which is centered on the vertical axis of the cloud model. Of course, the initial concentration of water vapor in the plume is not allowed to exceed the local air density. Following the initial equilibration of the plume, expansion is assumed to occur at a uniform rate determined by the strength of the background turbulence and wind shear fields (22,23). For the present short-term calculations (^1 day), a horizontal “eddy” diffusion coefficient of 10“ cm2/sec was adopted. This is probably a minimum average value for the mesosphere, thus yielding a conservative upper-limit to the lifetime of the rocket cloud. We neglect possible acceleration of the plume dispersion connected with energy deposition by the launch motors, as this effect is noticeable only at very early times (24). Contrails are usually seen close behind rockets, so that the initial spreading time of about 100 sec is artificial. The immediate adiabatic expansion and cooling of the exhaust gases is very rapid, and homogeneous nucleation can occur near the exit nozzle (25). At mesospheric altitudes, the plume quickly reaches pressure equilibrium, and then attains temperature equilibrium as ambient air is more slowly mixed in. The water cloud does not evolve significantly during the latter phase because most of the water is already condensed. In fact, the condensed water may pass through one or more “Mach discs,” evaporate, and renucleate beyond each disc (C. Park, private communication, 1980). Obviously, the processes determining the size of the condensed particles in the early trail are exceedingly complex and cannot be accurately simulated here. Nevertheless, it is unlikely that the water particle sizes would greatly exceed 1 /xm for several reasons. First, the onset of homogeneous nucleation creates immense numbers of growth sites for water vapor condensation. Second, the subsequent growth rate of the particles is moderated by rapidly decreasing water vapor pressures in the plume, and by heating of growing drops as a result of latent energy release. Finally, the particle aggregation rate due to coagulation is rapidly quenched as the plume expands and rarefies. Figure 4 depicts the critical stages in the evolution of an HLLV contrail at midlatitudes. In our simplified plume model, an initial burst of homogeneous water vapor nucleation occurs and, because of the high supersaturation, these particles quickly grow to sizes of 0.03 to 0.5 gm radius. Interestingly, these sizes are comparable to those obtained from a more detailed calculation by Bernhardt (26) for thermospheric conditions. During condensation, the water vapor in the plume is consumed, the supersaturation over the (presumed) frozen droplets falls to almost zero, and further nucleation and growth cease. Because water vapor pressures are quite low in the mesosphere, large particles do not grow at the expense of small particles as can happen in rain clouds. It is important to note that the vapor pressure over ice is significantly lower than the vapor pressure over liquid water (see Fig. 2). Homogeneous nucleation at temperatures si70 K (typical of the midlatitude mesopause) produces supercooled water droplets. These supercooled droplets do not freeze immediately, and may remain liquid throughout the growth phase. Upon freezing, the ice particles can absorb most of the remaining water vapor, and the contrail can take on the appearance of a cirrus cloud. Subsequent to termination of particle formation and growth, the dominant effect on the contrail is due to “turbulent” expansion, which rapidly dilutes the particle concentration. Water vapor remains in equilibrium with the condensed particles, which evaporate to maintain a constant concentration in the vapor phase. Coagulation and sedimentation have only a secondary influence. For example, the sedimentation rate of 1 gun radius ice spheres at 80 km (48 mi) is about 2.5 km/h (1.5 mi/h). (We have purposely neglected several secondary temperature coupling effects in the evolving
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