating with aircraft tracks landing due to a steeper angle of attack, an increased (Heymsfield et al. 2011; Lautaportti et al. 2014). wing area and drag due to flaps, and possibly turbulence. In liquid clouds—in addition to APIPs formed directly Changing the pressure distribution could influence the from vapor—ice particles can form through freezing of relative importance of liquid versus frozen HN particles cloud droplets in the cooled air over the aircraft wing in forming visible condensation. To establish the role of (Heymsfield et al. 2010, 2011). Using Gierens’s (2009) ambient liquid aerosol, an additional sensitivity study aerodynamic model, the maximum number of freezing would be required to account for strong lower-tropospheric 2 cloud droplets can be estimated from the thickness of CN particle variations in concentration (101–105 cm 3)and the homogeneous freezing layer above the wing, where size (0.01–0.1 mm) with location and altitude (Clarke

Tmin # 2388C (about 3 m at T0 52208C) and the and Kapustin 2010). Especially soot from aircraft ex- 2 number concentration of cloud droplets in an altocu- haust near runways (n 5 106 cm 3; Westerdahl et al. 2 mulus cloud (#120 cm 3; Fleishauer et al. 2002). Aver- 2008) may act as CCN when activated (Koehler et al. aged over the 3-m homogeneous freezing layer, the 2009). Different threshold atmospheric conditions (T, S, concentration of frozen cloud droplets leaving the and CN concentration) may apply for the formation of trailing edge is approximately three orders of magnitude overwing condensation during landing or takeoff. smaller than the number of homogeneously condensed Therefore, in this study we have limited our focus of 2 droplets (#105 cm 3), under the assumed atmospheric APIPs visibility to aerodynamic contrails formed during conditions (T0 52208C, Sw,0 5 1), true airspeed out-of-cloud cruise flight. 2 (218 m s 1), and angle of attack (5.08). However, homogeneous condensation may be less vigorous when the 6. Summary and conclusions airspeed is reduced—for example, in level flight at lower altitudes near the cloud base, or during climbout. In this study we investigated in detail the formation A consequence of the high relative humidity required process of aircraft produced ice particles due to the for visible aerodynamic contrail formation is that they appreciable adiabatic cooling over aircraft wings during remain an infrequently observed phenomenon because flight. We have examined the relative importance of two most aircraft cruise where the temperatures are colder possible modes of aerodynamic condensation: solution than 2408C. Gierens and Dilger (2013) developed a droplet growth, followed by homogeneous freezing, or climatology for aerodynamic contrail formation, com- homogeneous condensation followed by homogeneous bining global patterns of air traffic with global reanalysis freezing. Toward this end, a parcel model was adapted data and used the less constrictive criterion of S $ Si,sat to obtain growth rates of micron-scale solution droplets 3306 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 72 as well as nanometer-scale HDN clusters. Our key solution droplets for water vapor has yet to be verified in findings can be summarized as follows: the laboratory. Finally, more (quantitative) work is needed to better understand local meteorological 1) Homogeneous droplet nucleation followed by homoge- effects and atmospheric relevance of APIPs near air- neous freezing is likely to explain visible aerodynamic fields, such as inadvertent local cloud seeding through condensation at ambient air temperatures between 2208 the Wegener–Bergeron–Findeisen process (Heymsfield and 2508C. Because combustion contrails form at et al. 2010). temperatures below 2388C, there is little doubt that visible contrails are aerodynamically induced at higher Acknowledgments. This work was carried out with temperatures. support of the MMM/NCAR visitor fund and the Na- 2) Up to 1 m above the wing surface, HN droplets are tional Science Foundation. We wish to thank Dr. Klaus several orders of magnitude more numerous than Gierens for kindly providing the aerodynamic flow ambient solution droplets and outcompete them for model and for his helpful comments on the manuscript. water vapor such that frozen and liquid aerosol We thank Prof. Ulrich Schumann, Prof. Bernd Kärcher, particles remain invisible over and behind the wing. and three anonymous reviewers for reviewing the 3) The visibility of nascent aerodynamic contrails is manuscript and for their thoughtful suggestions. Thanks determined by the ambient relative humidity and also go to Jeffrey Schäfer and Dr. Massimo Santacroce number of ice particles that survive recompression at for allowing us to use their photographs, as well as the wing trailing edge. 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