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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS 118 ative ions (Wilson effect) and the excess positive ions become attached to cloud droplets. The enhanced electric field within the cloud would provide a positive feedback to the Wilson effect by increasing the polarization on the drops. If the field should reach about 10 kV/m the ion drift velocity would increase to a few meters per second. This is the situation where the velocity of positive ions is about the same as the fall speed of small raindrops. Consequently generation by selective ion charging and the simple feedback mechanism for the Wilson effect is limited. [The same limit does not apply to diffusion charging at cloud edges, Eq. (9.5)]. In the rain stage, microscale separation of charge from ion capture continues while new mechanisms make their appearance. The role of convection remains central to cloud development as well as the motion of charged droplets within the updraft. Transport and drift are important factors in ion movement within the cloud and to droplets at the boundaries. The Wilson effect appears to be responsible for some of the field enhancement but must be considered along with the additional mechanisms of breakup charging and induction charging. Breakup Charging The collisions between drizzle (R = 100-1000 Âµm) and cloud droplets (R = 10-100 Âµm) usually result in coalescence growth and the production of rain. In contrast the collisions between raindrops (R = 1-6 mm) and drizzle often result in only transient coalescence followed by fragmentation. Such events can result in charged drops in the presence of an electric field. The polarization charge of one sign on a spherical drop is This equation gives the net positive or negative charge that can be separated by "slicing" a polarized drop in half. To apply Eq. (9.7) to the rain stage, consideration of some details of drop collisions and the role of the electric field follows. Four general kinds of breakup phenomena are illustrated in Figure 9.4 (neck, sheet, disk, and bag) based on the laboratory study of McTaggart-Cowan and List (1975). The amount of charge separated in bag breakup is given approximately by Eq. (9.7) (Matthews and Mason, 1964), but the charge has not been determined for the other cases shown in Figure 9.4. The most frequent kinds of breakup result after a vertical elongation of the coalesced drop pair followed by a neck or sheet that tears into numerous droplets. This is not the ideal "slicing" required for Eq. (9.7). For example, an elongation increases the polarization charge by a factor of 4 if the distorted drop is modeled as a prolate spheroid with a major axis of 5 times the spherical diameter. Thus Eq. (9.7) gives a rather conservative estimate of the microscale charge separation in breakup. Figure 9.4 The four observed breakup types with percentages of occurrence: a, neck; b, sheet (two views taken perpendicular to each other); c, disk; d, bag (from McTaggart-Cowan and List, 1975). An important feature of breakup collisions is that they occur slowly compared with the charge-relaxation time (i.e., the time required to redistribute the charge). The breakup time is given roughly by the raindrop diameter divided by the velocity difference between the colliding drops (about 0.5 msec). In contrast, the charge relaxation time for pure water is about 100 times faster and for rainwater with impurities, 104 to 106 times faster. Thus, the distribution of polarization charge on a distorting raindrop is in approximate equilibrium with the electric field. In breakup charging, the electric field separates charge on individual drops by polarization, breakup separates charge between colliding drops, and gravity separates charge on a large scale. The sheet breakup shown in Figure 9.4b, with a downward directed field, will result in a positive charge on the large fragment (R > 1 mm) given approximately by Eq. (9.7) and a negative charge of the same magnitude distributed over the small fragments (R 100 Âµm). The difference in fall speed between these sizes (6 to 10 m/sec) gives the cloud-scale separation rate. Although breakup charging contains the microscale and cloud-scale mechanisms of charge separation necessary for cloud electrification, it does not reinforce the existing field. However, it may contribute significantly to drop charging found in both the rain and hail stages.